What is the ratio of 40:25

Polygon ABCD is reflected and dilated to give polygon PQRS. The coordinates of the preimage are (2, 2), (6, 8), (12, 8), and (16

HACTEHA [7]

Answer: The scale factor of the dilation is 0.5.

Explanation:

It is given that ABCD is polygon which is reflected and dilated , then we get PQRS.

The vertices of ABCD are (2, 2), (6, 8), (12, 8), and (16, 2) respectively. The vertices of image PQRS are (11, 15),(9, 12), (6, 12), and (4, 15) respectively.

The reflection affects the coordinates but does not affect the length of the sides.

But when we talk about dilation it affects the length of sides according to the scale factor or a constant factor.

If a line segment AB is dilated by scale factor k then length of A'B' is k times length of AB.

$|A'B'|=k\times |AB|$ .... (1)

So we have to find any side length of preimage and the side length of that side in image. it means we have to find AB and PQ.

Use distance formula to find the side length.

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$AB=\sqrt{(8-2)^2+(6-2)^2}=\sqrt{36+16}=2\sqrt{13}$

$PQ=\sqrt{(9-11)^2+(12-15)^2}=\sqrt{4+9}=\sqrt{13}$

It is noticed that the size of side in preimage is $2\sqrt{13}$ and the size of same side in image is $\sqrt{13}$ .

Using equation (1), we get

$\sqrt{13}=k \times 2\sqrt{13}$

$k=\frac{1}{2}$

$k=0.5$

Hence, the value of scale factor is 0.5.

7 0

3 years ago

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Rebotar Inc.makes basketballs.Their fixed costs are $3,450.

melomori [17]

Answer:

Since the profit is positive, Rebotar not only broke even, they had earnings.

Step-by-step explanation:

Function Modeling

The costs, incomes, and profits of Rebotar Inc. can be modeled by means of the appropriate function according to known conditions of the market.

It's known their fixed costs are $3,450 and their variable costs are $12 per basketball produced and sold. Thus, the total cost of Rebotar is:

C(x) = 12x + 3,450

Where x is the number of basketballs sold.

It's also known each basketball is sold at $25, thus the revenue (income) function is:

R(x) = 25x

The profit function is the difference between the costs and revenue:

P(x) = 25x - (12x + 3,450)

Operating:

P(x) = 25x - 12x - 3,450

P(x) = 13x - 3,450

If x=300 basketballs are sold, the profits are:

P(300) = 13(300) - 3,450

P(300) = 3,900 - 3,450

P(300) = 450

Since the profit is positive, Rebotar not only broke even, they had earnings.

8 0

3 years ago

Joseph owns a hot dog stand and sells specialized hot dogs. He charges $1.50 for a plain hot dog and then an additional $0.50 fo

Lilit [14]

Hot Dog Stand

Let

C--------> total cost of the hot dog

x-------> is the number of toppings

we know that

$C=0.5x+1.5$

where

The slope of the linear equation is equal to $0.5\frac{\$}{topping}$

The y-coordinate of the y-intercept of the linear function is equal to $\$1.5$

That means -------> This is the cost of the hot dog without topping

Hamburgers Stand

Let

C--------> total cost of the hamburger

x-------> is the number of toppings

we know that

$C=0.25x+2.50$

where

The slope of the linear equation is equal to $0.25\frac{\$}{topping}$

The y-coordinate of the y-intercept of the linear function is equal to $\$2.5$

That means -------> This is the cost of the hamburger without topping

therefore

the answer is

The linear equation of the hamburger cost is equal to

$C=0.25x+2.50$

4 0

3 years ago

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This please asapppppp

Tatiana [17]

Answer:

C.

Step-by-step explanation:

8 0

3 years ago

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2.5 QUIZ ALGEBRA 2

LUCKY_DIMON [66]

Answer:

Step-by-step explanation:

x²+24x+60=0

x²+24x+(24/2)²=-60+(24/2)²

(x+12)²=-60+144

(x+12)²=84

3 0

3 years ago