Please help me get ready for math finals?!?

Question

1. solve for a.
√5a+2 - √7a-8 = 0
a. -5
b. 5/6
c. 5
d. none

2. find the distance between the points (-4, -5) and (3,-1)
a. √65
b.√37
c. √17

3.What is the center of the circle that has a diameter whose endpoints are (2, 7) and (-6, -1)?
a.(4, 3)
b.(-2, 4)
c.(-2, 3)
4. Which of the following equations is of a parabola with a vertex at (0, -5)?
a.y = (x - 5)2
b.y = (x + 5)2
c.y = x2 - 5
d.y = x2 + 5

5. Which of the following is the factored form of the given equation?

6x^2 + 2x - 8 = 0

a.2(3x + 4)(x - 1) = 0
b.(6x + 1)(x - 8) = 0
c.2(3x + 4)(x + 1) = 0

Answer 1

1.

√5a + 2 - √7a - 8 = 0

Add √7a - 8 to each side

√5a + 2 = √7a - 8

Take square to each side

5a + 2 = 7a - 8

7a - 5a = 8 + 2

2a = 10

a = 5

C is the right choice.

 

Answer 2

2.

The two points are (-4 , -5) and (3 , -1)

The two points (x1,y1) and (x2, y2) then the distance = √(x2 - x1)² + (y2 - y1)²

                                                                             = √(3 + 4)² + (-1 + 5)²

                                                                             = √(7² + 4²)

                                                                             = √49 + 16

                                                                             = √65

a is the right choice.

Answer 3

3.

The center of the circle that has a diameter

It has end points (2 , 7) and (-6 , -1)

The center of the circle = the two end points of the mid point to the diameter

(x1 , y1) and (x2 , y2) are two points then the mid point = ((x1 + x2) / 2 , (y1 + y2) / 2)

Substitute x1 = 2 , x2 = -6 , y1 = 7 , y2 = -1

There fore the center of the circle = ((2 - 6) / 2 , (7 - 1) / 2)

                                                 = ((-4 / 2) , (6 / 2))

                                                 = (-2 , 3).

c is the right choice.

Answer 4

4.

The given vertex of a parabola  = (0 , -5)

The parabola equation standard form = (x - h)² = (y - k) where (h , k) is a vertex

There fore Substitute h = 0 , k = -5 in the above equatin

                                                       (x - 0)² = ( y -(-5))

                                                       x² = y + 5

                                                        y = x² - 5

c is the right choice.

 

 

Answer 5

5.

Factor form of the equation :

6x² + 2x - 8 = 0

6x² + 8x - 6x - 8 = 0

6x² - 6x + 8x - 8 = 0

Take out common term 6x and 8

6x(x - 1) + 8(x - 1) = 0

Take out common term x - 1

(x - 1)(6x + 8) = 0

2(3x + 4)(x - 1) = 0

a is the right choice.