Please prove or explain how to get AC, CM, & CP...AC = 15
CM = 20
CP = 12

Answers

Answer 1

Answer:

Explanation:

All of the right triangles are similar by AA similarity, so corresponding side lengths are proportional. The ratio of the long leg to the short leg is the same for the two smaller triangles, for example:

CP/AP = MP/CP

CP/9 = 16/CP . . . . . fill in the given numbers

CP² = 9·16 . . . . . . . multiply by 9·CP

CP = 3·4 = 12 . . . . . take the square root

Now, you can use the Pythagorean theorem to find AC and/or CM.

AC = √(9² +12²) = √225 = 15

CM = √(12² +16²) = √400 = 20

In summary, CP = 12, AC = 15, CM = 20.

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Once you have CM, you can see these are 3-4-5 right triangles, so you can determine the other lengths by using these side ratios.

3:4:5 = 9:12:15 = 12:16:20

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The altitude CP is called the "geometric mean" of AP and MP. It is the square root of their product. This is true for any right triangle, not just one with sides in the ratio 3:4:5. If you know this, you can write down your answers almost immediately. Above, we had to derive this fact using similarity.

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A limited-edition poster increases in value each year. After 1 year, the poster is worth $20.70. After 2 years, it is worth $23.81. Which equation can be used to find the value, y, after x years? (Round money values to the nearest penny.)A.y = 18(1.15)x

B. y = 18(0.15)x

C.y = 20.7(1.15)x

D.y = 20.7(0.15)

Answers

we try each

A. 18(1.15)^1=20.7 correct
B will decrease
C is too much
D also decrase

A is answer

If the ratio of men to women in a movie theater is 1.00 when written as a decimal, what must be true?

Answers

what must be true? answer is The ratio of women to men in the theater is 0.50 and this because it would be Number of Men is 1 = Number of Women = 1. Total people = 2. Ratio of women to total = 1

Answer:it’s actually ratio of women to total people in the theater is 0.50

Step-by-step explanation:

A ratio of 1.00 for men to Women indicates that the number of men is equal to the number of women. In other words half of the people in the theater are men and the other half or women. Therefore, the ratio of women to total people must be 1/2 = 0.50

Please help with this question thank you.

Answers

Answer:

x = 5

Step-by-step explanation:

You can rewrite the right side, then equate the arguments of the log function.

4·ln(x) = 2·ln(25)

4·ln(x) = 2·ln(5^2)

4·ln(x) = 4·ln(5) . . . . . . . use the rule ln(a^b) = b·ln(a)

x = 5 . . . . . . . . . . . . . . . .divide by 4 and take the antilog

Answer:

x = 5

Step-by-step explanation:

Just as a note, you can look at x = 25 and know that it is not the answer. If it was, then you would get

4ln(25) = 2 ln(25) which reduces down to 4 = 2 when you divide by ln(25) on both sides.

4 ln(x) = 2 ln(25) Represent 25 as ln(5)^2

4 ln(x) = 2 ln(5)^2 The power on the right can be brought down.

4 ln(x) = 2 * 2 * ln(5) Divide both sides by 4

4 ln(x)/4 = 4 ln(5)/4

ln(x) = ln(5) Take the antiln of both sides.

antiln(ln(x)) = antiln(5)

x = 5

ASAP!!! if my grade is a 91% and i get a 74% what will my grade be

Answers

Answer:

Step-by-step explanation:

you will have an 82.5
:)

you are saving $30 each month. you have a goal to accumulate $700 in savings. how long will it take you?

Answers

$700 ÷ $30 = approximately 23 months

It will take you 23 1/3 months or rounding 23 months the way you get the answer is you is you divide the goal over the amount of money each month 700/30.

Simply the expressions1. 4x + x + 3 + 8x

2. 9x - 5x + x - 3x

3. 5a - 4b + 2c - 3b - 6c + a