Mathematics High School
Answers
Answer 1
When reflecting a polygon over the x-axis or y-axis, the coordinates of the vertices change based on the location of the line of reflection.
- If reflecting over the x-axis, the y-coordinates of the vertices change sign. For example, if a vertex has coordinates (3,5), its reflection over the x-axis would have coordinates (3,-5).
- If reflecting over the y-axis, the x-coordinates of the vertices change sign. For example, if a vertex has coordinates (3,5), its reflection over the y-axis would have coordinates (-3,5).
- To find the reflected coordinates of all vertices, the same process is applied to each vertex in the polygon.
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Related Questions
As a certain engine's rotation speed increases, its temperature increases at a constant rate.
The table compares the engine's rotation speed (in cycles per second) and its temperature (in degrees Celsius).
Rotation (cycles per second) Temperature (degrees Celsius)
11
1111
23.8
23.823, point, 8
13
1313
25.4
25.425, point, 4
15
1515
27
2727
What is the increase in temperature that comes with an increase of
1
11 cycle per second in the rotation?
degrees Celsius
Answers
We can say that the increase in temperature that comes with an increase of 1 cycle per second in the rotation is 1.6 degrees Celsius, assuming that the constant rate of temperature increase remains the same for higher rotation speeds.
Based on the table, we can see that the engine's temperature increases by a constant rate as the rotation speed increases. To find the increase in temperature that comes with an increase of 1 cycle per second in the rotation, we can look at the difference in temperature between two adjacent rows where the rotation speed increases by 1 cycle per second.
For example, between the first two rows, the rotation speed increases from 11 to 1111 cycles per second, and the temperature increases from 23.8 to 25.4 degrees Celsius. The difference in temperature is 25.4 - 23.8 = 1.6 degrees Celsius. Therefore, we can say that the increase in temperature that comes with an increase of 1 cycle per second in the rotation is 1.6 degrees Celsius, assuming that the constant rate of temperature increase remains the same for higher rotation speeds.
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Savannah is decorating a ballroom ceiling with garland. If the rectangular ceiling is 16 meters
by 12 meters, how much garland will Savannah need to reach from one corner of the ceiling
to the opposite corner?
Answers
The length of the diagonal of the rectangular ceiling can be found using the Pythagorean theorem. Therefore, the length of the diagonal of the ceiling is the square root of the sum of the squares of the lengths of its sides, which is the square root of (16^2 + 12^2) = 20 meters (rounded to the nearest meter). Savannah will need at least 20 meters of garland to reach from one corner of the ceiling to the opposite corner.
In a rectangular ceiling, the diagonal is the longest line segment that can be drawn from one corner of the ceiling to the opposite corner. It forms a right triangle with the two sides of the rectangle as its legs. The Pythagorean theorem can be used to find the length of the diagonal, which is also the minimum length of garland needed to span the distance between the two corners.
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1)Suppose that 10 years ago you bought a home for $140,000, paying 10% as a down payment, and financing the rest at 9% interest for 30 years.
Your existing mortgage (the one you got 10 years ago)
How much money did you pay as your down payment?
2) How much money was your existing mortgage (loan) for?
3) What is your current monthly payment on your existing mortgage?
4)How much total interest will you pay over the life of the existing loan?
5)This year (10 years after you first took out the loan), you check your loan balance. Only part of your payments have been going to pay down the loan; the rest has been going towards interest. You see that you still have $112,681 left to pay on your loan. Your house is now valued at $190,000.
Your current situation
How much of the original loan have you paid off? (i.e, how much have you reduced the loan balance by? Keep in mind that interest is charged each month - it's not part of the loan balance.)
6)How much money have you paid to the loan company so far (over the last 10 years)?
7)How much interest have you paid so far (over the last 10 years)?
8) How much equity do you have in your home (equity is value minus remaining debt)
9) Refinancing
Since interest rates have dropped, you consider refinancing your mortgage at a lower 6% rate.
If you took out a new 30-year mortgage at 6% for your remaining loan balance, what would your new monthly payments be?
10)How much interest will you pay over the life of the new loan?
11) Analyzing the refinance
Notice that if you refinance, you are going to be making payments on your home for another 30 years. In addition to the 10 years you've already been paying, that's 40 years total.
How much will you save each month because of the lower monthly payment?
12) How much total interest will you be paying (consider the interest you paid over the first 10 years of your original loan as well as interest on your refinanced loan)?
Answers
The down payment made on the home was $14,000, and the existing mortgage (loan) was for $126,000 with a current monthly payment of $1,067.76.
1.The down payment made on the home was $14,000.
2.The existing mortgage (loan) was for $126,000.
