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nata0808 [166]
2 years ago
10

How many solutions does 9(z+8)=-9z-72 have

Mathematics
1 answer:
zloy xaker [14]2 years ago
4 0

Answer:

1 solution.

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Equality Properties

Step-by-step explanation:

<u>Step 1: Define equation</u>

9(z + 8) = -9z - 72

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Distribute 9:                              9x + 72 = -9z - 72
  2. Add 9z to both sides:               18z + 72 = -72
  3. Subtract 72 on both sides:       18z = -144
  4. Divide 18 on both sides:           z = -8

Here we see that we will get only 1 solution for <em>z</em>.

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A species of beetles grows 32% every year. Suppose 100 beetles are released into a field. How many beetles will there be in 10 y
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Given that a species of beetles grows 32% every year.

So growth rate is given by

r=32%= 0.32


Given that 100 beetles are released into a field.

So that means initial number of beetles P=100


Now we have to find about how many beetles will there be in 10 years.

To find that we need to setup growth formula which is given by

A=P(1+r)^n where A is number of beetles at any year n.

Plug the given values into above formula we get:

A=100(1+0.32)^n

A=100(1.32)^n


now plug n=10 years

A=100(1.32)^{10}=100(16.0597696605)=1605.97696605

Hence answer is approx 1606 beetles will be there after 20 years.


Now we have to find about how many beetles will there be in 20 years.

To find that we plug n=20 years

A=100(1.32)^{20}=100(257.916201549)=25791.6201549

Hence answer is approx 25791 beetles will be there after 20 years.



Now we have to find time for 100000 beetles so plug A=100000

A=100(1.32)^n

100000=100(1.32)^n

1000=(1.32)^n

log(1000)=n*log(1.32)

\frac{\log\left(10000\right)}{\log\left(1.32\right)}=n

33.174666862=n

Hence answer is approx 33 years.

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