Question

The triangles are similar
What is the value of x?
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x=

The triangles are similar
What is the value of x?
Enter your answer in the box.

x=

What is AE ?
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Hunter designs two flags for his adventure club.
What is the length of the base, x, of the larger flag?
Enter your answer, as a decimal, in the box.

A man throws a basketball from 30 in. above the ground. The basketball bounces off the floor and a boy catches it. The distance the ball traveled from the man to the floor is 45 in., and the distance the ball traveled from the floor to the boy is 40 in. The angles formed from by the basketball's path are congruent.

What is the distance, x, from the floor that the boy caught the ball?
Enter your answer, as a decimal, in the box. Round your answer to the nearest hundredth.

Answer 1

20/5 = x /4   x =  80/5 = 16

x - 10 / 39 = 5/15 = 1/3
3x - 30 =  39
3x = 69
x = 23

(2x + 10 ) * 4 = 10 *(x + 3)

8x + 40 = 10x + 30
2x = 10 
x = 4

AE = 2(5) + 10  =  20

Answer 2

The value of x for 1st figure is 16 units, for 2nd figure is 22, for 3rd figure is 5, for 4th figure is 6.25, and for 5th figure is 26.67. The value of AE and DE is 20 units and 8 units, respectively.

The given triangles in the figure are similar.

For similar triangles, the ratio of their sides is equal.

Now, solve for the value of x for all the triangles one by one,

For first figure,

$\dfrac{x}{4}=\dfrac{20}{5}\\\dfrac{x}{4}=4\\x=16$

For 2nd figure,

$\dfrac{x-10}{36}=\dfrac{5}{15}\\x-10=12\\x=22$

For the 3rd figure,

$\dfrac{AE}{DE}=\dfrac{AB}{CD}\\\dfrac{2x+10}{x+3}=\dfrac{10}{4}\\4x+20=5x+15\\x=5$

So, the value of AE and DE will be,

$AE=2x+10\\=2\times 5+10\\=20\\DE=x+3\\=8$

For the 4th figure,

$\dfrac{x}{5}=\dfrac{5}{4}\\x=\dfrac{25}{4}\\x=6.25$

For the 5th figure,

$\dfrac{x}{30}=\dfrac{40}{45}\\x=\dfrac{80}{3}\\x=26.67$

Therefore, value of x for 1st figure is 16 units, for 2nd figure is 22, for 3rd figure is 5, for 4th figure is 6.25, and for 5th figure is 26.67. The value of AE and DE is 20 units and 8 units, respectively.

For more details, refer to the link:

https://brainly.com/question/19738610