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3 years ago

Factor the following algebraic equation.

Mathematics

1 answer:

Dmitry [639]3 years ago

4 0

12z + 28 - 7z - 3

Combine like terms:
= 5z + 25

Take out common factor, 5:
= 5(z + 5)

Answer: 5(z + 5)

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Give the equation of a line that goes through the point ( − 21 , 2 ) and is perpendicular to the line 7 x − 4 y = − 12 . Give yo

nlexa [21]

Given:

Equation of line $7x-4y=-12$ .

To find:

The equation of line that goes through the point ( − 21 , 2 ) and is perpendicular to the given line.

Solution:

The given equation of line can be written as

$7x-4y+12=0$

Slope of line is

$\text{Slope}=-\dfrac{\text{Coefficient of x}}{\text{Coefficient of y}}$

$m_1=-\dfrac{7}{(-4)}$

$m_1=\dfrac{7}{4}$

Product of slopes of two perpendicular lines is -1. So, slope of perpendicular line is

$m_1m_2=-1$

$m_2=-\dfrac{1}{m_1}$

$m_2=-\dfrac{4}{7}$ $[\because m_1=\dfrac{7}{4}]$

Now, the slope of perpendicular line is $m_2=\dfrac{4}{7}$ and it goes through (-21,2). So, the equation of line is

$y-y_1=m_2(x-x_1)$

$y-2=-\dfrac{4}{7}(x-(-21))$

$y-2=-\dfrac{4}{7}x-\dfrac{4}{7}(21)$

$y-2=-\dfrac{4}{7}x-12$

$y=-\dfrac{4}{7}x-12+2$

$y=-\dfrac{4}{7}x-10$

Therefore, the required equation in slope intercept form is $y=-\dfrac{4}{7}x-10$ .

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