A 4-cup carton of frozen yogurt costs $3.64. What is the price per pint?

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

Harrizon [31]

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) Length = 20x+24 feet
Length = 20(1.5) + 24 feet = 54 feet
2) Width = 36x-20 feet
Width = 36(1.5)-20 feet = 34 feet

Your dimensions are 54 feet (length) by 34 feet (width).

3 0

3 years ago

Which of the following are the correct properties of slope? Check all that apply.

Grace [21]

It's up to you what you chose for A and or B because 0 slope of a line is for a flat horizontal line and an undefined slope is for a flat vertical line
With this information you should chose D regardless but that's also up to you I would though and E is correct.

8 0

3 years ago

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Whats 3/z = 2/5. Please HELP!! Due in 20 minutes!!!

attashe74 [19]

Step-by-step explanation:

Hey there!!

Given,

$\frac{3}{z} = \frac{2}{5}$

Cross multiply.

15 = 2z

Therefore, z= 15/2

Hope it helps..

3 0

3 years ago

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At the rate of $2.00 per square foot the cost of painting the rectangular board with a semicircular top shown in the figure is $

Elenna [48]

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions here.

it consists of a rectangle, dimensions L = 4ft and W = 3ft = Ar = 4ft x 3ft = 12 ft^2

then, you have one half of the area of the circle that has diameter R = 3ft - radius will be r = 1.5ft the area of that half will be:

Ac = r^2 $\pi$ / 2
= (1.5 ft)^2 x 3.14 / 2
= 2.25 ft^2 x 3.4/2
= 7.065 ft^2/ 2
= 3.5325ft^2

A = Ar + Ac
A = 12ft^2 + 3.5325ft^2
A = 15.5325ft^2

At the rate of $2 per square foot, the cost will be:
$ 15.5325*2 = 31.07

5 0

3 years ago

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What is the approximate value of b, rounded to the nearest tenth? Use the law of sines to find the answer.

vivado [14]

You can use the Law of Sines for this problem, but what makes it tough at first glance is that they put a step in before you can use it directly. That first step is to get m∠C. When solving a triangle, always get the third angle if you know the other two so that you can use the Law of Sines (or Law of Cosines) more directly.

The sum of the angles of any triangles is 180°. We know the measures of the two other angles. So we subtract them from 180° to find that third angle.

180° - 76° - 66° = 38°

Now we can use the proportion from the picture. Angle B measures 76°, side b is our unknown, Angle C measures 38°, and side c measures 3 units.

sin 76° sin 38°

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

b 3

Cross multiply to find b (the side). We carry out five places in these calculations to get more accuracy.

3 * sin 76° = b * sin 38°

b = 3 * sin 76° 3 * 0.56611 1.69832

--------------- = --------------- = ---------------- = 5.73044

sin 38° 0.29636 0.29636

To the nearest tenth, b - 5.7 units.

3 0

3 years ago

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