First, let's find the slope of the line we want to write. The line we want is perpendicular to y = -2x -3. Recall that if two lines are perpendicular to each other, their slopes are negative reciprocals of each other. What this means is that:

$m_1\cdot m_2=-1$

Plug -2 for one of the slopes.

$-2\cdot m_2=-1$

Divide by -2 to find the slope of our line.

$m_2=1/2$

Thus, our line needs to have a slope of 1/2.

Now, let's use the point-slope form. The point-slope form is given by:

$y-y_1=m(x-x_1)\\$

Plug in 1/2 for the slope m and let's let our point (6,-4) be x₁ and y₁. Thus:

$y-(-4)=\frac{1}{2}(x-6)\\$

Simplify and distribute:

$y+4=\frac{1}{2} x-3$

Subtract 4 from both sides:

$y=\frac{1}{2}x-7$

The above is the equation that passes the point (6,-4) and is perpendicular to y = -2x -3.

5 0

3 years ago

An ellipse has a center at the origin, a vertex along the major axis at (20, 0), and a focus at (16, 0). the equation of the ell

olga_2 [115]

If the center is at (0, 0) and the vertex is at (20, 0), then the distance, a, is the length from the center to the vertex, 20. The distance from the center to the focus is c. The distance from the center to the focus is 16, so c = 16. The formula we use to find the focus is $c^2=a^2-b^2$ . We have our c value and our a value, so we will sub in those to find b. $16^2=20^2-b^2$ and 256 = 400 - b^2. -b^2 = -144, so b = 12. There you go!

5 0

3 years ago

Read 2 more answers

Could u pleas show the work

Makovka662 [10]

Answer:

my answer is B

Step-by-step explanation:

4+5+-6

4+5-6

(4+5)=9

9-6=3

7 0

3 years ago