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2 years ago

Given the following points, write the equation of the line that goes through them. ( -12,56), (0,8), and (8,-24).

Mathematics

1 answer:

BaLLatris [955]2 years ago

8 0

Answer:

$y=-4x+8$

Step-by-step explanation:

step 1

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

take two points from the data

(0,8), and (8,-24).

substitute

$m=\frac{-24-8}{8-0}$

$m=\frac{-32}{8}$

$m=-4$

step 2

Find the equation of he line in slope intercept form

$y=mx+b$

we have

$m=-4$

$b=8$ ----> the y-intercept is given

substitute

$y=-4x+8$

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Answer:

c) H0 : p = 5.8%

H1 : p > 5.8%

Step-by-step explanation:

At the null hypothesis, we test that the percentage is equal to a certain value. At the alternate hypothesis, we have a test about this percentage, if it is more, less, or different from the tested value.

A psychologist claims that more than 5.8 percent of the population suffers from professional problems due to extreme shyness

At the null hypothesis, we test if the percentage is 5.8%

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2 years ago

Solve the following system of equations using a method of your choice.

dusya [7]

Answer:

Step-by-step explanation:

cant remember what this method is called but

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x + y = 10

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Find an equation of a line that is tangent to the graph of f and parallel to the given line. Please see picture

ivanzaharov [21]

Answer:

y = 3x - 2 (smaller y-intercept)

y = 3x + 2 (larger y-intercept)

Step-by-step explanation:

First let's write the generic equation of a line:

y = ax + b

This line needs to be parallel to the line 3x - y + 5 = 0, so it needs to have the same slope of this line.

The line 3x - y + 5 = 0 has a slope of 3, so our line has a = 3:

y = 3x + b

Now we need to find the values of b that make this line tangent to the function f(x) = x^3

Let's first find the derivative of f(x) in relation to x:

df(x)/dx = 3x^2

This derivative is the slope of the tangent line to the function for any value of x. We need a slope of 3, so:

3x^2 = 3

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x = ±1

Now, to find the y-values, we have:

f(1) = 1^3 = 1

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2 years ago