This is a vertical parabola which opens upwards
we have the general formula
(x - h)^2 = 4p(y - k) where p is the y coordinate of the focus
y/14 = x^2 - x /14 - 1/14
add 1/14 to both sides
y/14 + 1 /14 = x^2 - x /14
now complete the square
y/14 + 1/14 = x^2 - x/14 + 1/28^2
y/14 + 1/14 = (x - 1/28)^2
(x - 1/28)^2 = 1/14( y + 1)
comparing this with the general form:-
4p = 1/14
p = 1/56
so the focus is at (h,p) = (1/28, 1/56)
Use the information to write the dimensions of each rectangle in terms of w, the width of the 1st one.
1st rectangle;
l = 2w
w = 2
2nd rectangle:
w = w
l = 2w + 4
If the area of the 2nd rectangle is 70 square meters, you will use the area formula to write an equation that you will solve using the factoring.
A = lw
70 = w(2w + 4)
70 = 2w^2 + 4w
0 = 2w^2 + 4w -70
0 = 2 (w^2 +2w - 35)
0 = 2 (w + 7) (w - 5)
To get zero, the width would need to be -7 or 5. Because it is a distance, it has to be 5 meters.
The width of both rectangles is 5 meters.
Answer:
(x -5)² + (y +4)² = 100 Should be the correct answer, hope this helps :)
Step-by-step explanation:
A circle centered at (h, k) with radius r will have equation ...
... (x -h)² + (y-k)² = r²
The point satisfies the equation for the circle. Filling in the given numbers, we have ...
... (x -5)² + (y+4)² = (-3-5)² + (2+4)² . . . . . . (h, k) = (5, -4), (x, y) = (-3, 2)
... (x -5)² + (y +4)² = 64 +36
Answer:
x = 10
Step-by-step explanation:
9x - 40 = 3x + 20
<u>9</u><u>x</u><u> </u><u>-</u><u> </u><u>3</u><u>x</u> - 40 = <u>3x - 3x</u> + 20
6x - 40 = 20
6x <u>-</u><u> </u><u>40</u><u> </u><u>+</u><u> </u><u>40</u> = <u>20</u><u> </u><u>+</u><u> </u><u>40</u>
6x = 60
<u>6x</u><u> </u><u>/</u><u> </u><u>6</u> = <u>60</u><u> </u><u>/</u><u> </u><u>6</u>
x = 10
Now plug the x value in the equation to make the statement true that A is parallel to B.
9x - 40
<u>9</u><u>(</u><u>10</u><u>)</u> - 40
<u>90</u><u> </u><u>-</u><u> </u><u>40</u>
50
3x + 20
<u>3</u><u>(</u><u>10</u><u>)</u> + 20
<u>30</u><u> </u><u>+</u><u> </u><u>20</u>
50
Therefore, x = 10 making the statement true that A is parallel to B. Hope this helps and stay safe, happy, and healthy, thank you :) !!