find the equation of the line shown

The description of the one transformation that maps ∆ABC to ∆A'B'C' is a rotation counterclockwise, 90 degrees, with the center at the origin

A rotation transformation can be described as the angular motion of a rigid, geometric figure around a point

The vertices on the triangle ∆ABC are;

The vertices on the triangle ∆A'B'C' are;

The rotation of a point A(x, y), 90° counterclockwise about the origin gives the point A'(-y, x)

The reflection of a point (x, y) across the y–axis gives the point A'(-x, y)

Therefore;

The coordinates of the vertices of∆ABC following a 90° counterclockwise rotation gives;

A(-5, -2) → A'(2, -5)

B(-7, -4) → B'(4, -7)

C(-5, -5) → C'(5, -5)

Therefore;

The transformation that maps ∆ABC to ∆A'B'C' is therefore a rotation of 90° counterclockwise about the origin

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Ratio of length of cell A to the length of cell B will be 20 : 1.

What is mean by Ratio?

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

Given that;

Length of cell A = 4 x 10⁻⁵

Length of cell B = 0.000002 = 2 x 10⁻⁶.

Now,

Length of cell B into scientific notation = 2 x 10⁻⁶

Hence, The ratio of the length of cell A to cell B =  4 x 10⁻⁵ / 2 x 10⁻⁶

                                                                          = 2 x 10⁻⁵⁺⁶

                                                                          = 2 x 10¹

                                                                          = 20

Thus, Ratio of length of cell A to the length of cell B is 20 : 1.

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Answer:

2 apples and 4 bananas

Step-by-step explanation:

Given info:

Question given:

Determine the number of apples, x, and the number of bananas, y, that Juan bought.

Solution:

Since, we know that;

apples = x

bananas = y

Cost of each apple = $1 & Cost of each banana = $ 0.50

Total = 6

The equation that represents the following information:

x + y = 6

x + 0.5y = 4

We can multiply the top equation by -1 so it becomes -x -y = 6

-x - y = 6

x + 0.5y = 4

Now, we can use elimination to cancel out the x.

-0.5y = -2

y = 4

Because y=4, x must be 2 since x+y=6. So,

x = 2 and y = 4

Which means;

Juan bought 2 apples and 4 bananas.

~kavinsky

The inverse equation of the function is f'1(x) = 3 + √x

Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x)

The function f(x) is given as

f(x) = (x - 3)^2, x ≥ 3

As a general rule, we start by writing f(x) as a variable (say f(x) = y).

So, the equation of the function becomes

y = (x - 3)^2

The next step is to switch/swap the positions of x and y in the equation

The equation becomes

x = (y - 3)^2

Make y the subject of the formula in the equation

The equation becomes

y = 3 + √x

Express as an inverse function

f'1(x) = 3 + √x

Hence, the equation of the inverse function is f'1(x) = 3 + √x

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The number of times heavier that the largest dog is when compared with the smallest dog is B. 41.

It should be noted that from the information given, the biggest dig is the St Bernard and it has 145 pounds.

Also, it should be noted that the smallest dog is Yorkie and it had 3.5 pounds. Therefore, it should be noted that the number of times heavier will be:

= Weight of biggest fog / Weight of smallest dog

= 145 / 3.5

= 41.

It is 41 times heavier.

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Answer:

D

Step-by-step explanation:

The line needs to be dotted since the boundary is not included.

The line should be shaded above because of the > sign.

Each person will sell 8 shirts if 56 shirts were sold

Mandy and 6 of her teammates each sold an equal number of shirt

Mandy is one person, let add 1 plus six to get the total number

1 + 6

= 7

The total number of shirts sold is 56 shirts

Since there are 7 people, the number of shirt that each person will sell can be calculated by dividing 56 by 7

= 56/7

= 8

Hence 8 shirts will be sold by each person

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Answer:

A=14

B=pi 7^2

Step-by-step explanation:

All you need to do is put pi symbol on calculator and x by 7 squared to get answer

The scale of the drawing is expressed as, 1 inch : 2.5 yards.

A scale factor describes to what size an original image has been reduced or enlarged. If the scale factor of an enlargement is 2, it means every side lengths of the original image is increased times two to get the new image after enlargement.

On the other hand, if the reduction was done using a scale factor of 0.5 or 1/2, it means the size of the original image was reduced by half to get the new side lengths of the new image.

The scale factor of a scale drawing = dimension of new image/corresponding dimension of original image.

The figure by the right is the original figure, while the one on the left is the scale drawing which is the new figure.

