Y=1/20x^2 The directrix of the parabola is: x=-5 x=5 y=-5

Write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line.

Harrizon [31]

Answer:

Equation of the line that passes through the given point and is (a) parallel is: $\mathbf{y=-2x+11}$

Equation of the line that passes through the given point and is (b) perpendicular is: $\mathbf{y=\frac{1}{2}x+1}$

Step-by-step explanation:

We need to Write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line.

First we will find slope of the line given in graph

The slope can be found using formula: $Slope=\frac{y_2-y_1}{x_2-x_1}$

We have points (1,6) and (2,2)

Slope is:

$Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{2-6}{2-1}\\Slope=\frac{-4}{2}\\Slope=-2$

Part a)

Write an equation of the line that passes through the given point and is (a) parallel

When the lines are parallel, they have same slope. So, slope of required line: m = -2

Using slope m =-2 and point(4,3) we can find y-intercept b

$y=mx+b\\3=-2(4)+b\\3=-8+b\\b=3+8\\b=11$

The equation of line will be:

$y=mx+b\\y=-2x+11$

Equation of the line that passes through the given point and is (a) parallel is: $\mathbf{y=-2x+11}$

Part b)

Write an equation of the line that passes through the given point and is (b) perpendicular

When the lines are perpendicular they have opposite slope. So, slope of required line: m = 1/2

Using slope m =1/2 and point(4,3) we can find y-intercept b

$y=mx+b\\3=\frac{1}{2}(4)+b\\3=2+b\\b=3-2\\b=1$

The equation of line will be:

$y=mx+b\\y=\frac{1}{2}x+1$

Equation of the line that passes through the given point and is (b) perpendicular is: $\mathbf{y=\frac{1}{2}x+1}$

6 0

3 years ago

HELP PLEASEEEEEEEEEEEEEEEEEEEEEEEEE

umka21 [38]

Answer:

The solution set to the absolute value is:

$S = \{x \in \mathbb{R}| x \ge 0\}$ or $S = [0, +\infty)$

Negative real numbers are not included in the solution set, as for $x < 0$ , $|x| = - x$ .

Step-by-step explanation:

From Mathematics, we know that absolute values are defined by the following characteristics:

1) For $x \ge 0$ , $|x| = x$

2) For $x < 0$ , $|x| = - x$

Then, if $|x| = x$ , then the solution set to the absolute value is:

$S = \{x \in \mathbb{R}| x \ge 0\}$ or $S = [0, +\infty)$

Negative real numbers are not included in the solution set, as for $x < 0$ , $|x| = - x$ .

3 0

3 years ago

PLEASE HeLp!!!! Question BELow!

Law Incorporation [45]

I'm going to label them from top to bottom 1,2,3,4,5
your answer is 3,4,5,2,1

8 0

4 years ago

How do the measures of the side lengths of AABCcompare with those of AA'B'C' when AA'B'C' coincides with the other three triangl

Nadusha1986 [10]

Answer:

The measure of each side of is equal to the corresponding side of when coincides with the other three triangles. The side lengths of the triangle are preserved as the figure rotates.

7 0

4 years ago

Find the area of the figure below.

Bad White [126]

I am stuck on this too...
Maybe we can figure it out together

8 0

2 years ago