3.The current monthly payment on the existing mortgage is $1,067.76.
4.The total interest paid over the life of the existing loan will be $270,959.20.
5.The original loan was for $126,000, so the amount paid off so far is $13,319. This is because some of the monthly payments went towards interest and not towards the loan balance.
6.The total amount paid to the loan company over the last 10 years is $128,131.20.
7.The total interest paid so far over the last 10 years is $33,131.20.
8.The equity in the home is $77,319, which is calculated by subtracting the remaining loan balance of $112,681 from the current value of the home, which is $190,000.
9.The new monthly payment on the refinanced mortgage would be $676.13.
10.The total interest paid over the life of the new loan would be $97,606.80.
11.By refinancing, the monthly payment would be reduced by $391.63.
12.The total interest paid, considering both the original loan and the refinanced loan, would be $334,566.00.
The total interest paid over the life of the existing loan will be $270,959.20. The amount paid off so far is $13,319, and the equity in the home is $77,319. Refinancing the mortgage at a lower interest rate of 6% would result in a new monthly payment of $676.13, a savings of $391.63 per month. However, the total interest paid, considering both the original loan and the refinanced loan, would be $334,566.00 over a period of 40 years.
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Find the least common denominator of
8
x²+x-42
and
-2
x-6x
Answers
The required answer is the least common denominator of 8x² + x - 42 and -2x - 6x is 2(2x - 3)(2x + 7)(-8x).
Explanation:-
To find the least common denominator of these two expressions, we need to factor them first.
8x² + x - 42 can be factored as (2x + 7)(4x - 6)
-2x - 6x can be factored as -2(x + 3)x
Now we can see that the factors (2x + 7) and (4x - 6) are unique to the first expression, while the factor (x + 3) is unique to the second expression. The factor x is common to both expressions.
To find the least common denominator, we need to include all of the unique factors and the highest power of the common factor. So the least common denominator is:
(2x + 7)(4x - 6)(x + 3)
to include x as a factor, since it is already included in the expressions.
the least common denominator (LCD) of the given expressions, we first need to simplify and factor them. 1. Simplify the second expression: -2x - 6x = -8x 2. Factor the first expression: 8x² + x - 42. This can be factored into (4x - 6)(2x + 7). Now, we have two expressions: (4x - 6)(2x + 7) and -8x. 3. Factor out any common factors in the first expression: 2(2x - 3)(2x + 7). 4. Find the LCD: The LCD must contain all factors of both expressions. So, it will be 2(2x - 3)(2x + 7)(-8x). Therefore, the least common denominator of 8x² + x - 42 and -2x - 6x is 2(2x - 3)(2x + 7)(-8x)
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21n^3, 18n^2 what’s the GCF
Answers
The greatest common factor (GCF) of 21n^3 and 18n^2 is 3n^2.
To find the greatest common factor (GCF) of the terms 21n^3 and 18n^2, we need to identify the highest power of n that both terms share.
Let's break down the terms into their prime factors:
21n^3 can be written as 3 * 7 * n * n * n = 3 * 7 * n^3
18n^2 can be written as 2 * 3 * 3 * n * n = 2 * 3^2 * n^2
Now, we look for the common factors in both terms:
- Both terms have a factor of 3.
- Both terms have a factor of n^2.
To find the GCF, we take the product of the common factors with the lowest exponents:
GCF = 3 * n^2
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A Music fan randomly selects for CDs from a stack of 35 or six or by the same country western artist. What is the probability that all the cities chosen or buy that artist?
Answers
The total number of possible outcomes is the number of ways to choose 4 CDs out of 35, which can be found using the combination formula So the probability of selecting 4 CDs by the same country western artist is approximately 0.000276, or about 0.03%.
To find the number of ways to choose four CDs by the same artist, we can treat each artist's CDs as a separate group and use combinations again. Since there are six CDs by the same artist,This means that there are 15 possible combinations of four CDs that are all by the same country western artist.Artist" in this context refers to a country western musician whose CDs are in the stack of 35. The problem asks for the probability that all four CDs selected at random are by that same artist.
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Draw a picture show 6x3/6=
Answers
To Diagrammatically represent a picture that represents 6x3/6, we can start by drawing a rectangle with a length of 6 units and a width of 3 units. This rectangle represents the first part of the equation, 6x3, which is the multiplication of 6 and 3.
Next, we can divide this rectangle into six equal parts, since the second part of the equation involves dividing by 6. To do this, we can draw two horizontal lines across the rectangle, dividing it into three equal sections, and then draw two vertical lines across each section, dividing it into two equal parts. This will give us a total of six equal parts.
