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3 years ago

What is the line that goes through (-5,1) and perpendicular to y= 5/4x + 3

Mathematics

1 answer:

lesya [120]3 years ago

5 0

Sorry just commenting for something

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Write an equation of the perpendicular bisector of the segment with the endpoints (8,10) and ( -4,2).

ale4655 [162]

Answer:

The required equation is:

$y = -\frac{3}{2}x+9$

Step-by-step explanation:

To find the equation of a line, the slope and y-intercept is required.

The slope can be found by finding the slope of given line segment. A the perpendicular bisector of a line is perpendicular to the given line, the product of their slopes will be -1 and it will pass through the mid-point of given line segment.

Given points are:

$(x_1,y_1) = (8,10)\\(x_2,y_2) = (-4,2)$

We will find the slope of given line segment first

$m = \frac{y_2-y_1}{x_2-x_1}\\= \frac{2-10}{-4-8}\\=\frac{-8}{-12}\\=\frac{2}{3}$

Let m_1 be the slope of perpendicular bisector then,

$m.m_1 = -1\\\frac{2}{3}.m_1 = -1\\m_1 = \frac{-3}{2}$

Now the mid-point

$(x,y) = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})\\= (\frac{8-4}{2} , \frac{10+2}{2})\\=(\frac{4}{2}, \frac{12}{2})\\=(2,6)$

We have to find equation of a line with slope -3/2 passing through (2,6)

The equation of line in slope-intercept form is given by:

$y = m_1x+b$

Putting the value of slope

$y= -\frac{3}{2}x+b$

Putting the point (2,6) to find the y-intercept

$6 = -\frac{3}{2}(2)+b\\6 = -3+b\\b = 6+3 =9$

The equation is:

$y = -\frac{3}{2}x+9$

7 0

3 years ago

One-third of 2c subtracted frome 5 times nine

lilavasa [31]

-44.8 is the answer.

4 0

3 years ago

Read 2 more answers

F(x)=x^2. what is g(x)?

Degger [83]

Answer:

Step-by-step explanation:

g(x) = 4x²

g(x) is steeper than f(x) and the ordered pair (1, 4) fits in option C:

g(1) = 4(1)² = 4

7 0

3 years ago

Angela tried to solve an equation step by step. \begin{aligned} \dfrac34+m&=\dfrac54\\\\ \dfrac34+m-\dfrac34&=\dfrac54+\

Liono4ka [1.6K]

Answer:

The mistake she made was ; She didn't change the sign when subtracting -3/4 from both sides

She wrote 5/4+3/4 instead of 5/4-3/4

Step-by-step explanation:

Correct solution:

$\frac{3}{4} + m = \frac{5}{4}$

Subtract-3/4 from both sides

$\frac{3}{4} - \frac{3}{4} + m = \frac{5}{4} - \frac{3}{4}$

Simplify

$m = \frac{5}{4} - \frac{3}{4} \\ m = \frac{1}{2}$

7 0

3 years ago

A car salesman's total earnings, e, is a base salary plus a commission. The salesman has a base salary of $40,000 and receives a

stellarik [79]

E = $40,000 + $200c
$e = 40000 + 200c$

Hope this helps. - M

6 0

4 years ago