Find the slope of the line that passes through the points (–1, 6) and (2, 15)

Mathematics

1 answer:

11111nata11111 [884]3 years ago

7 0

Answer:

m=3

Step-by-step explanation:

$\frac{15-6}{2-(-1)} =\frac{9}{3} =3$

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3 equivalent ratios for : 4/3, 12/14, and 6/9

Mariana [72]

<span>So the question is what are three equivalent ratios for 4/3, 12/14 and 6/9. The simplest way to get the equivalent ratio of some other ratio is to either multiply the nominator and the denominator by the same number or to divide the nominator and the denominator with the same number. I need to point out that it's not always possible to divide them and get a whole number. First: (4/3)*(2/2)=8/6, (4/3)*(3/3)=12/9 and (4/3)*(4/4)=16/12. Second: (12/14)/(2/2)=6/7, (12/14)*(2/2)=24/28 and (12/14)*(3/3)=36/42. Third: (6/9)/(3/3)=2/3, (6/9)*(2/2)=12/18 and finally (6/9)*(3/3)=18/27.</span>

5 0

3 years ago

The city of Anvil is currently home to 21000 people, and the population has been growing at a continuous rate of 4% per year. Th

Yanka [14]

Answer:

They'll reach the same population in approximately 113.24 years.

Step-by-step explanation:

Since both population grows at an exponential rate, then their population over the years can be found as:

$\text{population}(t) = \text{population}(0)*(1 + \frac{r}{100})^t$

For the city of Anvil:

$\text{population anvil}(t) = 21000*(1.04)^t$

For the city of Brinker:

$\text{population brinker}(t) = 7000*(1.05)^t$

We need to find the value of "t" that satisfies:

$\text{population brinker}(t) = \text{population anvil}(t)\\21000*(1.04)^t = 7000*(1.05)^t\\ln[21000*(1.04)^t] = ln[7000*(1.05)^t]\\ln(21000) + t*ln(1.04) = ln(7000) + t*ln(1.05)\\9.952 + t*0.039 = 8.8536 + t*0.0487\\t*0.0487 - t*0.039 = 9.952 - 8.8536\\t*0.0097 = 1.0984\\t = \frac{1.0984}{0.0097}\\t = 113.24$