Ask question

Ask question

All categories

11111nata11111 [884]

4 years ago

6

7 Cassie wants to determine the length of the shadow that a 20-foot tall telephone pole casts without measuring it. If Cassie's

mailbox, which is 45 inches in height, casts a shadow that is 22.5 inches in length, how long is the shadow that the telephone pole casts?

1 answer:

Sophie [7]4 years ago

7 0

Answer:

10 ft

Step-by-step explanation:

In order to solve this question, we need to set up a proportion:

$\frac{\textrm{Height of mailbox}}{\textrm{Length of shadow}} = \frac{\textrm{Height of telephone pole}}{\textrm{Length of shadow}}$

Replacing with actual values:

$\frac{45 \textrm{ in}}{22.5 \textrm{ in}} = \frac{20 \textrm{ ft}}{x \textrm{ ft}}$

Cross-multiplying:

$45\times{x} = 20\times{22.5}\\45x = 450$

Dividing both sides by 45:

$\frac{45x}{45} = \frac{450}{45}\\\\x = 10$

Therefore, the length of the telephone pole's shadow is 10 ft.

You might be interested in

35 POINTS AVAILABLE

aliina [53]

Answer:

Part 1) The length of each side of square AQUA is $3.54\ cm$

Part 2) The area of the shaded region is $(486\pi-648)\ units^{2}$

Step-by-step explanation:

Part 1)

<em>step 1</em>

Find the radius of the circle S

The area of the circle is equal to

$A=\pi r^{2}$

we have

$A=25\pi\ cm^{2}$

substitute in the formula and solve for r

$25\pi=\pi r^{2}$

simplify

$25=r^{2}$

$r=5\ cm$

<em>step 2</em>

Find the length of each side of square SQUA

In the square SQUA

we have that

SQ=QU=UA=AS

$SU=r=5\ cm$

Let

x------> the length side of the square

Applying the Pythagoras Theorem

$5^{2}=x^{2} +x^{2}$

$5^{2}=2x^{2}$

$x^{2}=\frac{25}{2}\\ \\x=\sqrt{\frac{25}{2}}\ cm\\ \\ x=3.54\ cm$

Part 2) we know that

The area of the shaded region is equal to the area of the larger circle minus the area of the square plus the area of the smaller circle

<em>Find the area of the larger circle</em>

The area of the circle is equal to

$A=\pi r^{2}$

we have

$r=AB=18\ units$

substitute in the formula

$A=\pi (18)^{2}=324\pi\ units^{2}$

step 2

Find the length of each side of square BCDE

we have that

$AB=18\ units$

The diagonal DB is equal to

$DB=(2)18=36\ units$

Let

x------> the length side of the square BCDE

Applying the Pythagoras Theorem

$36^{2}=x^{2} +x^{2}$

$1,296=2x^{2}$

$648=x^{2}$

$x=\sqrt{648}\ units$

step 3

Find the area of the square BCDE

The area of the square is

$A=(\sqrt{648})^{2}=648\ units^{2}$

step 4

Find the area of the smaller circle

The area of the circle is equal to

$A=\pi r^{2}$

we have

$r=(\sqrt{648})/2\ units$

substitute in the formula

$A=\pi ((\sqrt{648})/2)^{2}=162\pi\ units^{2}$

step 5

Find the area of the shaded region

$324\pi\ units^{2}-648\ units^{2}+162\pi\ units^{2}=(486\pi-648)\ units^{2}$

7 0

3 years ago

For which pair of functions is the vertex of k(x)7 units below the vertex of f(x)?

kvv77 [185]

Answer: Option C

$f(x) = x^2;\ k (x) = x ^ 2 -7$

Step-by-step explanation:

Whenever we have a main function f(x) and we want to transform the graph of f(x) by moving it vertically then we apply the transformation:

$k (x) = f (x) + b$

If $b> 0$ then the graph of k(x) will be the graph of f(x) displaced vertically b units down.

If $b> 0$ then the graph of k(x) will be the graph of f(x) displaced vertically b units upwards.

In this case we have

$f (x) = x ^ 2$

We know that this function has its vertex in point (0,0).

Then, to move its vertex 7 units down we apply the transformation:

$k (x) = f (x) - 7\\\\k (x) = x ^ 2 -7$ .

Then the function k(x) that will have its vertex 7 units below f(x) is

$k (x) = x ^ 2 -7$

3 0

3 years ago

Gina drew a circle with right triangle PRQ inscribed in it, as shown below:

Darina [25.2K]

I think the correct answer is b 75

3 0

3 years ago

Read 2 more answers

Iodine-131 is a radioactive material with half-life of eight days. A scientist starts with 100 grams of iodinie- 131. Which func

MrRissso [65]

The correct answer is Choice A.

This is an example of an exponential equation, so we need the formula $y=ab^x$ .

The a value is the starting value of 100. The b value must be a decimal lower than 1 because it is decreases.

If you substitute in 8 for x, you will see that the output is about 50 (half of 100).

6 0

3 years ago

Read 2 more answers

Add: 8p + (-6p6 + 5)

Alika [10]

Answer:

$-6p^6 +8p + 5$

Step-by-step explanation:

$8p + -6p^6 + 5$

$-6p^6 +8p + 5$

6 0

3 years ago

Read 2 more answers