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2 years ago

These two lines are parallel. Write an equation for each. Either upload a picture or type in the answer box.

Mathematics

2 answers:

yaroslaw [1]2 years ago

7 0

Answer:

(top line) y=4/5x + 0, (bottom line) y=4/5-0.32

Step-by-step explanation:

so take the equation y=mx+b

b is the y intercept, which is where the line crosses (0,b)

the m is the slope, which is rise/run.

If the lines are parallel, the slopes are the same, just different y intercept

scoray [572]2 years ago

7 0

Step-by-step explanation:

the usual equation for a line is

y = ax + b

a is the slope. it is always the factor of x and is expressed as ratio y/x. this indicates how many units y changes, when x changes a certain amount of units when moving from one point to another.

(0, -3.2) is one point. and (4, 0) is another.

x changes by +4 (from 0 to 4).

y changes by +3.2 (from -3.2 to 0)

the slope is therefore

3.2/4 = 32/10 / 4 = 32/40 = 4/5

b is the y-intercept. that is the point, where the line crosses the y-axis (the y value when x = 0).

the given point specifies this already.

so, the line equation of the lower line is

y = (4/5)x - 3.2 or (4/5)x - 32/10 or (4/5)x - 16/5

the upper line is parallel, so the slope is the same.

and what is b, the y-intercept ? we see that the line goes directly through the origin (0, 0). so, b = 0.

the line equation of the upper line is

y = (4/5)x

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Answer:

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Step-by-step explanation:

First find the midpoint of the segment from (2, -6) to (-4, -16)

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Now find the distance between the 2 given points and divide by 2 to get the radius of the circle

d = $\sqrt{(2 + 4)^{2} + (-6 + 16)^{2} }$

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= $\sqrt{36 + 100}$

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r = $\sqrt{136}$ /2

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Let x be the number of times they raise the price on the newspaper. Then the new cost of the newspaper is

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Plugging the value of y in the first expression we have that the income will be

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Then the income is given by the function

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$\begin{gathered} \frac{df}{dx}=\frac{d}{dx}(-x^2+18x+175) \\ =-2x+18 \end{gathered}$

no we equate the derivative to zero and solve for x.

$\begin{gathered} \frac{df}{dx}=0 \\ -2x+18=0 \\ -2x=-18 \\ x=\frac{-18}{-2} \\ x=9 \end{gathered}$

This means that we have an extreme value of the function when x=9. Now we need to find out if this value is a maximum or a minimum. To do this we need to take the second derivative of the function, then

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Since the second derivative is negative in the point x=9, we conclude that this value is a maximum of the function.

With this we conclude that the number of times that they should raise the price to maximize the income is 9. This means that they will raise the price of the newspaper (9)($0.05)=$0.45.

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