Now, we can shade in three of these parts, representing the division of 6x3 by 6. Since we have divided the rectangle into six equal parts, shading in three of these parts represents taking half of the rectangle. Therefore, 6x3/6 is equal to half of the original rectangle, which can be visualized in the shaded portion of the picture.
To express this mathematically, we can simplify the expression 6x3/6 as 3x1/2, which is equal to 1.5. This means that the shaded portion of the rectangle represents 1.5 units, which is half of the total area of the rectangle.
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Complete Question
Explain the steps to diagrammatically represent the expression 6 x 3/6.
what is the equation of the translated function?
f(x)=(x-1)^2-5
f(x)=(c+1)^2+5
f(x)=(x-5)^2-1
f(x)=(x+5)^2+1
Answers
Therefore, the correct equation of the translated function is f(x) = (x - 1)^2 - 5.
Let's break down the given function f(x) = (x - 1)^2 - 5 to understand how it represents a vertical translation of the parent function f(x) = x^2.
(x - 1): The term (x - 1) represents a horizontal shift of the graph. In the parent function f(x) = x^2, the graph is centered around the y-axis. However, in f(x) = (x - 1)^2 - 5, the term (x - 1) shifts the graph one unit to the right. This means that the vertex of the parabola, which represents the minimum point, will now occur at x = 1 instead of x = 0.
-5: The term -5 represents a vertical shift of the graph. In the parent function f(x) = x^2, the graph intersects the y-axis at the origin (0, 0). However, in f(x) = (x - 1)^2 - 5, the term -5 shifts the entire graph five units downward. This means that the graph will intersect the y-axis at the point (0, -5).
By combining the horizontal shift of one unit to the right and the vertical shift of five units downward, the function f(x) = (x - 1)^2 - 5 represents a translated parabola compared to the parent function f(x) = x^2.
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Find how long it takes $1,900.00 to double if it is invested at 6% compounded monthly.
It will take
years. (Round answer to 3 decimal places.)
> Next Question
Answers
It will take approximately 11.552 years for $1,900.00 to double if it is invested at 6% compounded monthly.
To find the amount of time it takes for an investment to double, we use the compound interest formula: A = P(1 + r/n)^(nt), where A is the amount after t years, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.
In this case, we know that P = $1,900.00, r = 6%, and n = 12 (since interest is compounded monthly). We want to solve for t when A = 2P = $3,800.00. Substituting these values into the formula, we get:
$3,800.00 = $1,900.00(1 + 0.06/12)^(12t)
Simplifying and solving for t, we get:
ln(2) = 12t ln(1 + 0.06/12)
t = ln(2)/(12 ln(1 + 0.06/12)) ≈ 11.552
Therefore, it will take approximately 11.552 years for $1,900.00 to double if it is invested at 6% compounded monthly. It is important to understand the effects of compounding on investments to make informed financial decisions.
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In triangle ABC, ZA-25°, ZC-55° and AB-60. What are the approximate measures of the remaining side lengths of
the triangle?
Answers
We can use the Law of Sines and some trigonometric functions to approximate the remaining side lengths of the triangle ABC. We find that the length of side BC is approximately 48.4 and the length of side AC is approximately 54.1.
Let's start by using the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides of the triangle. We can use this law to find the ratio of the lengths of the sides of triangle ABC.
sin(A)/a = sin(B)/b = sin(C)/c
Since we know the measure of angle B and the length of side AB, we can use this ratio to find the length of side BC:
sin(60°)/AB = sin(55°)/BC
Solving for BC, we get:
BC ≈ AB * sin(55°) / sin(60°) ≈ 48.4
Next, we can use the Law of Cosines to find the length of side AC. This law relates the lengths of the sides of a triangle to the cosine of one of its angles:
c^2 = a^2 + b^2 - 2ab*cos(C)
We know the length of side AB and can use the Law of Sines to find the sine of angle A:
sin(A)/AB = sin(60°)/BC
sin(A) ≈ AB * sin(60°) / BC ≈ 0.866
Now we can use the fact that the sum of the angles in a triangle is 180° to find the measure of angle C:
C = 180° - A - B ≈ 100°
Substituting the given values into the Law of Cosines, we can solve for the length of side AC:
AC^2 = AB^2 + BC^2 - 2ABBCcos(C)
AC ≈ sqrt(AB^2 + BC^2 - 2ABBCcos(C)) ≈ 54.1
Therefore, the approximate measures of the remaining side lengths of triangle ABC are BC ≈ 48.4 and AC ≈ 54.1.
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A bag contains marbles that are the same size and shape.
