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3 years ago

Find the equation of the line containing (3,-2) and (5,5).

Mathematics

2 answers:

Mars2501 [29]3 years ago

7 0

Answer:

y = 3.5x - 12.5

Step-by-step explanation:

First, find the slope using rise over run (y2 - y1 / x2 - x1) with the 2 points:

(-2 - 5) / (3 - 5)

-7/-2

= 3.5

Then, plug the slope and a point into y = mx + b to solve for b:

y = mx + b

5 = 3.5(5) + b

5 = 17.5 + b

-12.5 = b

Plug the slope and the y intercept into the equation y = mx + b

y = 3.5x - 12.5 will be the equation

yanalaym [24]3 years ago

5 0

Answer:

y=7/2x-12.5

Step-by-step explanation:

use the y=mx+b and the $\frac{y2-y1}{x2-x1}$ method

$\frac{5-(-2)}{5-3}$

7/2= thats ur slope

now plug in the slope and one of the point into the y=mx+b method

-2=7/2(3)+b

-2=21/2+b

subtract 21/2 both sides

-25/2 or -12.5

ik this doesnt make sense but hope this helps

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The population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year. A) Estimate how lo

VLD [36.1K]

Answer:

A) 63.36 years.

B) 100.42 years.

Step-by-step explanation:

We have been given that the population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year.

A) Since we know that population increases exponentially, therefore we will use our given information to form an exponential model for population increase and then we will solve for the time by which our population will be double.

$P(t)=7.1(1.011)^{t}$

$7.1 \times 2=7.1(1.011)^{t}$

$\frac{7.1 \times 2}{7.1} =(1.011)^{t}$

$2 =(1.011)^{t}$

Now let us solve for t using logarithm.

$ln(2) =ln (1.011)^{t}$

$ln(2) =t \cdot ln(1.011)$

$0.6931471805599453 =t \cdot 0.0109399400383344$

$t=\frac{0.6931471805599453}{0.0109399400383344}$

$t=63.3593217267282743049\approx 63.36$

Therefore, it will take 63.36 years the population to be double.

B) Now we will find the number of years it will take the population to be triple of its size.

$7.1 \times 3=7.1(1.011)^{t}$

$\frac{7.1 \times 3}{7.1} =(1.011)^{t}$

$3 =(1.011)^{t}$

Now let us solve for t using logarithm.

$ln(3) =ln (1.011)^{t}$

$ln(3) =t \cdot ln(1.011)$

$1.0986122886681097 =t \cdot 0.0109399400383344$

$t=\frac{1.0986122886681097}{0.0109399400383344}$

$t=100.4221490079915311298\approx 100.42$

Therefore, it will take 100.42 years the population to triple of its size.

6 0

3 years ago

4. Divide, using synthetic division: 16x^3 +80x^2+x+5/x+5

fgiga [73]

Answer:

Step-by-step explanation:

x+5=0

x=-5

-5) 16 80 1 5

| -80 0 -5

____________

| 16 0 1 | 0

quotient=16x²+1

Remainder=0

8 0

3 years ago

Imani spent half of her weekly allowance playing mini-golf. To earn more money, her parents let her wash the car for $4. What is

joja [24]

Answer:

$16

Step-by-step explanation:

This method is probbaly working backwards. I'm not sure.

12 - 4 = 8 (How much she was left with if she didn't wash the car for 4 dollars)

8 x 2 = 16 (They mentioned she spent half of her weekly allowance)

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3 years ago

On the first day of June, there were about 17.71 h of daylight in a city. Five months later, there were about 5.30 h of daylig

Andru [333]

Answer:

Percentage increases and decreases, are found by setting the problem up proportionally.

You are trying to find what percentage of 17.37 is 8.30 first.

so What %/100 = 8.30/17.37

Now define a variable:

Let x = What%

x/100 = 8.30/17.37

17.37x = 830

x = 830/17.37

x ≈ 47.78

8.30 is approximately 47.78% of 17.37, so the percentage decrease is 100% - 47.78% = 52.22%

The percentage decrease is approximately 52.22%

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