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SVETLANKA909090 [29]
3 years ago
7

There are two buildings that you want to have in the amusement park, but the size hasn’t been determined yet. Although you don’t

know the specific dimensions, you do know the relationships between the sides. The first is the rectangular gift shop. You know that the length will be 20x+24 feet and the width will be 36x-20 feet. a) Write the expression that represents the area of the gift shop, in terms of x. b) Write the expression that represents the perimeter of the gift shop, in terms of x. c) If the perimeter is going to be 176 feet, what are the dimensions of the building?
Mathematics
1 answer:
Harrizon [31]3 years ago
3 0
A) The area of a rectangle is A = lw, where l=length of the rectangle and w=width of the rectangle. You know the length of the gift shop, l = 20x + 24. You know the width, w = 36x - 20. Plug those expressions into the equation for area of a rectangle and multiply/foil:
A = lw\\
A = (20x + 24)(36x - 20)\\
A = (20x)(36x) + (20x)(-20) +  (24)(36x) + (24)(-20)\\
A = 720x^{2} - 400x + 864x - 480\\
A = 720x^{2} + 464x - 480

The expression for the area of the gift shop is 720x^{2} + 464x - 480.

B) The equation for the perimeter of the gift shop is P = 2(l+w), where l = length and w = width. Plug your values for l and w into this equation:
P = 2(l+w)\\
P = 2(20x + 24 + 36x - 20)\\
P = 2(56x + 4) = 2(56x) + 2(4)\\
P = 112x + 8

The expression for the perimeter of the gift shop is 112x + 8

C) Since you know the perimeter is going to be 176 ft, that means P = 176. Plug that into the equation you found in part B, P = 112x + 8, and solve for x.
P = 112x + 8\\
176 = 112x + 8\\
112x =  168
x = 1.5

Once you solve for x, you can plug x into your equations for width and length to find the dimensions. x = 1.5, so:
1) L<span>ength = 20x+24 feet 
</span>Length = 20(1.5) + 24 feet = 54 feet
2) Width = <span>36x-20 feet
Width = 36(1.5)-20 feet = 34 feet

Your dimensions are 54 feet (length) by 34 feet (width).
</span>
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Tickets to the zoo cost $14 for adults and $10 for children. A group of 12 people went to the zoo, and the tickets cost $140. Th
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lets multiply the first equation by -10 and then add it to the second equation:
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</span>-----------------------
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8 0
3 years ago
The temperature has been going down at a constant rate.In 4 hours it went down 12 degrees.Which expression best shows the temper
fomenos

Answer:

<u>t = t₀ - 3n</u>

Step-by-step explanation:

Let t be the temperature and t₀ be the initial temperature of the day

Let n be the number of hours after the initial temperature ( t₀) was registered

Let -3 be the constant of change of temperature ( In 4 hours it went down 12 degrees)

Now, let's write down the expression that shows the temperature change each hour, this way:

t = t₀ - 3n

After 2 hours

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After 5 hours

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After 3 hours and 30 minutes

t = t₀ - 3 * 3.5 = t₀ - 10.5

5 0
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WILL MARK BRAINLIST FOR ANSWER!!!!!!!!!!<br> |2 1/3 x+0.3|=3.5
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THE ANSWER ISSSS


1.37142
6 0
3 years ago
Please help i have no idea with this lesson
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Answer:

40

Step-by-step explanation:

ABD-CBD=ABD

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3 0
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Read 2 more answers
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