• 20% are red marbles
1/4 are blue marbles
•The rest are green marbles
What is the probability that you will pull a green marble from the bag, replace it, and then pull a blue marble?
A: 13.75%
B: 11/60
C: 55%
D: 1/20
Answers
The probability of pulling a green marble from the bag and replacing it is 100% - 20% - 25% = 55%. The probability of pulling a blue marble from the bag after replacing the green marble is 1/4.
To find the probability of both events happening, we multiply the probabilities:
55% x 1/4 = 0.1375 or 13.75%
Therefore, the answer is A: 13.75%.
The question gives us the percentage of red and blue marbles, so we can find the percentage of green marbles by subtracting the sum of the other two from 100%.
When we replace the green marble, the total number of marbles in the bag remains the same, so the probability of pulling a blue marble remains 1/4. To find the probability of both events happening, we multiply the probabilities.
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Determine the exact value of 2 sin²60° x tan 30°
Answers
The exact value of 2 sin²60° x tan 30° is 1/2.
Evaluate sin²60°. Since sin 60° = √3/2, we square it to get sin²60° = (√3/2)² = 3/4.
Evaluate tan 30°. Since tan 30° = sin 30° / cos 30°, and sin 30° = 1/2 and cos 30° = √3/2, we have tan 30° = (1/2) / (√3/2) = 1/√3 = √3/3.
Multiply the two values: 2 sin²60° x tan 30° = 2 * (3/4) * (√3/3) = (6√3)/12 = √3/2.
Simplify the expression: √3/2 can be written as (√3/2) * (2/2) = √3/4.
Further simplify: (√3/4) can be written as (√3/4) * (4/4) = √3/4.
Finally, √3/4 is equal to 1/2 * (√3/2), and since (√3/2) is equal to sin 60°, we can rewrite it as 1/2 * sin 60° = 1/2 * (√3/2) = 1/2.
Therefore, the exact value of 2 sin²60° x tan 30° is 1.
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Regenerate response
a car traveled 360km in 6h. a train traveled 400km in 8h. a boat traveled 375km in 5h. which had the fastest average speed?
Answers
The boat had the fastest average speed, traveling at 75 km/h.
To determine which vehicle had the fastest average speed, we need to calculate the average speeds for the car, train, and boat using the provided distances and travel times.
Your question is: A car traveled 360km in 6h, a train traveled 400km in 8h, and a boat traveled 375km in 5h. Which had the fastest average speed?
Step 1: Calculate the average speed for each vehicle using the formula: Average Speed = Distance / Time.
Car:
Average Speed = 360 km / 6 h = 60 km/h
Train:
Average Speed = 400 km / 8 h = 50 km/h
Boat:
Average Speed = 375 km / 5 h = 75 km/h
Step 2: Compare the average speeds of the three vehicles.
Car: 60 km/h
Train: 50 km/h
Boat: 75 km/h
Si, the boat had the fastest average speed, traveling at 75 km/h.
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If n is a positive integer, which of the following must be odd? A. n + 1 B. n +2 C. 2n + 1 D. 2n + 2 E. n^2 + 1
Answers
Based on this analysis, the expressions that must be odd are: A. n + 1 and C. 2n + 1.
To determine which of the expressions must be odd when n is a positive integer, we can analyze each expression individually:
A. n + 1:
When we add 1 to any positive integer n, the result will always be odd. So, n + 1 must be odd.
B. n + 2:
When we add 2 to any positive integer n, the result will always be even. So, n + 2 cannot be guaranteed to be odd.
C. 2n + 1:
When we multiply a positive integer n by 2 and add 1, the result will always be odd. So, 2n + 1 must be odd.
D. 2n + 2:
When we multiply a positive integer n by 2 and add 2, the result will always be even. So, 2n + 2 cannot be guaranteed to be odd.
E. n^2 + 1:
When we square a positive integer n and add 1, the result will not always be odd. For example, if n = 2, then n^2 + 1 = 5, which is odd. However, if n = 3, then n^2 + 1 = 10, which is even. So, n^2 + 1 cannot be guaranteed to be odd.
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Find the volume of the following figure using unit cubes.
27 units3
25 units3
None of the above.
23 units3
Answers
The volume of the following figure is 27 cubic units. (option a).
To determine the volume of a figure using unit cubes, you need to count the number of cubes that fit inside the figure and then multiply that number by the volume of each cube.
Volume is a physical quantity that measures the amount of space occupied by a three-dimensional object. It is a measure of the total amount of enclosed space that an object occupies. Volume is typically measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet.
In this case, since the side value of the unit cubes is 3, the volume of each cube is
=> 3³ or 27 cubic units.
