Fabio is designing a flashlight that uses a parabolic reflecting mirror and a light source. the shape of the mirror can be modeled by (x-2)^2=10(y-3), where x and y are measured in inches. where is the focus of the flashlight? a. (–2, –0.5) b. (2, –5.5) c. (2, 5.5) d. (5.5, 2)

(2, 11/2)

Step-by-step explanation:

This is a vertical parabola; we know that because x is squared here, while y is not.  The standard equation of a vertical parabola with vertex (h,k) is

4p(y-k) = (x-h)^2, where p is the distance between the vertex and the focus.  Comparing

4p(y-k) = (x-h)^2 to

10(y-3)  = (x-2)^2, we see that 4p = 10.  Therefore, p = 10/4 = 5/2, which is the vertical distance between the focus and the vertex.

Since the coordinates of the vertex are easily read from the given equation

(x-2)^2=10(y-3):  (h,k) = (2, 3)

all we need to do is to add p (5/2) to the y-coordinate (3);

The focus is at (2, 3 + 5/2), or (2, 11/2).

answer: for each 3 girls there is 2 boys . 3: 2

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d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.