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puteri [66]
3 years ago
15

D is between C and E, CD = x 2 , CE = 32-2x, and DE = 12x. Find CD, DE, and CE.

Mathematics
1 answer:
Gemiola [76]3 years ago
3 0

Answer:

  • CD = 4
  • DE = 24
  • CE = 28

Step-by-step explanation:

The segment addition theorem tells you ...

  CD +DE = CE

  x^2 +12x = 32 -2x

Subtract the right side to put this in standard form.

  x^2 +14x -32 = 0

  (x +16)(x -2) = 0

  x = -16 or 2

In order for DE to have a positive length, we must have x > 0. So ...

  CD = x^2 = 2^2 = 4

  DE = 12x = 12(2) = 24

  CE = 32 -2x = 32 -2(2) = 28

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Type the correct answer in each box.
Mariulka [41]

Answer:

(x-5)^2+(y+4)^2=100

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The distance between the center and any point that lie on the circle is equal to the radius

we have the points

(5,-4) and (-3,2)    

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

substitute the values

r=\sqrt{(2+4)^{2}+(-3-5)^{2}}

r=\sqrt{(6)^{2}+(-8)^{2}}

r=\sqrt{100}\ units

r=10\ units

step 2

Find the equation of the circle

we know that

The equation of a circle in standard form is equal to

(x-h)^2+(y-k)^2=r^2

where

(h,k) is the center

r is the radius

we have

(h,k)=(5,-4)\\r=10\ units

substitute

(x-5)^2+(y+4)^2=10^2

(x-5)^2+(y+4)^2=100

6 0
3 years ago
Suppose that a box contains 45 light bulbs, of which 36 are good and the other 9 are defective. Consider randomly selecting thre
Andrew [12]

Answer:

Step-by-step explanation:

Given that a box contains 45 light bulbs, of which 36 are good and the other 9 are defective.

Probability for any one to be defective as of now is \frac{36}{45} =0.80

a) P(E) = 0.80

b) After I draw we have 35 good ones and 9 defective

P(F/E) =\frac{35}{44} \\=0.796

c) P(G/EF)

This is the probability for iii bulb to be good given I and II are goog.

Once I and ii are good we have 43 bulbs with 34 good ones

P(G/EF) =\frac{34}{43} \\=0.7907

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2 years ago
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Step-by-step explanation:

i) \overline{AB} = \sqrt{(x_A - x_B)^2 + (y_A - y_B)^2}

\:\:\:\:\:\:\:=\sqrt{(2)^2 + (12)^2} = 12.3

ii) m = \dfrac{y_A - y_B}{x_A - x_B} = \dfrac{-12}{2} = -6

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\:\:\:\:\:\:\:=(3,\:-2)

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3 years ago
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Answer:

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2 years ago
Find the equation of the line passing through the points (3,-2) and (4,6) in slope intercept form.​
noname [10]

Hey!

------------------------------------------------

They already give us the slope, so we can solve the y-intercept.

We can use (3, -2).

y = 8x + b

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-2 - 24 = 24 + b - 24

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------------------------------------------------

Hence, the answer is \Large\boxed{\mathsf{y~=~8x~+~-26}}

------------------------------------------------

Hope This Helped! Good Luck!

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3 years ago
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