Cylinder a has a radius of 12 inches and a height of 6 inches. Cylinder b has a volume of 648

Length of the median CP

ehidna [41]

Given:

ΔABC $\sim$ ΔDEF

To find:

The length of median CP

Solution:

In ΔABC,

AP = 12, BP = 12 and PC = 3x - 12

In ΔDEF,

DQ = 16, QE = 16 and FQ = 2x + 8

If two triangles are similar, then their median is proportional to the corresponding sides.

$$\Rightarrow \frac{AP}{DQ} =\frac{PC}{FQ}$

$$\Rightarrow \frac{12}{16} =\frac{3x-12}{2x+8}$

Do cross multiplication.

$$\Rightarrow 12(2x+8)=16(3x-12)$

$$\Rightarrow 24x+96=48x-192$

Add 192 on both sides.

$$\Rightarrow 24x+96+192=48x-192+192$

$$\Rightarrow 24x+288=48x$

Subtract 24x from both sides.

$$\Rightarrow 24x+288- 24x=48x- 24x$

$$\Rightarrow 288=24x$

Divide by 24 on both sides.

⇒ 12 = x

Substitute x = 12 in CP.

CP = 3(12) - 12

= 36 - 12

= 24

The length of median CP is 24.

7 0

3 years ago

Solve the expression (7th grade math): -0.8m+3-12.5m+95.36m

Lana71 [14]

Step-by-step explanation:

Combine Like-Terms:

-0.8m + 3 - 12.5m + 95.36m

-13.3m + 3 + 95.36m

82.06m + 3

82.06m + 3 is your simplified expression.

7 0

2 years ago

Many poker games start with each player being dealt five cards, called the player's "hand". Remember, there are 52 cards in a st

jek_recluse [69]

Answer:

The number of different possible poker hands is found by counting the number of ways that 5 cards can be selected from 52 cards, where the order is not important. It is a combination, so we use c n r

Step-by-step explanation:

The possible number of the poker hands is probably . C 52 5= 52!/5!x47!= 2598960

5 0

3 years ago

This is an off topic question but i feel the need to let other peoples brains keep running so these are the questions i will giv

serg [7]

−4.6−(0.4+7.2)
−20+(−40)+(−60)

4 and 5 is properties of addition

-80 is your answer

hope this helps

6 0

3 years ago

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A segment in the complex plane has a midpoint at –1 + i. If the segment has an endpoint at –5 – 7i, what is the other endpoint?

morpeh [17]

Answer:

The other end point is: s+ti = 3+9i

Step-by-step explanation:

Mid-Point(M) in the complex plane states that the midpoint of the line segment joining two complex numbers a+bi and s+ti is the average of the numbers at the endpoints.

It is given by: $M = \frac{a+s}{2} +(\frac{b+t}{2})i$

Given: The midpoint = -1 + i and the segment has an endpoint at -5 - 7i

Find the other endpoints.

Let a + bi = -5 -7i and let other endpoint s + ti (i represents imaginary )

Here, a = -5 and b = -7 to find s and t.

then;

$-1+i = \frac{-5+s}{2} + ( \frac{-7+t}{2})i$ [Apply Mid-point formula]

On comparing both sides

we get;

$-1 = \frac{-5+s}{2}$ and $1 = \frac{-7+t}{2}$

To solve for s:

$-1 = \frac{-5+s}{2}$

or

-2 = -5+s

Add 5 to both side we have;

-2+5 = -5+s+5

Simplify:

3 = s or

s =3

Now, to solve for t;

$1 = \frac{-7+t}{2}$

2 =-7+t

Add 7 to both sides we get;

2+7 = -7+t+7

Simplify:

9 = t

or

t =9

Therefore, the other end point (s+ti) is, 3+9i

4 0

3 years ago

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