1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
riadik2000 [5.3K]
3 years ago
6

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

Mathematics
1 answer:
katovenus [111]3 years ago
5 0
<h3>Explanation:</h3>

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.

_____

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

_____

The altitude CP is called the "geometric mean" of AP and MP. It is the square root of their product. This is true for <em>any</em> 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.

You might be interested in
For a circle with a radius of 6 feet, what is the measurement of the central angle (in degrees) that intercepts an arc with a le
sp2606 [1]
<h3>The measurement of the central angle is 135 degrees</h3>

<em><u>Solution:</u></em>

<em><u>The length of arc when angle given in degrees is given as:</u></em>

Arc\ length = \frac{ \theta }{360} \times 2 \pi r

Where,

r is the radius

\theta is the central angle in degrees

From given,

r = 6\ feet\\\\Arc\ length = \frac{ 9 \pi }{2}\ feet

Substituting the values we get,

\frac{9 \pi }{2} = \frac{ \theta }{ 360} \times 2 \times \pi \times 6\\\\9 \times 360= \theta \times 24\\\\\theta = 135

Thus the measurement of the central angle is 135 degrees

4 0
3 years ago
A heart beat takes 0.8 second ,how many seconds is this writtin as a fraction
NeX [460]
The answer to your Question is 8/10 but if you simplify it the answer is 4/5.

5 0
3 years ago
Read 2 more answers
Enter an equation for the function that includes the points.Give your answer in a(b)x. In the event that a=1 , give your answer
Andrews [41]

Answer:

f(x) = \frac{24}{25} * \frac{5}{6}^x

Step-by-step explanation:

Given

(x_1,y_1) = (2,\frac{2}{3})

(x_2,y_2) = (3,\frac{5}{9})

Required

Write the equation of the function f(x) = ab^x

Express the function as:

y = ab^x

In: (x_1,y_1) = (2,\frac{2}{3})

y = ab^x

\frac{2}{3} = a * b^2 --- (1)

In (x_2,y_2) = (3,\frac{5}{9})

y = ab^x

\frac{5}{9} = a * b^3 --- (2)

Divide (2) by (1)

\frac{5}{9}/\frac{2}{3} = \frac{a*b^3}{a*b^2}

\frac{5}{9}/\frac{2}{3} = b

\frac{5}{9}*\frac{3}{2} = b

\frac{5}{3}*\frac{1}{2} = b

\frac{5}{6} = b

b = \frac{5}{6}

Substitute 5/6 for b in (1)

\frac{2}{3} = a * b^2

\frac{2}{3} = a * \frac{5}{6}^2

\frac{2}{3} = a * \frac{25}{36}

a = \frac{2}{3} * \frac{36}{25}

a = \frac{2}{1} * \frac{12}{25}

a = \frac{24}{25}

The function: f(x) = ab^x

f(x) = \frac{24}{25} * \frac{5}{6}^x

7 0
3 years ago
Create an expression, to equal 13, using any grouping of addition, subtraction, multiplication, and division. You must use all t
aleksandrvk [35]
(29 - 2 + (6 * 2)) / 3 = 13
4 0
3 years ago
Read 2 more answers
Every 3 weeks 8 students will lose their metro cards... How many will lose it in 9 weeks
Marina86 [1]
First we must divide 9 by 3.

9/3 = 3

Then multiply it by 8

3*8 = 24. Hope this helps!

7 0
3 years ago
Read 2 more answers
Other questions:
  • Have a wonderful day lvu&lt;3 free points <br> 1357+46689=?
    7·2 answers
  • Tom has been given 35 chores to complete today this morning he finished seven of them how many chores does he have left to do
    5·1 answer
  • The vertices of ΔDEF have coordinates D(–1, 2), E(3, 3), and F (2, –4).What are the coordinates of the vertices of r(90°, O)(ΔDE
    11·1 answer
  • What is 534.076 rounded to the nearest hundredth? A. 534.07 B. 534 C. 500 D. 534.08
    13·2 answers
  • Which statement shows two polynomials 4x+6 and 2x^2-8x demonstrating the closure property when multiplied?
    7·1 answer
  • Describe two different ways to solve: -10=1/4(8y-12)
    8·1 answer
  • Yo can someone help me out
    12·2 answers
  • I NEED HELP ASAP PLS
    12·2 answers
  • Represent 56÷ 8 = 7 using subtraction. Explain your reasoning.
    7·1 answer
  • 1. A small garden has a perimeter of 24 1/4 ft. If the lengths is 8 ft, what is the area of the garden.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!