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3 years ago

Factor 16a+72 to identify the equivalent expressions. choose 2 answers a.4(4a+18) b.8(2a+9) c.2(8+36a) d.2(8a+72)

Mathematics

1 answer:

Dimas [21]3 years ago

6 0

Answer:

$\boxed{\sf b. \ 8(2a + 9)}$

Step-by-step explanation:

$\sf Factor \: the \: following: \\ \sf \implies 16a + 72 \\ \\ \sf Factor \: 8 \: out \: of \: 16a + 72: \\ \sf \implies 8 \times 2a + 8 \times 9 \\ \\ \sf \implies 8(2a + 9)$

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4 years ago

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3 years ago

The population of a town grows at a rate proportional to the population present at time t. The initial population of 500 increas

tiny-mole [99]

Answer:

The population in 20 years will be 781.

Step-by-step explanation:

The population of the town can be modeled by the following equation:

$P(t) = P(0)e^{rt}$

In which P(t) is the population after t years, P(0) is the initial population and r is the growth rate, as a decimal.

The initial population of 500 increases by 25% in 10 years.

This means that $P(0) = 500, P(10) = 1.25*P(0) = 625$

We use this to find r.

$P(t) = P(0)e^{rt}$

$625 = 500e^{10r}$

$e^{10r} = 1.25$

Applying ln to both sides

$\ln{e^{10r}} = \ln{1.25}$

$10r = \ln{1.25}$

$r = \frac{\ln{1.25}}{10}$

$r = 0.0223$

$P(t) = 500e^{0.0223t}$

What will be the population in 20 years

This is P(20)

$P(20) = 500e^{0.0223*20} = 781$

The population in 20 years will be 781.

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4 years ago

Anisa is cooling water in her fridge.The waters temperature starts at 85 degrees and she cools it 3.5 degrees every minute for 1

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The temperature starts at 85 degrees.
t = 85

After 1 minute, it loses 3.5 degrees.
t = 85 - 3.5

After 2 minutes, it loses another 3.5 degrees.
t = 85 - 3.5 * 2

After 3 minutes, it loses another 3.5 degrees.
t = 85 - 3.5 * 3

etc.

After 12 minutes, it loses another 3.5 times 12 degrees.
t = 85 - 3.5 * 12

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3 years ago