Therefore, the correct answer is option a.
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Complete Question:
Find the volume of the following figure using unit cubes.
a) 27 units³
b) 25 units³
c) None of the above.
d) 23 units³
Which of the following are equations for the line shown below? Check all that apply (-2,3) and (2,2)
A.y-3= -0.25(x+2)
B. y+ 3 = -0.25(x-2)
C. y-2=-0.25(x-2)
D. y-3= -0.25(x-2)
Answers
The equations that represent the line passing through (-2,3) and (2,2) are A. y-3= -0.25(x+2) and C. y-2=-0.25(x-2).
The question asks us to identify the equations that represent a line passing through two given points (-2,3) and (2,2). In this problem, we can use the point-slope form of a linear equation to find the equation of the line. The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. To find the slope of the line passing through (-2,3) and (2,2), we can use the slope formula: m = (y2 - y1)/(x2 - x1) = (2 - 3)/(2 - (-2)) = -0.25.
Now, we can use the point-slope form of the linear equation and substitute the slope and one of the given points into the equation to find the equation of the line. Let's choose the point (-2,3):
y - y1 = m(x - x1)
y - 3 = -0.25(x - (-2))
y - 3 = -0.25(x + 2)
y - 3 = -0.25x - 0.5
y = -0.25x + 2.5
This is the equation of the line passing through (-2,3) and (2,2). We can now check which of the given equations also represent this line.
To check each equation, we can rearrange them to the slope-intercept form y = mx + b and compare the slope and y-intercept values with the equation we found. Let's check each option:
A. y-3= -0.25(x+2)
y - 3 = -0.25x - 0.5
y = -0.25x + 2.5
This equation matches the equation we found, so it is correct.
B. y+ 3 = -0.25(x-2)
y + 3 = -0.25x + 0.5
y = -0.25x - 2.5
This equation has the correct slope but the y-intercept is different, so it is not correct.
C. y-2=-0.25(x-2)
y - 2 = -0.25x + 0.5
y = -0.25x + 2.5
This equation matches the equation we found, so it is correct.
D. y-3= -0.25(x-2)
y - 3 = -0.25x + 0.5
y = -0.25x + 3.5
This equation has the correct y-intercept but the slope is different, so it is not correct.
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A garden measures 32 feet by 126 feet, and the owner of the garden wishes to divide the garden
into two parts by installing a fence from corner to corner. Find the cost of the total length of fence
if the fence costs $5.81 per foot.
Answers
The total cost of the fence is $1,144.66.
1. To find the length of the fence, you need to calculate the distance from one corner to the opposite corner of the garden, which is the hypotenuse of a right triangle formed by the garden's dimensions.
2. Use the Pythagorean theorem: a² + b² = c², where a = 32 feet, b = 126 feet, and c is the length of the fence.
3. Calculate the square of the two sides: a² = 32² = 1024, and b² = 126² = 15876.
4. Add the squares of the two sides: a² + b² = 1024 + 15876 = 16900.
5. Calculate the square root of the sum to find the length of the fence: c = √16900 = 130 feet.
6. Now, calculate the cost of the fence by multiplying its length by the cost per foot: 130 feet × $5.81/foot = $754.30.
The total cost of the fence, which measures 130 feet in length, is $1,144.66.
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The point (-7, 1) when reflected across the origin maps onto
A) (1, -7).
B) (7, 1).
OC) (7,-1).
D) (-1,7).
Answers
A) (1, -7). The reflected point is (7, -1). This matches option A) (1, -7) in the given choices.
When a point is reflected across the origin, its x and y coordinates switch signs. To reflect the given point (-7, 1) across the origin, you need to change the sign of both the x and y coordinates. The x-coordinate -7 becomes positive 7, and the y-coordinate 1 becomes negative 1. Therefore, the reflected point is (7, -1). This matches option A) (1, -7) in the given choices.
Calculation Steps:
1. Identify the coordinates of the given point: (-7, 1)
2. Reflect the point across the origin by changing the signs of the coordinates:
a. Change the sign of the x-coordinate: -7 -> 1
b. Change the sign of the y-coordinate: 1 -> -7
3. The reflected point is (1, -7), which matches option A.
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Points A (0,0), B (0,8), and C (x, Points A (0,0), B (0,8) and C (x,y) form a triangle in the ry.coordinate plane. If the area of this triangle is 12 square units, then which of the following are possible coordinates for point
o(-3,8)
(4,0)
(2,8)
• (-6,0)
Answers
Option (2,8) is the only possible coordinate for point C, as it satisfies the area formula with a base of 8 and a height of 3, giving an area of 12 square units. The other options do not satisfy the formula, and therefore cannot be the coordinates for point C in this triangle.
