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3 years ago

PLEASE HELP! What is AD? A. 15 B. 12 C. 3 D. 20

Mathematics

1 answer:

ki77a [65]3 years ago

3 0

Answer:

A. 15

Step-by-step explanation:

To solve this you need to compare the lengths given to you in the question statement.

Because the lines originate from a single point, they're like triangles. We can easily see a triangle AGF and a triangle ADE, right?

Both triangles are similar triangles, so we can see triangle ADE as a larger version of angle AGF.

They give you the dimension of A F and A E (through A F + F E) to establish a ratio... and they give you A G, asking for A D.

So, A F = 16, A E = 20 (16 + 4), A G = 12.

Since A D is to A G what A E is to A F, we can easily make the following cross-multiplication:

$\frac{A D}{A G} = \frac{A E}{A F}$

So, A D = (A G * A E)/A F

A D = (12 * 20) / 16 = 15

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Given f(x)=4/5x + 13, find the inverse f-¹(x) Given f(x)= 3/x+10 + 4 find the inverse f-¹(x)

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f-¹(x) = 69/5y
f-¹(x) = 13 + 4y/(y + 10)

<h3>How to determine the inverse </h3>

The steps involved in determining the inverse of a function are;

Replace f(x) with y in the equation describing the function
Interchange x and y
Solve for y
Replace y by f-1(x)

If f(x) = 4/5x + 13

y = 4/5y + 13

y = 4 + 65 /5y

f^-1 = 4 + 65 /5y

f^-1(x)= 69/5y

If f(x)= 3/x+10 + 4

y = 3/y + 10 + 4

y = 3 + 4y + 10/(y + 10)

y = 13 + 4y/(y + 10)

f^-1(x) = 13 + 4y/(y + 10)

Thus, the inverse of the functions is 69/5y and 13 + 4y/(y + 10)

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Mike wants to fence in part of his backyard. He wants the length of the fenced-in area to be at least 20 feet long, l ≥ 20. He h

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I added a screenshot of the complete question along with the given choices.

Answers:

w = 10 ft and l = 50 ft ................> second option

w = 20 ft and l = 60 ft ...............> third option

w = 50 ft and l = 40 ft ...............> fifth option

Explanation:

We are given that:

length should be at least 20 ...........> length ≥ 20

equation for perimeter is : 2l + 2w ≤ 200

We will check each option as follows:

Option 1:

w = 50 ft and l = 10 ft

This option is incorrect as the proposed length is less than 20.

Option 2:

w = 10 ft and l = 50 ft

Since the length is greater than 20, the first condition is satisfied.

Now, we check the second condition:

2l + 2w = 2(50) + 2(10) = 100 + 20 = 120 ≤ 200

The second condition is also satisfied.

This option is correct

Option 3:

w = 20 ft and l = 60 ft

Since the length is greater than 20, the first condition is satisfied.

Now, we check the second condition:

2l + 2w = 2(60) + 2(20) = 120 + 40 = 160 ≤ 200

The second condition is also satisfied.

This option is correct

Option 4:

w = 90 ft and l = 30 ft

Since the length is greater than 20, the first condition is satisfied.

Now, we check the second condition:

2l + 2w = 2(30) + 2(90) = 60 + 180 = 240 > 200

The second condition is not satisfied.

This option is incorrect

Option 5:

w = 50 ft and l = 40 ft

Since the length is greater than 20, the first condition is satisfied.

Now, we check the second condition:

2l + 2w = 2(50) + 2(40) = 100 + 80 = 180 ≤ 200

The second condition is also satisfied.

This option is correct

Hope this helps :)

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