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Goryan [66]
2 years ago
10

A rectangle has a width of 9 inches and a length of 15 inches. If the rectangle is enlarged by a scale factor of 3/2, what is th

e perimeter of the dilated rectangle
Mathematics
1 answer:
asambeis [7]2 years ago
6 0

Answer:

P = 48 in²

Step-by-step explanation:

Given: A rectangle; Width = 9 inches, length = 15 inches, enlarged by a scale factor of \frac{3}{2}

To find: Perimeter of the dilated rectangle

Formula: P=2(l+w)

Solution: After a dilation with a scale factor of one-half, then the lengths on the image would be one-half , one-half , and one-half . To find the perimeter of an enlarged figure, you can multiply the original figure's perimeter by the scale factor.

P=2(l+w)=2 × (15+9)=48in

Therefore, the perimeter of the detailed rectangle that was enlarged is 48 in²

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A company that teaches self-improvement seminars is holding one of its seminars in Lancaster. The company pays a flat fee of $98
alukav5142 [94]

Answer:

Step-by-step explanation:

Let x represent the number of attendees that it will take the company to break even.

The company pays a flat fee of $98 to rent a facility in which to hold each session. Additionally, for every attendee who registers, the company must spend $16 to purchase books and supplies. This means that the total cost that the company would pay for x attendees is

16x + 98

Each attendee will pay $65 for the seminar. This means that the total revenue that the company would generate from x attendees is 65x.

At the break even point,

total cost = total revenue

Therefore,

16x + 90 = 65x

65x - 16x = 98

49x = 98

x = 98/49

x = 2

It will take 2 attendees and the total expenses and revenues is

2 × 65 = $130

4 0
3 years ago
Carl and rose live in the same straight road. From their balconies they can see a flagpole in the distance. The angle that each
Andreyy89

Carl and Rose' balconies make up the base of an isosceles triangle.

Their distances from the flagpole is the same.

From the question, we understand that:

  • Carl and Rose live on a straight line
  • The measure of angle from each person's balcony to the flagpole is the same

The above highlights mean that:

The relationship between Carl and Rose' balconies and the flagpole is an isosceles triangle.

Where Carl and Rose' balconies form the base of the isosceles triangle.

Hence, their distances from the flagpole is the same.

Read more about distances at:

brainly.com/question/12961022

6 0
2 years ago
twice the sum of a number and 6 is equal to 3 times the difference of the number and 8. Find the number
Serhud [2]

In order to solve this problem, we must solve an equation.

First, we need to define our unknown.

Let's call our number "n".


So, the sum of the number and 6 is the same as saying n+6

Then we need to multiply it by 2 (since it's twice the sum)

2(n+6)

This whole thing is equal to three times of the difference of the number and 8

n-8 is equal to the difference between the number and 8, then we need to multiply it by three.

3(n-8)

now, we set both sides equal and solve

2(n+6)=3(n-8)\\2n+12=3(n-8)\\2n+12=3n-24\\12=n-24\\36=n

The number is 36

5 0
2 years ago
Air pressure may be represented as a function of height (in meters) above the
denis-greek [22]

Answer: OPTION C.

Step-by-step explanation:

<h3> The complete exercise is: "Air pressure may be represented as a function of height (in meters) above the surface of the Earth, as shown below:</h3><h3>  P(h) =P_0e^{-0.00012h} </h3><h3> In this function P_o   is the air pressure at the surface of the earth, and h is the height above the surface of the Earth, measured in meters. At what height will the air pressure equal 50% of the air pressure at the surface of the Earth"</h3><h3></h3>

Given the following function:

P(h) =P_0e^{-0.00012h}

In order to calculate at what  height the air pressure will be equal 50% of the air pressure at the surface of the Earth, you can follow these steps:

1. You need to substitute P(h)=0.5P_o into the function:

0.5P_o=P_0e^{-0.00012h}

2. Finally, you must solve for h.

Remember the following property of logarithms:

ln(b)^a=a*ln(b)\\\\ln(e)=1

Then, you get this result:

0.5P_o=\frac{P_o}{e^{0.00012h}}\\\\(0.5P_o)(e^{0.00012h})=P_o\\\\e^{0.00012h}=\frac{P_o}{0.5P_o}\\\\ln(e)^{0.00012h}=ln(2)\\\\0.00012h*1=ln(2)\\\\h=\frac{ln(2)}{0.00012}\\\\h=5576.2

7 0
3 years ago
Two fair dice, one blue and one red, are tossed, and the up face on each die is recorded. Define the following events:
ZanzabumX [31]

Answer:

Step-by-step explanation:

Given that two fair dice, one blue and one red, are tossed, and the up face on each die is recorded.

a) P(E) = P(the difference of the numbers is 3 or more}

Favourable events are (1,4) (1,5)(1,6) (2,5) (2,6) (3,6) (4,1) (5,1) (5,2) (6,1) (6,2)(6,3)

P(E) = \frac{12}{36} =\frac{1}{3}

b)P(F)

Favourable events for F = (1,1) (2,2)...(6,6)

P(F) = \frac{6}{36} =\frac{1}{6}

c) P(EF)

There is no common element between E and F

P(EF) =0

4 0
2 years ago
Read 2 more answers
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