The possible coordinates for point C can be found by using the formula for the area of a triangle, which is A = 1/2 * base * height. We know that the base is the distance between points B and C, which is the difference between their y-coordinates, and the height is the distance between point A and the line containing points B and C, which is the absolute value of the x-coordinate of point C. By plugging in the coordinates of each given point and solving for the x and y coordinates of point C, we can determine which option(s) give an area of 12 square units.
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Option (2,8) is the only possible coordinate for point C, as it satisfies the area formula with a base of 8 and a height of 3, giving an area of 12 square units. The other options do not satisfy the formula, and therefore cannot be the coordinates for point C in this triangle.
The possible coordinates for point C can be found by using the formula for the area of a triangle, which is A = 1/2 * base * height. We know that the base is the distance between points B and C, which is the difference between their y-coordinates, and the height is the distance between point A and the line containing points B and C, which is the absolute value of the x-coordinate of point C. By plugging in the coordinates of each given point and solving for the x and y coordinates of point C, we can determine which option(s) give an area of 12 square units.
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A recipe for bread calls for 3 cups of flour for every
2
1
cup of water. Using the same recipe, how much water will you need for 5 cups of flour?
Start by setting up a table that could be used to find how many cups of water you will need for 5 cups of flour. Cups of Flour Cups of Water
3
2
1
5
?
Great job!
How many cups of water will you need for 5 cups of flour?
Answers
You will need 3 and 3/4 cups of water, which can be simplified to 3 and 1/2 cups of water, for 5 cups of flour according to the recipe.
According to the recipe for bread, you will need 3 and 1/2 cups of water for 5 cups of flour.
To find out how much water is needed for 5 cups of flour using the recipe, we can set up a proportion:
3 cups of flour / 2 and 1/4 cups of water = 5 cups of flour / x cups of water
Simplifying this proportion, we get:
3/2.25 = 5/x
Cross-multiplying, we get:
3x = 2.25 x 5
3x = 11.25
x = 11.25/3
x ≈ 3.75
Therefore, you will need 3 and 3/4 cups of water, which can be simplified to 3 and 1/2 cups of water, for 5 cups of flour according to the recipe.
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A train track through a mountain is 1700 feet long and makes an angle of 1.4 degrees with the horizontal. What is the change in elevation from one end of the tunnel to the other?
Answers
The change in elevation from one end of the tunnel to the other is approximately 40.16 feet.
To calculate the change in elevation from one end of the tunnel to the other, we need to use trigonometry and the given information about the length of the tunnel and the angle it makes with the horizontal.
First, we need to find the vertical component of the length of the tunnel. We can do this by using the sine of the angle, which gives us:
sin(1.4) = opposite/hypotenuse
where the opposite side is the change in elevation we are trying to find, and the hypotenuse is the length of the tunnel.
Rearranging this formula, we get:
opposite = sin(1.4) x hypotenuse
Substituting the values we have, we get:
opposite = sin(1.4) x 1700 feet
Using a calculator, we get:
opposite = 40.16 feet
Therefore, the change in elevation from one end of the tunnel to the other is approximately 40.16 feet.
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13. Greenvard's manufactures and sells vard furniture made out of recy- cled materials. It is considering making a lawn chair from rceyded aluminum and labrk products. The expense and revenue functions are E = -1,8507 + 800,000 and R = -1009 - 201,00 . a. Determine the profit function, b. What is the profit if the price is set at $110?
Answers
The profit function is given by:
Profit = Revenue - Expense
Profit = (-1009 - 201x) - (-18507 + 800000)
Simplifying:
Profit = -1009 - 201x + 18507 - 800000
Profit = -781502 - 201x
Therefore, the profit function is P(x) = -781502 - 201x.
b. To find the profit when the price is set at $110, we need to determine the quantity sold. We can use the revenue function to do this:
R = px
-1009 - 201x = 110x
Simplifying:
311x = 1009
x = 3.25 (rounded to two decimal places)
Therefore, the quantity sold is 3.25 units. To find the profit, we can substitute x = 3.25 into the profit function:
P(3.25) = -781502 - 201(3.25)
P(3.25) = -782113.25
Rounding to the nearest cent, the profit when the price is set at $110 is approximately -$782,113.25. This indicates a loss.
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According to the U.S. Census Bureau, about 12% of all workers use a carpool to get to work. Melinda surveys a random sample of workers in two towns. Her data is shown in the table. Compare the samples with the national percent.
Answers
To compare the samples with the national percent, you need to calculate the carpool usage percentage for each town based on Melinda's random sample data. Then, you can compare these percentages to the national average of 12%.
