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3 years ago

Find the slope of the line. Write in simplest form Show your work

Mathematics

1 answer:

Marina86 [1]3 years ago

6 0

Answer:

The slope is -2.

Step-by-step explanation:

Following the line starting at the x intercept, move down 2 over right 1.

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Use the exponential decay model, Upper A equals Upper A 0 e Superscript kt, to solve the following. The half-life of a certai

Akimi4 [234]

Answer:

It will take 7 years ( approx )

Step-by-step explanation:

Given equation that shows the amount of the substance after t years,

$A=A_0 e^{kt}$

Where,

$A_0$ = Initial amount of the substance,

If the half life of the substance is 19 years,

Then if t = 19, amount of the substance = $\frac{A_0}{2}$ ,

i.e.

$\frac{A_0}{2}=A_0 e^{19k}$

$\frac{1}{2} = e^{19k}$

$0.5 = e^{19k}$

Taking ln both sides,

$\ln(0.5) = \ln(e^{19k})$

$\ln(0.5) = 19k$

$\implies k = \frac{\ln(0.5)}{19}\approx -0.03648$

Now, if the substance to decay to 78% of its original amount,

Then $A=78\% \text{ of }A_0 =\frac{78A_0}{100}=0.78 A_0$

$0.78 A_0=A_0 e^{-0.03648t}$

$0.78 = e^{-0.03648t}$

Again taking ln both sides,

$\ln(0.78) = -0.03648t$

$-0.24846=-0.03648t$

$\implies t = \frac{0.24846}{0.03648}=6.81085\approx 7$

Hence, approximately the substance would be 78% of its initial value after 7 years.

5 0

3 years ago

Mary bought a pair of jeans on sale for 25% off. The original price for jeans was $79. What was the sale price before tax? Expla

TEA [102]

<h3>Answer: $59.25</h3>

========================================================

Explanation:

There are two approaches

Method 1

25% of 79 = 0.25*79 = 19.75

Mary saves $19.75 and the price before tax is 79 - 19.75 = 59.25

-----------------------------

Method 2

She saves 25% so she must pay the remaining 75%

75% of 79 = 0.75*79 = 59.25

This is a slight shortcut, and it's very useful when it comes to chaining multiple discounts together.

5 0

2 years ago

Kevin wants to change the engine in her car. The current engine is 250 cubic centimeters and has a 14 inch fan belt. The new eng

Simora [160]

Option A) 14/250 = N/350 is correct.

Kevin wants to change the engine in her car. The current engine is 250 cubic centimeters and has a 14 inch fan belt. The new engine is 350 cubic centimeters and has proportionally larger fan belt.

<h3>What is proportionality?</h3>

proportionality can be defined as, how much the number is relatable to other number i.e. x =2y x is two times proportion to y.

Hence, in the question
for 250 cc engine it has 14 inch belt
for 350 cc engine it has N inch belt(let)
proportionality can be given as
14 ∝ 250
N ∝ 350
dividing both equation
N/14=350/250
or 14/250=N/350

Thus, the required proportion is given as 14/250=N/350.

Learn more about proportionality here:
brainly.com/question/8598338

#SPJ2

5 0

2 years ago

Read 2 more answers

In order to qualify for a bowling tournament, bowlers bowl 20 games. The results are normal. The average score was 167 with a st

Ksenya-84 [330]

Answer:

189

Step-by-step explanation:

bc that's just what I think