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3 years ago

* If 120% of a is equal to 80% of b, and a=12, then what is the value of a+b?

Mathematics

1 answer:

makkiz [27]3 years ago

5 0

120% of a=80% of b
1.2(12)=0.8b
14.4=0.8b
b=18
a+b=?
12+18=30
30 is your final answer

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An old bone contains 80% of its original carbon-14. Use the half-life model to find the age of the bone. Find an equation equiva

Ira Lisetskai [31]

Answer:

An old bone contains 80% of its original carbon-14 in 1844.6479 years

Step-by-step explanation:

We know that

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so, h=5730

now, we can use formula

$P(t)=P_0(\frac{1}{2})^{\frac{t}{h} }$

we can plug back h

and we get

$P(t)=P_0(\frac{1}{2})^{\frac{t}{5730} }$

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so,

P(t)=0.80Po

we can plug it and then we solve for t

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$0.80=(\frac{1}{2})^{\frac{t}{5730} }$

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$t=-\frac{5730\ln \left(0.8\right)}{\ln \left(2\right)}$

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So,

An old bone contains 80% of its original carbon-14 in 1844.6479 years

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ANSWER

The restrictions are

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The function is defined for all values of a, except

$5a^2+16a+3=0$

This has become a quadratic trinomial, so we need to split the middle term.

We do that by multiplying the coefficient of $x^2$ which is 5 by the constant term which is 3. This gives us 15.

The factors of 15 that adds up to 16 are 1 and 15.

We use these factors to split the middle term.

$5a^2+15a+a+3=0$

We now factor to get,

$5a(a+3)+1(a+3)=0$

We factor further to get,

$(a+3)(5a+1)=0$

This implies that,

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