Solve the system of linear equations using substitution.

Plz help due tonight

Assoli18 [71]

It is 1. 2 and 3 are base angles.

4 0

3 years ago

Please help me with this

Eduardwww [97]

Answer:

$r^{6}$

Step-by-step explanation:

Using the rule of exponents

$\frac{a^{m} }{a^{n} }$ = $a^{(m-n)}$ , then

$\frac{r^{9} }{r^{3} }$ = $r^{(9-3)}$ = $r^{6}$

5 0

3 years ago

Carbon-14 is a radioactive isotope that has a half-life of 5,730 years. Approximately how many years will it take for carbon-14

PilotLPTM [1.2K]

Answer:

<em>Carbon-14 will take 19,035 years to decay to 10 percent.</em>

Step-by-step explanation:

<u>Exponential Decay Function</u>

A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay.

An exponential decay can be described by the following formula:

$N(t)=N_{0}e^{-\lambda t}$

Where:

No = The quantity of the substance that will decay.

N(t) = The quantity that still remains and has not yet decayed after a time t

$\lambda$ = The decay constant.

One important parameter related to radioactive decay is the half-life:

$\displaystyle t_{1/2}=\frac {\ln(2)}{\lambda }$

If we know the value of the half-life, we can calculate the decay constant:

$\displaystyle \lambda=\frac {\ln(2)}{ t_{1/2}}$

Carbon-14 has a half-life of 5,730 years, thus:

$\displaystyle \lambda=\frac {\ln(2)}{ 5,730}$

$\lambda=0.00012097$

The equation of the remaining quantity of Carbon-14 is:

$N(t)=N_{0}e^{-0.00012097\cdot t}$

We need to calculate the time required for the original amout to reach 10%, thus N(t)=0.10No

$0.10N_o=N_{0}e^{-0.00012097\cdot t}$

Simplifying:

$0.10=e^{-0.00012097\cdot t}$

Taking logarithms:

$ln 0.10=-0.00012097\cdot t$

Solving for t:

$\displaystyle t=\frac{log 0.10}{-0.00012097}$

$t\approx 19,035\ years$

Carbon-14 will take 19,035 years to decay to 10 percent.

6 0

3 years ago

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PLS help will gift 20 extra point for the first to answer it

Sonja [21]

Answer:

No, his inference is not valid

Step-by-step explanation:

the data shown represents the statistic of 100 people's preferred ways to view movies in total

out of that 30/100 people prefer to watch in theatre.

trent inferences that out of 400 people 300 would prefer to watch in theatre another way to write this is 300/400

if we multiply the data we're given so that the denominators match Trent's inference. The data tells us that 120/400 would prefer to watch in theatre, so his inference is not valid.

4 0

3 years ago

What equation is equivalent to 2^4x= 8^x-3?

Elenna [48]

The answer to this problem is D. 2^4x=2^3x-9

7 0

3 years ago

Read 2 more answers