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3 years ago

What is the equation of the new function?

Mathematics

1 answer:

ElenaW [278]3 years ago

7 0

The image g(x) of f(x) by shifting RIGHT h units is given by
g(x)=f(x-h)
Given f(x)=x^2, and h=-12 (LEFT makes h negative)
we get
g(x)=f(x-(-12))=f(x+12)=(x+12)^2 (if we do not expand expression)
=x^2+24x+144 (if we expand expression)

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3 years ago

Find the slope of the line through each pair of points (-18, 13) and (-14, -20) *

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Answer:

The answer is

$- \frac{33}{4} \\$

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

$m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\$

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-18, 13) and (-14, -20)

The slope is

$m = \frac{ - 20 - 13 }{ - 14 - - 18} = \frac{ - 33}{ - 14 + 18} = - \frac{33}{4} \\$

We have the final answer as

$- \frac{33}{4} \\$

Hope this helps you

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3 years ago

Find the slope of each line and then determine if the lines are parallel, perpendicular or neither. If a value is not an integer

Aleonysh [2.5K]

As given by the question

There are given that the point of two-line

$\begin{gathered} (1,\text{ 7) and (5, 5)} \\ (-1,\text{ -3) and (1, 1)} \end{gathered}$

Now,

From the condition of a parallel and perpendicular line

If the slopes are equal then the lines are parallel

If the slopes are negative reciprocal then the lines are perpendicular

If the slopes are neither of the above are true then lines are neither

Then,

First, find the slope of both of line

So,

For first-line, from the formula of slope

$\begin{gathered} m_1=\frac{y_2-y_1}{x_2-x_1} \\ m_1=\frac{5_{}-7_{}}{5_{}-1_{}} \\ m_1=-\frac{2}{4} \\ m_1=-\frac{1}{2} \end{gathered}$

Now,

For second-line,

$\begin{gathered} m_1=\frac{y_2-y_1}{x_2-x_1} \\ m_1=\frac{1_{}-(-3)_{}}{1-(-1)_{}} \\ m_1=\frac{4}{2} \\ m_1=2 \end{gathered}$

The given result of the slope is negative reciprocal because

$\begin{gathered} -\frac{1}{2}=-(-\frac{2}{1}) \\ -\frac{1}{2}=2 \end{gathered}$

Hence, the slope of line1 is -1/2, and slope of line2 is 2 and the lines are perpendicular.

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