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Rina8888 [55]
2 years ago
14

Find the factorization of each of the following number: A.18 B.24 C.38 D.81

Mathematics
1 answer:
const2013 [10]2 years ago
6 0

Answer:

A: (3^2)*2

B: (2^3)*3

C: 2*19

D: (3^2)*9

Step-by-step explanation:

We have:

A) 18= 3*3*2= (3^2)*2

B) 24=2*2*2*3=(2^3)*3

C) 38 = 2*19

D) 81 =3*3*9=(3^2)*9

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9. Water is added to two containers for 16 minutes. The equations below model the ounces of
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The two containers hold 328 ounces at the they hold same amount of water.

<u>Step-by-step explanation:</u>

The equations below model the ounces of  water, y, in each container after x minutes.

y = 16x + 104

y = -2x^{2} +40x+160

At the time after the start when the containers hold  the same amount of water, the two equations must be equal.

⇒ 16 x + 104 = -2x^{2}  + 40 x + 160

The first step is to divide everything by 2 to make it simplified.

⇒ 8 x + 52 = - x^2 +20 x + 80

Now put everything on the left .

x^2 + 8 x - 20 x + 52 - 80 = 0

Add the like terms together to further reduce the equation

x^2 - 12 x - 28 = 0

Factorizing the equation to find the roots of the equation.

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  • b is the sum of the roots ⇒ -14 + 2 = -12
  • c is the product of the roots ⇒ -14 × 2 = -28
  • Therefore, (x-14) (x+2) = 0
  • The solution is x = -2 or x = 14

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∴ The two containers hold 328 ounces at the they hold same amount of water.

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