Look at screenshot 11 points and brainleist!

What is the scale factor in the dilation if the coordinates of A prime are (–7, 6) and the coordinates of C prime are (–4, 3)?

olchik [2.2K]

Option A: $\frac{1}{3}$ is the dilation factor

Explanation:

The Coordinates of the square ABCD are A(-21,18), B(-12,18), C(-12,9), D(-21,9)

Also, the coordinates of the square A'B'C'D' are A'(–7, 6), B'(-4,6), C'(-4,3), D'(-8,3)

Now, we shall determine the scale factor in the dilation if the coordinates A' and C'.

Since, the dilation is the enlargement of the image in the same shape but different size.

To determine the scale factor, let us divide A'C' by AC

Thus, we have,

$\begin{aligned}A^{\prime} C^{\prime} &=\sqrt{(-4+7)^{2}+(3-6)^{2}} \\&=\sqrt{3^{2}+(-3)^{2}} \\&=\sqrt{9+9} \\&=\sqrt{18}\\&=3\sqrt{2} \end{aligned}$

Also,

$\begin{aligned}A C &=\sqrt{(-12+21)^{2}+(9-18)^{2}} \\&=\sqrt{9^{2}+(-9)^{2}} \\&=\sqrt{81+81} \\&=\sqrt{162}\\&=9\sqrt{2} \end{aligned}$

Dividing A'C' by AC, we have,

$\frac{A'C'}{AC} =\frac{3\sqrt{2} }{9\sqrt{2}} =\frac{1}{3}$

Thus, $\frac{1}{3}$ is the dilation factor

3 0

3 years ago

Read 2 more answers

1+1 what does it equal heolpgvfegfvegf

VashaNatasha [74]

It equals 2, explanation 1+1=2

3 0

4 years ago

Read 2 more answers

A market analyst is hired to provide information on the type of customers who shop at a particular store. A random survey is tak

sveta [45]

Complete question:

A market analyst is hired to provide information on the type of customers who shop at a particular store. A random survey is taken of 100 shoppers at this store. Of these 100, 73 are women. The shoppers The data is summarized below. we grouped in three age categories, under 30, 30 up to 50 and 50 and over. Women under 30 are 30, Men under 30 are 8 Women 30 to 50 are 25 and Men are 14 Women 50 and over are 18 and Men are 5.

Let W be the event that a randomly selected shopper is a woman. Let A be the event that a randomly selected shopper is under 30. a.) Find the probability of W. W (women Shoppers) = Find the probability of A. b.) Find the probability of A and W. c.) P (A and W) (Shoppers) d.) Find the probability of A or W. P(A or W) (Shoppers) e.) Find the probability of A given W

Answer:

A) P(W) = 73/100; B) P(A) = 38/ 100 C) 30 / 100

D) 81/100 E) 30/73

Step-by-step explanation:

- - - - - - - - Women Men Total

Under 30 - - - 30 - - - 8 - - 38

30 to 50 - - - - 25 - - 14 - - 39

50 & over - - - 18 - - - 5 - - -23

Totals - - - - - - 73 - - -27 - - 100

Recall:

Probability : P= (required outcome / Total possible outcomes)

A) probability of women shoppers: P(W)

Number of women shoppers = 73; total shoppers = 100

P(W) = 73/100

B) Probability of under 30: P(A)

= number of shoppers under 30 = 38

Tital number of shoppers = 100

P(A) = 38/ 100

C) probability of A and W; This is the probability that the selected person is a woman and under 30.

(W n A) = 30

= 30 / 100

D) probability of A or W:

P(A) + P(W) - P(A n W) :

(38 / 100 + 73 / 100 - 30 / 100) = (38+73-30) /100

= 81/100

E) probability of A given W:

P(A n W) / P(W) = 30/73

5 0

3 years ago

Lena bought 14 yards of wire. How many inches of wire did she buy? ( 1 yard =36 inches)

KengaRu [80]

Answer:

504 inches

Step-by-step explanation:

Multiply 14 by 36 and get your answer

3 0

2 years ago

Please 100 points and brainliest if u do them all plsssssss I rlly need help asap

AysviL [449]

Answer:

<u>Question 1</u>

F

T

The volume of figure A can be found by multiplying (5 · 7)(2).

<u>Question 2</u>

T

F

The total volume of the figure is 442 mm³

<u>Question 3</u>

T

F

T

The volume of the triangular prism is 108 in³

Step-by-step explanation:

<u>Formula used</u>

Volume of a prism = base area × height

Area of a rectangle = width × length

Area of a triangle = 1/2 × base × height

Volume of a cube = s³ (where s is the side length)

---------------------------------------------------------------------------------------------------

<h3><u>Question 1</u></h3>

⇒ Volume of Figure A = (5 · 7)(2)

= 70 cm³

⇒ Volume of Figure B = (13 · 7)(2)

= 182 cm³

⇒ Total Volume = Volume of Figure A + Volume of Figure B

= 70 + 182

= 252 cm³

The first statement is false.

<u>Rewritten statement</u>:

The volume of figure A can be found by multiplying (5 · 7)(2).

---------------------------------------------------------------------------------------------------

<h3><u>Question 2</u></h3>

⇒ Volume of rectangular prism = (15 · 15)(2)

= 450 mm³

⇒ Volume of central cube = 2³

= (2 · 2 · 2)

= 8 mm³

⇒ Total Volume = Volume of rectangular prism - Volume of cube

= 450 - 8

= 442 mm³

The third statement is false.

<u>Rewritten statement</u>:

The total volume of the figure is 442 mm³

---------------------------------------------------------------------------------------------------

<h3><u>Question 3</u></h3>

⇒ Volume of rectangular prism = (12 · 3)(8)

= 288 in³

⇒ Volume of triangular prism = (1/2 · 12 · 6)(3)

= 108 in³

⇒ Total Volume = Volume of rectangular prism + Volume of triangular prism

= 288 + 108

= 396 in³

The second statement is false.

<u>Rewritten statement</u>:

The volume of the triangular prism is 108 in³

7 0

2 years ago