Before rearranging his game room, Carlos made a diagram of the current arrangement. He drew rectangle ABCD
to represent a tennis table with vertices A(1, 1)
, B(1, 12)
, C(8, 12)
, and D(8, 1)
. He moved the table twice, first translating it 3 units left and 2 units up, then rotating it 270° clockwise about the origin. What are the coordinates, written as integers, of the vertices of the final image after these transformations are applied?

The perimeter of the trapezoid is given as follows:

44 cm.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The missing side is a side of a right triangle, in which the other side is of 18 - 10 = 8 cm, while the hypotenuse is of 10 cm, hence:

8² + h² = 10²

64 + h² = 100

h² = 36

h = 6.

Hence the perimeter is given as follows:

P = 18 + 10 + 10 + 6 = 44 cm.

The trapezoid is given by the image presented at the end of the answer.

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Answer:

Step-by-step explanation:

1. No it is not a solution and doesn't work

2. Yes it does work for both

3. Only works for the first one

Answer:

9

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(h(x)=x^2+0.5\)

What do you want to do with the function, as there is no question included?

Answer:

42,795

Step-by-step explanation:

114.12/4=28.53

28.53x1500=42,795

The interval of the graph at which Susan is running fastest is from point A ( 0 , 0 ) to B ( 10 , 3 )

Given data ,

Susan is running a 5k race. The graph of distance vs. time is shown

So , the slope of the first line is m₁

And , the slope of the second line is m₂

where the points are A ( 0 , 0 ) , B ( 10 , 3 ) , C ( 20 , 4 )

Now , slope of AB is

m₁ = ( 3/10 ) = 0.3

And , m₁ = 0.3 kilometers per minute

And , slope of BC is

m₂ = ( 4 - 3 ) / ( 20 - 10 )

m₂ = 1/10

m₂ = 0.1 kilometers per minute

Therefore , the interval is fastest at second line from B ( 10 , 3 ) , C ( 20 , 4 )

Hence , Susan is running fastest is from point A ( 0 , 0 ) to B ( 10 , 3 )

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Answer:

3.94

Step-by-step explanation:

3.944     rounded to nearest hundredth  = 3.94    becuase the thousandth digit is <5  you do not change the hundredth

Answer:

in 2050 we will use about 131 million barrels a day

btw please rate this the brainliest

The given two points of data can be expressed as a linear model by

finding the slope and intercept.

Response:

First part:

Second part:

Third part:

Fourth part:

First part:

The amount of oil used in 2000 = 76 million barrel

The amount of oil used in 2010 = 87 million barrel

The slope of the graph is therefore;

\(Slope = \mathbf{\dfrac{87 - 76}{2010 - 2000}} = 1.1\)

The equation of the graph is therefore;

y - 87 = 1.1·(x - 10)

Which gives;

y = 1.1·x - 11 + 87 =  = 1.1·x + 76

The oil consumption, y, x years after 2000 is; y = 1.1·x + 76

Second part:

Taking trend can be made less linear by assuming a higher

consumption than the consumption in 2010, thereby making the model

look like a parabola.

Third part:

Fourth part:

The consumption in 2050 is given by plugging in x = 50 in the linear equation, y = 1.1·x + 76

Which gives;

y = 1.1 × 50 + 76 = 131

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Answer:

10 /12

Step-by-step explanation:

10 divided by 12 is 0.8333333333 and so on

The first debt that Alice would have to pay based on the Stack method would be the third debt. Option C

From the stack method, the debt that Alice would have to pay off first would be the debt that has the highest interest rate.

The amount of 150 dollars would then be added to the debt that has the second highest rate.

Hence the amount of debt that would be paid off first would be the first debt based on the stack method.

