1.

1. A basketball player made 8 out of 50 free throws she attempted which is 16%. She wants to know how many consecutive free throws more in a row she would have to make to raise her overall successful baskets divided by attempts or percent of successful free throws to 60%.

(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 60%?

1 pt for correct answer to part (b), 4 pts for showing steps you took to get the correct answer and showing the formula with variable x that you used in part (a).

Note: correct answer to part (a) has only one variable, the variable x. Need to set up a ratio and cross multiply to solve for x.

X represents how many more consecutive tries she needs to make in a row

to raise her overall average up to 60%

2.

Simplify the expression 3x-12/x^2-15x+44. Show your work.

(NOTE: Must show your factoring work using either the big X strategy covered in class, or the quadratic formula method. Must show how you get factors. Not just give me factors.)

3.

1. Write the expression as a simplified rational expression. Show your work.

14x+4

-----------

2 1

----- + -----

3x 2x+1

Thank you for any help.

Guest Apr 21, 2021

#1**+2 **

1. A basketball player made 8 out of 50 free throws she attempted which is 16%. She wants to know how many consecutive free throws more in a row she would have to make to raise her overall successful baskets divided by attempts or percent of successful free throws to 60%.

(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 60%?

a) [ 8 + x ] / [ 50 + x ] = .60 where x is the numbere of additional consecutive FTs needed

b) cross-multiply and we get

8 + x = .60 [ 50 + x ]

8 + x = 30 + .60x

x - .60x = 30 - 8

.40x = 22

x = 22 / .40 = 55 = additional consecutive FTs needed

CPhill Apr 21, 2021

#2**+2 **

2.

Simplify the expression 3x-12/x^2-15x+44. Show your work.

(NOTE: Must show your factoring work using either the big X strategy covered in class, or the quadratic formula method. Must show how you get factors. Not just give me factors.)

3x - 12 = 3 ( x - 4)

Since we're being asked to simplify this, we might guess that (-4) (-11) = 44

And -4 + -11 = -15

So...the polynomial in the denominator must be ( x - 4) ( x - 11)

So

3 ( x - 4) / [ (x - 4) ( x -11) ] = 3 / [ x - 11 ]

CPhill Apr 21, 2021

#3**+2 **

3.

1. Write the expression as a simplified rational expression. Show your work.

14x+4

-----------

2 1

----- + -----

3x 2x+1

Easiest to simplify the denominator, firtst

2 ( 2x + 1) + 1 ( 3x) 4x + 2 + 3x 7x + 2

__________________ = ___________ = __________

3x (2x + 1) 3x (2x + 1) 3x (2x + 1)

And the numerator simplifies to 2 ( 7x + 2)

So we have

2 ( 7x + 2)

____________________ invert the denominator and multiply

(7x + 2) / [3x (2x + 1) ]

2 ( 7x + 2) [ 3x ( 2x + 1) ]

______________________ = 2 [ 3x ( 2x + 1) ] = 2 [ 6x^2 + 3x] = 12x^2 + 6x

(7x + 2)

CPhill Apr 21, 2021