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2 years ago

7. 3x + 4(x – 6) – 3(x – 7) (1 point) 4x – 45 4x – 3 10x – 3 10x + 45

Mathematics

1 answer:

charle [14.2K]2 years ago

3 0

Answer:

4x -3

Step-by-step explanation:

The distributive property applies.

3x +4(x -6) -3(x -7)

= 3x +4x +4(-6) -3x -3(-7) . . . . use the distributive property

= 3x +4x -24 -3x +21 . . . . . . . . simplify

= x(3 +4 -3) +(-24 +21) . . . . . . . group like terms, use the distributive property again

= 4x -3 . . . . simplify

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The natural growth of some magnitudes can be modeled by the equation:

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Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.

The actual population of deer in a forest is Po=800 individuals. It's been predicted the population will grow at a rate of 20% per year (r=0.2).

We have enough information to write the exponential model:

$P(t)=800(1+0.2)^t$

$P(t)=800(1.2)^t$

It's required to find the number of years required for the population of deers to double, that is, P = 2*Po = 1600. We need to solve for t:

$800(1.2)^t=1600$

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$(1.2)^t=1600/800=2$

Taking logarithms:

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Dividing by log 1.2:

$t=\frac{\log 2}{ \log 1.2}$

Calculating:

t = 3.8 years

Answer: C. 3.8 years

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