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Answer:

huhh what this is question is too hard

5×(4+3×2)=5×(4+6)=5×10=50

then its answer C

Answer:

y = (-1/4)x + 3

Step-by-step explanation:

to find the perpendicular slope you just find the reciprocal of 4 which is (-1/4)

then find the y-intercept making the line go through (-8, 5) so you do:

y = (-1/4)x + b

5 = (-1/4)(-8) + b

5 = 2 + b

-2  -2

3 = b

Answer:

alternate interior angles (congruent), vertically opposite (congruent), corresponding (congruent), interior (add up to 180 in total)

Step-by-step explanation:

Answer:

A. QRS = TUV

Are the two triangles that are congruent by ASA

Answer: I tried to help but i just got confused

Sorrry I didnt know the answer

The graph that does not represent a function is graph b

From the question, we have the following parameters that can be used in our computation:

Graphs A to C

As a general rule of the vertical line test

For a graph to represent a function, a line drawn from the x-axis must intersect with the graph at most once

using the above as a guide, we have the following:

The graph b would intersect with a line from the x-axis twice

Hence, the graph is b

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Step-by-step explanation:

72 inches = 6 feet

There are 12 inches in a foot, so to convert inches to feet, you divide the number of inches by 12.

72 inches / 12 inches/foot = 6 feet

Answer:

136 cm²

Step-by-step explanation:

Area of the composite figure = area of the triangle + area of the rectangle

= ½*bh + L*W

Where,

b = 16 - 8 = 8 cm

h = 13 - 7 = 6 cm

L = 16 cm

W = 7 cm

Plug in the values into the equation

Area of the composite figure = ½*8*6 + 16*7

= 24 + 112

= 136 cm²

a)

Answer: 3

b)

Answer: 2

c)

Answer: 0

d)

Answer: -2

Answer:

50

Step-by-step explanation:

because forty is eighty percent of 50

Answer:

There is a answer to the question

A) For car 1, a linear function, for car 2, an exponential function can be used to describe its value.  B) Functions are Car 1: f(x) = 18500 - 1104x and Car 2: f(x) = 17500 * (1 - 0.05)^x.  C) The value of Car 1 after 9 years is $8564 and that of car 2 is $11029.36.

Part A:

The value of Car 1 decreases by a fixed amount each year, so a linear function can be used to describe its value. The value of Car 2 decreases by a percentage each year, so an exponential function can be used to describe its value.

Part B:

The following functions can be used to describe the value of each car:

Car 1: f(x) = 18500 - 1104x

Car 2: f(x) = 17500 * (1 - 0.05)^x

Part C:

The value of Car 1 after 9 years is f(9) = 18500 - 1104 * 9 = $8564.

The value of Car 2 after 9 years is f(9) = 17500 * (1 - 0.05)^9 = $11029.36.

There is a significant difference in the value of the two cars after 9 years. Car 2 will have a value of $11029.36, while Car 1 will have a value of $8564. This difference is due to the fact that Car 2 depreciates at a slower rate than Car 1.

Here is a table showing the value of each car after 9 years:

Car Value after 9 years

Car 1 $8564

Car 2 $11029.36

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The value of x is given as follows:

x = 4.8.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

In the context of this problem, the parameters are given as follows:

Applying the Pythagorean Theorem, the value of x is obtained as follows:

x² + 14² = (x + 10)²

x² + 196 = x² + 20x + 100

20x = 96

x = 96/20

x = 4.8.

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To dilate a figure, the coordinates of its points must be multiplied by the dilation factor (k)

Symbolically:

Original point → Dilated point

(x, y) → (x*k,y*k)

Answer:

The answer is C.

Step-by-step explanation:

Answer:

C. 3x = 13.5

Step-by-step explanation:

To find which equation has a solution of x = 4.5, we must input 4.5 in each equation in for x.

A. 7 - 4.5 = 3.5

This is untrue, as 7 - 4.5 is 2.5, not 3.5

B. 2 (4.5) = 10

This is untrue, as 2 x 4.5 is 9, not 10

D. 4.5 + 4 = 4.9

This is untrue, as 4.5 + 4 is 8.5, not 4.9

C. 3 (4.5) = 13.5

This is true, because 3 x 4.5 is 13.5!

I hope this helps.

(a) The mean of the relevant distribution is 2.4 defective pistons.

(b) The standard deviation of the distribution is 1.539.

