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2 years ago

What are the zeros of the quadratic function f(x) = 6x^2 + 12x - 7?

Mathematics

1 answer:

Sergeeva-Olga [200]2 years ago

4 0

Answer:

-12 + √(144- 4(-42)/12

-12 + √312/12

-12 + 17.6 / 12

= +.47 and -.47

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A fossil was analyzed and determined to have a carbon-14 level that is 80 % that of living organisms. the half-life of c-14 is 5

liq [111]

Answer:

The fossil is 1860 years old.

Step-by-step explanation:

The equation for the amount of fossil has the following format:

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

In which Q(t) is the amount after t years, Q(0) is the initial amount and r is the rate of change.

Half-life of c-14 is 5730 years.

This means that $Q(5730) = 0.5Q(0)$

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

$0.5Q(0) = Q(0)e^{5730r}$

$e^{5730r} = 0.5$

$\ln{e^{5730r}} = \ln{0.5}$

$5730r = \ln{0.5}$

$r = \frac{\ln{0.5}}{5730}$

$r = -0.00012$

$Q(t) = Q(0)e^{-0.00012t}$

How old is the fossil?

This is t for which

$Q(t) = 0.8Q(0)$

$Q(t) = Q(0)e^{-0.00012t}$

$0.8Q(0) = Q(0)e^{-0.00012t}$

$e^{-0.00012t} = 0.8$

$\ln{e^{-0.00012t}} = \ln{0.8}$

$-0.00012t = \ln{0.8}$

$t = -\frac{\ln{0.8}}{-0.00012}$

$t = 1860$

The fossil is 1860 years old.

4 0

2 years ago

Use substitution to solve each system of equations <br> X=y-2<br> 4x+y=2

Mariulka [41]

Answer:

Step-by-step explanation:

x = y - 2.........(1)

4x + y = 2......(2)

Substituting x in (1) in (2)

4(y - 2) + y = 2

4y - 8 + y = 2

5y = 2 + 8

5y = 10

y = 10/5

y = 2

Putting x in (1)

x = y - 2

x = 2 - 2

x = 0

6 0

3 years ago

Brian deposits $7000 into an account that pays simple interest at an annual rate of 3%. He does not make any more deposits. He m

Andre45 [30]

Answer:

A)1050

B)8050

Step-by-step explanation:

to find interest we use the formula A= P(1+rt) where P is the initial investment, r is the rate percent, and t is the time interval

for this question we have A=7000(1+3(5)) which gives 8,050 dollars which is the answer to part B

for part A we simply subtract the answer from B from the initial investment so 8050 - 7000 = 1050 made from interest

4 0

2 years ago

Jenny had $175,but she is spending $28 per month the algebraic expression that models the situation is

ExtremeBDS [4]

Considering there is not much information my best guess would be 175-28x

7 0

2 years ago

A college-entrance exam is designed so that scores are normally distributed with a mean of 500 and a standard deviation of 100.

Crank

Answer: 1.25

Step-by-step explanation:

Given: A college-entrance exam is designed so that scores are normally distributed with a mean $(\mu)$ = 500 and a standard deviation $(\sigma)$ = 100.

A z-score measures how many standard deviations a given measurement deviates from the mean.

Let Y be a random variable that denotes the scores in the exam.

Formula for z-score = $\dfrac{Y-\mu}{\sigma}$

Z-score = $\dfrac{625-500}{100}$

⇒ Z-score = $\dfrac{125}{100}$

⇒Z-score =1.25

Therefore , the required z-score = 1.25

6 0

3 years ago