Scale of the drawing = 1 inches to 5/2 yards

Scale = 1 inch : 2.5 yards.

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The most appropriate choice of percentage will be given by-

The store have to increase the price of the item by [tex]11\frac{1}{9}[/tex] %  in order to sell it for the original amount.

What is Percentage?

Percentage is a ratio expressed as a percentage of 100.

Let the original price be x

Percentage decrease in price due to sale = 10%

Decrease in price due to sale = [tex]\frac{10}{100} \times x[/tex]

                                                  = [tex]\frac{x}{10}[/tex]

New price = ([tex]x - \frac{x}{10}[/tex])

                 = [tex]\frac{10x-x} {10}[/tex]

                 = [tex]\frac{9x}{10}[/tex]

Now,

Increase in price from [tex]\frac{9x}{10}[/tex] to [tex]x[/tex] = [tex]\frac{x}{10}[/tex]

Percentage by which the store have to increase the price of the item in order to sell it for the original amount =

                                                                  [tex]\frac{\frac{x}{10} }{\frac{9x}{10} } \times 100[/tex]

                                                              =[tex]\frac{x}{10} \times \frac{10}{9x} \times 100[/tex]

                                                              = [tex]\frac{100}{9}[/tex]

                                                              = [tex]11\frac{1}{9}[/tex] %

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Answer:

See below

Step-by-step explanation:

(9x^2 - 4 y ) *  (9x^2 + 4 y )

The slope of the line from the pair of given points would be [tex]m = 5[/tex].

Hope this helps!

Answer:

Step-by-step explanation:

If its 15000:65000

Then we divide both sides by 1000 first :

15 : 65

Then we divide both sides by 5 :

3 : 13

This is simplified

If K is a unit then it will be 3k : 13k by doing the above steps but skipping the first.

Hope this helped and have a good day

Answer:

x = -3

Step-by-step explanation:

You have to isolate x:

7x + 12 = x - 6

7x = x - 6 - 12 = x - 18

6x = -18

x = -3

To be a function, a relation can't have more than 1 value of 'y' for the same value of 'x'

For example, if you have points (3,7) and (3,-6) does not represent a function but points (3,7) and (-3,7) does.

In this problem, none of the graphed pairs have 2 or more values of 'y' for a single value of 'x'. They are all different, so yes, this relation is a function

The x intercepts are 0, 1, -2, 2.

What is intercepts?

The term "intercept" refers to the x- and y-intercepts of of a given equation. The x-intercept is the point at which a line crosses the x-axis and the y-intercept is the point at which a line crosses the y-axis.

In the linear equation, we have the general form as y=mx+b

where m and b are constants.

We have to find the x intercept of the given function.

Given equation is [tex]x^{4} +x^{3} -4x^{2} -4x[/tex]

put this equation equals to 0

x^{4} +x^{3} -4x^{2} -4x = 0

[tex]x(x^{3} +x^{2} -4x-4)=0[/tex]

from this x = 0

x =1 is also the root of the equation

we get [tex]x^{2} -4=0[/tex]

from this

x = -2, 2

The intercept are 0,1,2,-2.

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The addition, subtraction, multiplication and division of the two functions are 4 · x + x¹⁰, 4 · x - x¹⁰, 4 · x¹¹ and 4 / x⁹, respectively.

In functions there are two fundamental operations (addition, multiplication) and two derivate operations (subtraction, division). In this problem we must look for the following definitions:

Addition

(f + g)(x) = f(x) + g(x)

Subtraction

(f - g)(x) = f(x) - g(x)

Multiplication

(f · g)(x) = f(x) · g(x)

Division

(f / g)(x) = f(x) / g(x), for x ≠ 0.

If we know that f(x) = 4 · x and g(x) = x¹⁰, then the expression behind the operations are, respectively:

Addition

(f + g)(x) = 4 · x + x¹⁰

Subtraction

(f - g)(x) = 4 · x - x¹⁰

Multiplication

(f · g)(x) = (4 · x) · x¹⁰ = 4 · x¹¹

Division

(f / g)(x) = (4 · x) / x¹⁰ = 4 / x⁹

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Answer:

No it's not a function

Step-by-step explanation:

You can use the vertical line test to determine whether it's a function or not. If the vertical line touches the graph at more than one point, the graph is not a function therefore the answer is no.

The value of x for the given arithmetic sequence is x = 4.

A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.

Given,

First three terms of an arithmetic sequence are x, 2x + 4, 5x

The difference of 1 and 2 term equals the difference of 3 and 2 term.

