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andreev551 [17]
3 years ago
11

PLEASE HELP

Mathematics
1 answer:
Ipatiy [6.2K]3 years ago
8 0
Direct variation equal is written as :  y = kx

K is the constant of variation. 

12 = k4
12/4 = k
k = 3

y = 3x

Answer: <span>B. y = 3x </span>
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Triangle b is larger than triangle a
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Which function is the inverse of f(x) = –5x – 4?
makvit [3.9K]
Y = -5x - 4
switch x and y and solve for y
x = -5y - 4
x+4 = -5y
(x+4)/ -5 = y^-1 ( the inverse)

4 0
3 years ago
D is the midpoint of RJ⎯⎯⎯⎯. R has coordinates (−4,7), and D has coordinates (2,−1). Identify the coordinates of J.
Aleksandr [31]

Answer:

(8,-9)

Step-by-step explanation:

If the x-coordinate of R is 6 units away from D's x-coordinate, then so will J's x-coordinate. If the y-coordinate of R is 8 units away from D's y-coordinate, then so will J's y-coordinate.

Side note/Extra information:

The line would be y=\frac{-4}{3} x+\frac{5}{3}

3 0
2 years ago
What is the equation of a parabola with a directrix of y=2 and a focus point of 0,-2
KiRa [710]
Hope this helped. :)

Any point, <span><span>(<span><span>x0</span>,<span>y0</span></span>)</span><span>(<span><span>x0</span>,<span>y0</span></span>)</span></span> on the parabola satisfies the definition of parabola, so there are two distances to calculate:

<span>Distance between the point on the parabola to the focusDistance between the point on the parabola to the directrix</span>

To find the equation of the parabola, equate these two expressions and solve for <span><span>y0</span><span>y0</span></span> .

Find the equation of the parabola in the example above.

Distance between the point <span><span>(<span><span>x0</span>,<span>y0</span></span>)</span><span>(<span><span>x0</span>,<span>y0</span></span>)</span></span> and <span><span>(<span>a,b</span>)</span><span>(<span>a,b</span>)</span></span> :

<span><span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span><span>(<span><span>y0</span>−b</span>)</span>2</span></span><span>‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾</span>√</span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span><span>(<span><span>y0</span>−b</span>)</span>2</span></span></span>

Distance between point <span><span>(<span><span>x0</span>,<span>y0</span></span>)</span><span>(<span><span>x0</span>,<span>y0</span></span>)</span></span> and the line <span><span>y=c</span><span>y=c</span></span> :

<span><span><span>∣∣</span><span><span>y0</span>−c</span><span>∣∣</span></span><span>| <span><span>y0</span>−c</span> |</span></span>

(Here, the distance between the point and horizontal line is difference of their <span>yy</span> -coordinates.)

Equate the two expressions.

<span><span><span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span><span>(<span><span>y0</span>−b</span>)</span>2</span></span><span>‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾</span>√</span>=<span><span>∣∣</span><span><span>y0</span>−c</span><span>∣∣</span></span></span><span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span><span>(<span><span>y0</span>−b</span>)</span>2</span></span>=<span>| <span><span>y0</span>−c</span> |</span></span></span>

Square both sides.

<span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span><span>(<span><span>y0</span>−b</span>)</span>2</span>=<span><span>(<span><span>y0</span>−c</span>)</span>2</span></span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span><span>(<span><span>y0</span>−b</span>)</span>2</span>=<span><span>(<span><span>y0</span>−c</span>)</span>2</span></span></span>

Expand the expression in <span><span>y0</span><span>y0</span></span> on both sides and simplify.

<span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span>b2</span>−<span>c2</span>=2<span>(<span>b−c</span>)</span><span>y0</span></span><span><span><span>(<span><span>x0</span>−a</span>)</span>2</span>+<span>b2</span>−<span>c2</span>=2<span>(<span>b−c</span>)</span><span>y0</span></span></span>

This equation in <span><span>(<span><span>x0</span>,<span>y0</span></span>)</span><span>(<span><span>x0</span>,<span>y0</span></span>)</span></span> is true for all other values on the parabola and hence we can rewrite with <span><span>(<span>x,y</span>)</span><span>(<span>x,y</span>)</span></span> .

Therefore, the equation of the parabola with focus <span><span>(<span>a,b</span>)</span><span>(<span>a,b</span>)</span></span> and directrix <span><span>y=c</span><span>y=c</span></span> is

<span><span><span><span>(<span>x−a</span>)</span>2</span>+<span>b2</span>−<span>c2</span>=2<span>(<span>b−c</span>)</span>y</span></span>

3 0
3 years ago
How do I rotate a figure 90 degrees clockwise
cricket20 [7]

Step-by-step explanation:

You have to have tracing paper or patty paper (cause that's what my teacher uses). Next you draw the figure along with the x and y-axis on it as well. Then you mark the x and y-axis and rotate the paper 90 degrees clockwise. Lastly if the x-axis is on the y-axis, mark it as the y-axis and if the y-axis is on the x-axis, also mark it as the x-axis.

I hope this helped :)

5 0
2 years ago
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