Emelina write the equation of a line in point slope form as shown below

Miranda enlarged a picture twice as shown below, each time using a scale factor of 3.

lyudmila [28]

Answer:

The area of the second enlargement is 1,944 square inches

The area of the second enlargement is (3 squared) squared times the original area.

The ratio of the area of the first enlargement to the area of the original equals the square of the scale factor

Step-by-step explanation:

<u><em>Verify each statement</em></u>

1) The area of the first enlargement is 72 square inches.

The statement is false

Because

we know that

The original dimensions of the rectangle are

length 6 inches and width 4 inches

so

First enlargement

Multiply the original dimensions by a scale factor of 3

$Length: 6(3)=18\ inches\\Width: 4(3)=12\ inches$

The area of the first enlargement is

$18(12)=216\ in^2$

2) The area of the second enlargement is 1,944 square inches

The statement is true

Multiply the dimensions of the first enlargement by a scale factor of 3

$Length: 18(3)=54\ inches\\Width: 12(3)=36\ inches$

The area of the second enlargement is

$54(36)=1,944\ in^2$

3) The area of the second enlargement is (3 squared) squared times the original area.

The statement is true

Because

The original area is 24 square inches

$[(3^2)]^2(24)=1,944\ in^2$

4) The area of the second enlargement is 3 times the area of the first enlargement

The statement is false

Because

$3(216)=648\ in^2$

so

$648\ in^2 \neq 1,944\ in^2$

5) The ratio of the area of the first enlargement to the area of the original equals the square of the scale factor

The statement is true

Because

The square of the scale factor is 3^2=9

and the ratio is equal to

$\frac{216}{24}=9$

8 0

2 years ago

Read 2 more answers

What is the equation of the line perpendicular to the line y=3x+2 and passing through the point (3, -4)

aleksklad [387]

Answer:

Step-by-step explanation:

$(3, -4)=(x,y)\\y=3x+2\\\\m_1 =3\\In\: perpendicular\: line ;\\\\m_2 = \frac{-1}{m_1} \\m_2 = \frac{-1}{3} \\m_2 = -1/3\\\\Substitute \:new\:values\:into\: ;y=mx+b\\\\-4 = -\frac{1}{3} (3) + b\\-4 = -1 +b\\-4+1 =b\\-3 =b\\Substitute \:new\:values\:into\: ;y=mx+b\\y =-\frac{1}{3}x -3$

5 0

3 years ago

If there are 9 stars for every 2 hearts, how many stars for 4 hearts?

Archy [21]

Answer:

18 stars

Step-by-step explanation:

We can use a ratio to solve

9 stars x

--------- = -----------

2 hearts 4 hearts

Using cross products

9*4 = 2x

36 = 2x

Divide by 2

36/2 =2x/2

18 =x

18 stars

3 0

3 years ago

Read 2 more answers

salini's mother's present age is 8 times salini's present age five years from now salini's age will be 1/4th of of his mother's

choli [55]

Answer:

salini -= 5 years

mother = 40years

Step-by-step explanation:

$salini = x \\ mother =8x \\ x + 5 = 1 \: of \: 8x \\ x + 5 = 2x \\ 5 = x$

$5 = x$

then you equate the values of x

8 0

3 years ago

A lender estimates the closing costs on a home loan will be 3% of the loan amount of $180,000. The actual closing costs are list

Anvisha [2.4K]

Based on the information provided, it can be inferred that the lender made an excellent estimate; was equal to actual closing costs (option A)

<h3>How do you know what the lender's estimate was? </h3>

Based on the information provided, the lender estimated that the closing cost is equal to 3% of the $ 180,000 loan. To calculate that value we must do the following operation:

$ 180,000 / 100 x 3% = $ 5,400.

Based on the above, the estimated closing cost for that loan is $ 5,400.

<h3>How to know the real cost of closing the loan? </h3>

To know the real cost of the loan closing we must add the following values:

Closing Cost Charge Loan origination $ 345
Title insurance $ 600
Attorney's fees $ 1,350
Appraisal $ 480
Inspection $ 550
Recording fees $ 175
Escrow $ 1,900

$ 1,900 + $ 175 +% 550 + $ 480 + $ 1,350 + $ 600 + $ 345 = $ 5,400.

According to the above, the lender made a very precise estimate because his calculation hit the exact value of the closing cost (option A)

Learn more about lender in: brainly.com/question/3268275

3 0

2 years ago