Allison is planning to cover the lateral surface of a large cylindrical garbage can with decorative fabric for a theme party. The can has a diameter of 3 feet and a height of 3.5 feet. How much fabric does she need? Round to the nearest square foot.

Given that ▱FGHI and ▱TUVW are similar figures, the scale factor from ▱TUVW to ▱FGHI  is 8/9.

The value of x is 32.

What is the Area of Similar Figures?

• If a and b are corresponding sides of two similar shapes with areas A and B respectively, the ratio of their areas is, a/b = a²/b² = A/B.
• Scale factor = a/b.

Therefore, the scale factor from TUVW to FGHI would be:

√64/√81 = 8/9

Find the value of x:

x/36 = 8/9

x = 32

Thus, given that ▱FGHI and ▱TUVW are similar figures, the scale factor from ▱TUVW to ▱FGHI  is 8/9.

The value of x is 32.

Learn more about similar figures on:

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Final answer:

The perimeter of a square with a side length of 5/7 units is 20/7 units or approximately 2.86 units.

Explanation:

The question is asking for the perimeter of a square where the side length is 5/7 units. The formula for the perimeter of a square is 4x, where 'x' is the length of the side. Thus, to get the perimeter, you substitute 5/7 for 'x' in the formula. So, 4*(5/7) = 20/7 units, which is approximately 2.86 units.

Learn more about Perimeter of a Square here:

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Answer:   a = -3

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Work Shown:

The point (1, -3) is on the blue graph p(x) = a|x|

This means x = 1 and y = -3 pair up.

Use these two values to find 'a'

p(x) = a|x|

y = a|x|

-3 = a*|1|

-3 = a*1

-3 = a

a = -3

The negative 'a' value will apply the reflection over the x axis. The fact that |a| = 3 is larger than 1 indicates the graph is vertically stretched by a factor of 3.