⇒ 2x + 4 - x = 5x - 2x - 4

⇒ x + 4 = 3x - 4

⇒ 2x = 8

⇒ x = 4

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The predicted distance of the ball is 271.93 feet.

The speed of an item, which is a scalar quantity in everyday usage and kinematics, is the size of the change in that object's position over time or the size of the change in that object's position per unit of time. Speed is what it means. the speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

Given Data

The speed, s, is measured in miles per hour, and distance, y, is

measured in yards.

The line of fit is given by ý = 3.98 +53.59s.

When s = 5 sec

y = 3.98 + 53.59(5)

y = 3.98 + 267.95

y = 271.93

The predicted distance of the ball is 271.93 feet.

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Step-by-step explanation:

x = age of one of the twin boys

when they had together 21 years of age,

Bill was x years old

Ross was x years old

Mark was x+3 years old

so, we have

x + x + (x + 3) = 21

3x + 3 = 21

3x = 18

x = 6

Bill and Ross were 6 years old.

Mark was 6+3 = 9 years old.

Mark was born in 1990.

1990 + 9 = 1999

so, it was 1999 when they had together 21 years of age.

Answer:

96 boxes of muffins

Step-by-step explanation:

so how you would get to this answer would be 1152÷12

12 is equal to a dozen and so that is why you divide it by 12

the answer would be 96

The area of the kitchen will be:

Answer:

1/2, 1/5, 1/7, 1/9, 1/28

7/14, 7/21, 7/42, 7/49

10/18, 10/20, 10/50, 10/100

If you have ​$50 in your bank account and each week you plan to deposit ​$8 from your allowance and ​$20 from your paycheck. The number of  weeks from now that you will have ​$210 in your bank​ account is: 5.71w.

The given equation is:

b=50+​(20+8​)w

Where:

b  is the amount in your account after w weeks.

w = Number of week

Hence,

b = 50+​(20+8​)w

b = 50+28w

b-50 = 28w

(b-$50)/28 = w

(210-$50)/28 = w

160/28 = w

5.71 = w

Therefore we can conclude that you will have the amount of  $210 in your account in 5.71 weeks.

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The points are (1, -2) or (2, 1).

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

The equation for the hole

x² + y² = 5.............(1)

and, equation for bean bag can be represented by

y = 0.5x² – 1.5x – 4............................(2)

By solving above two equation we get

0.25 [tex]x^4[/tex] + 1.5 x³ -0.75 x² -12 x +11 =0

we het x1=1 and x2 = 2

then y1= -2 and y2 = 1

hence, the points are (1, -2) or (2, 1).

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Answer:30 in.

Step-by-step explanation:13+5+12

Total material remains from original piece if overall length of sheet is

[tex]18\frac{3}{4}[/tex] in and two plates are cut of length [tex]10\frac{1}{2}[/tex] in and [tex]6\frac{15}{16}[/tex] in ,two saw of length 1/16 in is 35 / 16 in.

As given,

Overall length of steel sheet=[tex]18\frac{3}{4}[/tex] in

                                                =(75 /4) in

                                                =(300 /16)in

Length of two plates is [tex]10\frac{1}{2}[/tex] in  and [tex]6\frac{15}{16}[/tex] in

Total length of two plates=[tex]10 \frac{1}{2} + 6\frac{15}{16}[/tex]

                                           =(21 /2) +(95/16)

                                           =(168 +95)/16

                                           =263 /16

Total length of saw cut=(1/16) +(1/16)

                                      =2/16

Material remains from original piece=(300/16) - (263/16 +2/16)

                                                            = 35 /16

Therefore, total material remains from original piece if overall length of sheet is  [tex]18\frac{3}{4}[/tex] in and two plates are cut of length [tex]10\frac{1}{2}[/tex] in and [tex]6\frac{15}{16}[/tex] in ,two saw of length 1/16 in is 35 / 16 in.

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By completing squares, we will see that the two solutions of the quadratic equaiton are:

m = -7 + √(145)/2

m = -7 - √(145)/2

Here we have the quadratic equation:

m^2 + 7m - 51/4 = 0

If we multiply both sides by 4, we will get

4m^2 + 28m - 51 = 0

Now, remember the relation:

(a + b)^2 = a^2 + 2ab + b^2

Then to complete the squares we can write:

(2m)^2 + 2*14*m + (14)^2 - (14)^2 - 51 = 0

(2m + 14)^2 - 14^2 - 51 = 0

(2m + 14)^2 = 145

We already completed squares, now the solutions are:

2m = -14 ± √145

m = (-14 ± √145)/2

m = -7 + √(145)/2

m = -7 - √(145)/2

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