The mean of the relevant distribution is the expected number of defective pistons that we would expect to get from a sample of 80 pistons produced by this machine. The mean is calculated by multiplying the probability of a defective piston (3%) with the number of pistons in the sample (80). In this case, the mean is 2.4 defective pistons. The standard deviation of the distribution quantifies the uncertainty of our estimate. It is calculated by taking the square root of the variance, which is the expected value of the squared differences between the number of defective pistons in the sample and the mean. In this case, the standard deviation is 1.539. This means that, in theory, we would expect 68% of the samples to contain between 0.861 and 4.139 defective pistons.

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Answer:

D. 3/4

Step-by-step explanation:

In order for the transformed line to be less steep than f(x), it must have an "a" value less than the slope of f(x). The slope of f(x) is 1, therefore, the only number less than 1 is 3/4.

Answer: o.5 , z >-3

Step-by-step explanation:

just divide

Answer:

z > -3  (this is correct)

z < 5  (this is also correct)

z < 4  (this is incorrect)

z Less-than-or-equal-to 4  (this is correct)

z > 0  (this is incorrect)

It looks like you're given

F'(x) = 3x² + 7

and

F (0) = 5

and you're asked to find F(b) for the values of b in the list {0, 0.1, 0.2, 0.5, 2.0}.

The first is done for you, F (0) = 5.

For the remaining b, you can solve for F(x) exactly by using the fundamental theorem of calculus:

\(F(x)=F(0)+\displaystyle\int_0^x F'(t)\,\mathrm dt\)

\(F(x)=5+\displaystyle\int_0^x(3t^2+7)\,\mathrm dt\)

\(F(x)=5+(t^3+7t)\bigg|_0^x\)

\(F(x)=5+x^3+7x\)

Then F (0.1) = 5.701, F (0.2) = 6.408, F (0.5) = 8.625, and F (2.0) = 27.

On the other hand, if you're expected to approximate F at the given b, you can use the linear approximation to F(x) around x = 0, which is

F(x) ≈ L(x) = F (0) + F' (0) (x - 0) = 5 + 7x

Then F (0) = 5, F (0.1) ≈ 5.7, F (0.2) ≈ 6.4, F (0.5) ≈ 8.5, and F (2.0) ≈ 19. Notice how the error gets larger the further away b gets from 0.

A better numerical method would be Euler's method. Given F'(x), we iteratively use the linear approximation at successive points to get closer approximations to the actual values of F(x).

Let y(x) = F(x). Starting with x₀ = 0 and y₀ = F(x₀) = 5, we have

x₁ = x₀ + 0.1 = 0.1

y₁ = y₀ + F'(x₀) (x₁ - x₀) = 5 + 7 (0.1 - 0)   →   F (0.1) ≈ 5.7

x₂ = x₁ + 0.1 = 0.2

y₂ = y₁ + F'(x₁) (x₂ - x₁) = 5.7 + 7.03 (0.2 - 0.1)   →   F (0.2) ≈ 6.403

x₃ = x₂ + 0.3 = 0.5

y₃ = y₂ + F'(x₂) (x₃ - x₂) = 6.403 + 7.12 (0.5 - 0.2)   →   F (0.5) ≈ 8.539

x₄ = x₃ + 1.5 = 2.0

y₄ = y₃ + F'(x₃) (x₄ - x₃) = 8.539 + 7.75 (2.0 - 0.5)   →   F (2.0) ≈ 20.164

For the function \(f(x) = 5x^3 - ax^b\) to be odd (a) b must be an odd whole number.

If f(-x) = f(x) then the function is even and symmetric about the x-axis.

If f(-x) = -f(x) The function is odd and symmetric about the origin.

Given, \(f(x) = 5x^3 - ax^b\) is an odd function.

Now, for the function to be odd b must be an odd whole number

because we know an odd number raise to the power even or odd is an odd number.

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Answer:

84 ways

Step-by-step explanation:

The order in which the books are positioned is not important, so we use the combinations formula to solve this question.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In how many ways can this be done

2 math books, from a set of 7.

3 computer science books, from a set of 4.

So

\(T = C_{7,2}*C_{4,3} = \frac{7!}{2!5!}*\frac{4!}{1!3!} = 84\)

This can be done in 84 ways