However, you have not provided the data table. Please provide the data for each town, including the number of workers surveyed and the number of workers using carpools. Once you provide this information, I'd be happy to help you compare the samples with the national percent.
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this is timed please help!!
Which ordered pair would form a proportional relationship with the point graphed below?
Ty
(-20, 40)
30 -
20
10-
-40 -30 -20 -19
10 20 30 40
20
O (-40, 20)
O (-10, -20)
O (15, -30)
Answers
The ordered pair that would form a proportional relationship with the point graphed (-20, 40) is (15, -30).
To determine which ordered pair would form a proportional relationship with the point (-20, 40), we need to find a pair that has the same constant of proportionality when compared to the given point.
The constant of proportionality (k) is found by dividing the y-coordinate by the x-coordinate. For the given point, k = 40 / -20 = -2.
Now, let's check each of the provided ordered pairs to see which one has the same constant of proportionality:
1. (-40, 20): k = 20 / -40 = -0.5 (Not proportional)
2. (-10, -20): k = -20 / -10 = 2 (Not proportional)
3. (15, -30): k = -30 / 15 = -2 (Proportional)
So, the ordered pair that would form a proportional relationship with the point graphed (-20, 40) is (15, -30).
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If it unsafe for amateur divers to swim where the water pressure is more that 65 psi. How deep can an amateur diver safely swim ? find the depth when the pressure is 65
Answers
To determine the depth at which the water pressure reaches 65 psi, we need to use the formula for pressure:
Pressure = Density x Gravity x Depth
Assuming the density and gravity of seawater, we can rearrange the formula to solve for depth:
Depth = Pressure / (Density x Gravity)
At a pressure of 65 psi, the depth can be calculated as:
Depth = 65 psi / (64 lb/ft3 x 32.2 ft/s2)
Depth = 65 psi / 2060.8 lb-ft/s2
Depth = 0.0315 feet, or approximately 0.38 inches
This means that at a pressure of 65 psi, the water is only about 0.38 inches deep. However, it's important to note that water pressure increases with depth, so even relatively shallow dives can be dangerous if the diver exceeds safe pressure limits. It's always best to follow safe diving practices and consult with a professional before attempting any new dives.
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1:Résoudre les équations suivantes
(E): 3(x+ 1) = 2(3x-5)
(F): (-5- 2x) = 3x
(G) : 4(2x + 4)- 3(5-x) =2 (x+ 1)
(H): 2x-4=5x+3
(D: -3x +2=1+4
(J: 2(x+4) = 3(2 -x)
Answers
The values of equations of x is 13/3, -1, 1/9, -7/3, -1 and -2 /5 respectively.
(E): 3(x+1) = 2(3x-5)
3x + 3 = 6x - 10 (distributing)
3x - 6x = -10 - 3 (subtracting 3x and 3 from both sides)
-3x = -13
x = 13/3
(F): (-5-2x) = 3x
-5 = 5x (adding 2x to both sides)
x = -1
(G): 4(2x+4) - 3(5-x) = 2(x+1)
8x + 16 - 15 + 3x = 2x + 2 (distributing)
11x + 1 = 2x + 2 (combining like terms)
9x = 1
x = 1/9
(H): 2x-4=5x+3
-3x = 7 (subtracting 2x and 3 from both sides)
x = -7/3
(D): -3x+2=1+4
-3x = 3 (subtracting 2 from both sides)
x = -1
(J): 2(x+4) = 3(2-x)
2x + 8 = 6 - 3x (distributing)
5x = -2
x = -2/5
The equations have been solved above.
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Does anyone know how to solve this problem? The goal is to find an equation or equations for the point "p".
Answers
To find an equation for the point "p", we need to have some information about its coordinates or its relationship with other points. Without any such information, it is impossible to provide a specific equation for "p".
Without any specific information about the point "p", it is impossible to provide a particular equation for it. However, if we have some information about the coordinates of "p" or its relationship with other points, we can find its equation. For example, if we know that "p" is the midpoint of a line segment joining two points A and B, we can use the midpoint formula to find its coordinates. The midpoint formula is (x,y) = ((x1+x2)/2,(y1+y2)/2), where (x1,y1) and (x2,y2) are the coordinates of A and B, respectively.
Another way to find the equation of a point is to use its distance from a given point or line. For instance, if we know that "p" is a point on the circle with center C and radius r, we can find its equation by using the distance formula. The distance formula is d = sqrt((x-x1)^2 + (y-y1)^2), where (x1,y1) are the coordinates of the center C, and d is the distance between C and "p", which is equal to r. By equating d to r and simplifying the equation, we can find the equation of the circle.
