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3 years ago

Rewrite the expression in factored form: x^2+12x+27

Mathematics

1 answer:

max2010maxim [7]3 years ago

4 0

Answer:

c. (x+3)(x+9)

Step-by-step explanation:

x^2+12x+27

The middle number is 12 and the last number is 27.

We need two numbers that...

Add together to get 12

Multiply together to get 27

Try 3 and 9:

3+9 = 12

3*9 = 27

Fill in the blanks in

(x+_)(x+_)

with 3 and 9 to get...

(x+3)(x+9)

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3 years ago

A scientist begins with 250 grams of a radioactive substance. After 250 minutes, the sample has decayed to 32 grams. Rounding to

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Answer:

Part 1 : $A=250 e^{-0.008223t}$

Part 2 : Half life is 84 minutes ( approx )

Step-by-step explanation:

Part 1 : Suppose the function that shows the amount( in grams ) of the substance after t minutes,

$A=A_0 e^{kt}$

If t = 0 min, A = 250 grams,

$250=A_0 e^{0}$

$\implies A_0 = 250$

If t = 250, A = 32 grams,

$32 = A_0 e^{250k}$

$32 = 250 e^{250k}$

$0.128 = e^{250k}$

Taking ln both sides,

$\ln(0.128) = 250k$

$\implies k =\frac{\ln(0.128)}{250}=-0.008223$

Hence, the equation that shows this situation,

$A=250 e^{-0.008223t}$

Part 2 : If A = 250/2 = 125,

$125 = 250 e^{-0.008223t}$

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Taking ln both sides,

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Step-by-step explanation:

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