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1. A basketball player made 12 out of 15 free throws she attempted. She wants to know have many consecutive free throws she would have to make to raise the percent of successful free throws to 85%.

(A) Write an equation to represent this situation.

(B) Solve the equation. How many consecutive free throws would she have to make to raise her percent to 85%?

2. Simplify the expression . Show your work.

3. Write the expression as a simplified rational expression. Show your work. Dec 11, 2018

#1
+2

First one

Let x be the number of additional FT's......so we have that

[ 12 + x]

_______  =     .85           multiply both sides by  15 + x

[15 + x ]

12 + x  =  85 [ 15 + x]     simplify

12 + x = 12.75 + .85x        subtract 12, .85x   from both sides

.15x  =  .75     divide both sides by  .15

x =  5

So....she needs 5 more consecutive FT's     [ 12 + 5 =  17   total]   Dec 11, 2018
edited by CPhill  Dec 11, 2018
#2
+2

Second one

x^2 + 3x - 28    factors as    (x + 7) (x - 4)

x^2  -7x + 12  factors as   (x - 3) (x - 4)

So

(x + 7) ( x - 4)               ( x + 7)

_____________  =     _______

(x - 3) ( x - 4)                ( x - 3)   Dec 11, 2018
#3
+2

Last one

The denominator is the only problem

1 / 6   +   1 / [ x + 1 ]    =

[ 1] [x + 1]                        [ 6]

__________  +        __________ =

6 *[x + 1]                [ x + 1 ] *6

[ x + 1 ] + 6

__________   =

6 [ x + 1]

x + 7

_______

6x + 6

So

[ 5 /1 ]  /   (   [  x + 7]  / [ 6x + 6 ] )  =       { invert the second fraction and multiply }

5         *       [ 6x + 6]                  30x + 30

__              ________   =          ________

1                 [ x + 7]                      x + 7   Dec 11, 2018