Similarly, we can find the equation of a point on a line by using its distance from a given point or another line. For example, if we know that "p" is a point on the line passing through two points A and B, we can find its equation by using the point-slope formula. The point-slope formula is y - y1 = m(x - x1), where (x1,y1) are the coordinates of any point on the line, and m is the slope of the line. We can find the slope of the line by using the slope formula, which is m = (y2-y1)/(x2-x1), where (x2,y2) are the coordinates of the other point on the line. By substituting the values of m, x1, and y1, we can find the equation of the line passing through A and B. Then, we can use the distance formula to find the distance between "p" and the line. Finally, we can equate the distance to zero and solve for "p" to get its coordinates.
In conclusion, to find the equation of a point "p", we need to have some information about its coordinates or its relationship with other points. Without any such information, it is impossible to provide a specific equation for "p". However, we can use general methods like the midpoint formula, the distance formula, and the point-slope formula to find the equation of a point in different scenarios.
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A jar contains three red marbles, four blue marbles, and two yellow marbles. If I randomly select one marble, what is the
probability | select a blue marble, keep it, then select another blue marble?
Answers
The probability of selecting a blue marble, keeping it, and then selecting another blue marble is 1/6.
To find the probability of selecting a blue marble, keeping it, and then selecting another blue marble from the jar, we need to consider the following steps:
1. Calculate the probability of selecting the first blue marble.
2. Calculate the probability of selecting a second blue marble after keeping the first one.
Step 1: Probability of selecting the first blue marble
There are a total of 3 red marbles, 4 blue marbles, and 2 yellow marbles, which gives us 9 marbles in the jar. The probability of selecting a blue marble is the number of blue marbles divided by the total number of marbles, so:
P(first blue marble) = 4 blue marbles / 9 total marbles = 4/9
Step 2: Probability of selecting a second blue marble after keeping the first one
After keeping the first blue marble, there are now 3 remaining blue marbles and a total of 8 marbles in the jar. The probability of selecting another blue marble is:
P(second blue marble) = 3 blue marbles / 8 total marbles = 3/8
To find the overall probability, multiply the probabilities from each step:
P(select a blue marble, keep it, then select another blue marble) = (4/9) * (3/8) = 12/72 = 1/6
So, the probability of selecting a blue marble, keeping it, and then selecting another blue marble is 1/6.
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You are taking a weather balloon ride. When the balloon is 700 m in the air, you see
o
o
a lake at S40°W
with an angle of depression of 25
• You rise another 350 m and
see a school at S30°E with an angle of depression of 45
How far from the lake is
the school? Note: round your answer to a whole number.
Answer: The lake is
__ meters from from the school.
Pls provide explanation
No links or I’ll report you
Answers
The distance between lake and school = 451.15 m.
The figure according to given instances is given below,
Now, B is the position of balloon in the 700 m in air.
A is the position of balloon in the air after further 350 m rise from 700m.
C and D are the position of lake and school respectively.
OB = 700m
OA = 700 + 350 = 1050 m.
Now for the right angled triangle OBC, using trigonometric functions we get,
tan 25 = OB/OC
OC = OB/(tan 25) = 700/(tan 25) = 1501.15 (approximate to nearest hundredth)
Now for the right angled triangle OAD, using trigonometric functions we get,
tan 45 = OA/OD
OD = OA/(tan 45) = 1050/1 = 1050
So the distance between lake and school = OD - OC = 1501.15 - 1050 = 451.15 m.
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Question 2 Multiple Choice Worth 2 points)
Find an equation in standard form for the hyperbola with vertices at (0, +9) and foci at (0, +11).
Oy?
x2
= 1
40 81
y² x²
= 1
81 121
y?
x2
= 1
81
40
O
y?x
121 81
= 1
Answers
The equation in standard form for the hyperbola with vertices at (0, ±9) and foci at (0, ±11) is (x²/121) - (y²/81) = 1.
To find the equation of the hyperbola, we need to determine the values of a and b in the standard form equation (x²/a²) - (y²/b²) = 1, where a is the distance from the center to the vertices and b is the distance from the center to the co-vertices.
In this case, a = 9 (distance from center to vertices) and c = 11 (distance from center to foci). We can use the relationship c² = a² + b² to find b. Solving for b, we get:
c² - a² = b²
11² - 9² = b²
121 - 81 = b²40 = b²
So, b = √40.
Now, we can plug the values of a² and b² into the standard form equation:
(x²/121) - (y²/40) = 1
The equation in standard form for the given hyperbola is (x²/121) - (y²/40) = 1.
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