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ikadub [295]
3 years ago
13

Create a list of steps, in order, that will solve the following equation 1/4(x+5)^2-1=3

Mathematics
1 answer:
Paul [167]3 years ago
7 0

Answer:

Add 1 to each side

Multiply each side by 4

Take the square root of each side

Subtract 5 from each side

Combine terms

Step-by-step explanation:

1/4(x+5)^2-1=3

Add 1 to each side

1/4(x+5)^2-1+1=3+1

1/4(x+5)^2=4

Multiply each side by 4

4*1/4(x+5)^2=4*4

(x+5)^2=16

Take the square root of each side

sqrt((x+5)^2)=±sqrt(16)

x+5 = ±4

Subtract 5 from each side

x+5-5 = -5  ±4

x = -5  ±4

Combine terms

x = -5+4       x = -5-4

x = -1            x = -9

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Katyanochek1 [597]
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A 41 gram sample of a substance that's used to detect explosives has a k-value of 0.1392. Find the substance's half life, in day
-BARSIC- [3]

Answer:

The substance half-life is of 4.98 days.

Step-by-step explanation:

Equation for an amount of a decaying substance:

The equation for the amount of a substance that decay exponentially has the following format:

A(t) = A(0)e^{-kt}

In which k is the decay rate, as a decimal.

k-value of 0.1392.

This means that:

A(t) = A(0)e^{-0.1392t}

Find the substance's half life, in days.

This is t for which A(t) = 0.5A(0). So

A(t) = A(0)e^{-0.1392t}

0.5A(0) = A(0)e^{-0.1392t}

e^{-0.1392t} = 0.5

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-0.1392t = \ln{0.5}

t = -\frac{\ln{0.5}}{0.1392}

t = 4.98

The substance half-life is of 4.98 days.

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2 years ago
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