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]
2 years ago
6

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

Mathematics
1 answer:
katovenus [111]2 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
Garrett buys tickets to a concert. He pays $24.50 for each ticket plus a
Kay [80]

24.50 x 8.50 = 33.0

131 ÷ 33 = 3.9696969697

8 0
2 years ago
Find a. Round your answer to the nearest hundredth
il63 [147K]
Angle C is 40degree
Then Angle B is supposed to be 180-90-40 which will be 50 degree
3 0
2 years ago
Read 2 more answers
The product of a number X and six is for more than the product of the number and 3/8. Which answer represents this situation?
stiks02 [169]

Answer:3/8y+(6x+4)

Step-by-step explanation:

I’m 99% sure to is is right

6 0
3 years ago
Suppose that y = k * (x - 1/3) ^ 2 is a parabola in the xy -plane that passes through the point (2/3, 1) :Find k and the length
Dennis_Churaev [7]

Answer:

k = 9

length of chord = 2/3

Step-by-step explanation:

Equation of parabola:   y=k (x-\frac13)^2

<u />

<u>Part 1</u>

If the curve passes through point (\frac23 ,1), this means that when x=\dfrac23, y = 1

Substitute these values into the equation and solve for k:

\implies 1=k \left(\dfrac23-\dfrac13\right)^2

\implies 1=k \left(\dfrac13 \right)^2

Apply the exponent rule \left(\dfrac{a}{b} \right)^c=\dfrac{a^c}{b^c} :

\implies 1=k \left(\dfrac{1^2}{3^2} \right)

\implies 1=\dfrac{1}{9}k

\implies k=9

<u>Part 2</u>

  • The chord of a parabola is a line segment whose endpoints are points on the parabola.  

We are told that one end of the chord is at (\frac23 ,1) and that the chord is horizontal.  Therefore, the y-coordinate of the other end of the chord will also be 1.  Substitute y = 1  into the equation for the parabola and solve for x:

\implies 1=9 \left(x-\dfrac13 \right)^2

\implies \dfrac19 = \left(x-\dfrac13 \right)^2

\implies \sqrt{\dfrac19}  = x-\dfrac13

\implies \pm \dfrac13  = x-\dfrac13

\implies x=\dfrac23, x=0

Therefore, the endpoints of the horizontal chord are: (0, 1) and (2/3, 1)

To calculate the length of the chord, find the difference between the x-coordinates:  

\implies \dfrac23-0=\dfrac23

**Please see attached diagram for drawn graph. Chord is in red**

6 0
2 years ago
6,000 multiplied by power of 10
larisa86 [58]
An easy way of finding the answer to your question is by using a scientific calculator. When I plugged in 6,000^10 it gave me 6.0466176x10^37. Yes the answer is in scientific notation, but if you want the answer shortened out to the nearest hundredth place the answer is 6.05.
7 0
3 years ago
Other questions:
  • 32.determine the rate of change of the graph
    8·2 answers
  • Can one angle of a parallelogram be equal to 40° and another one 50°?
    7·1 answer
  • What is the probability of rolling an even prime number with one toss of a die?<br><br> Thanks!!!
    7·1 answer
  • What is the factorization of the trinomial below? 2x^2 +11x+15
    7·1 answer
  • I need to know how to work this out: 24 red marbles is 40% of ______ marbles.
    8·1 answer
  • Which property was used to simplify the expression? <br> 3c+9+4c=3c+4c+9
    12·1 answer
  • Fill in the missing numbers to complete the pattern: ___, 7.0 ,7.2 ,___ , 7.6, 7.8 what are the missing numbers
    5·2 answers
  • Select the correct answer.
    14·1 answer
  • Help this is geometry! Help me please!
    15·1 answer
  • N(p)=4 means that there a four elements in a set P. Given:
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!