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# Algebra

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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.

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   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 ]   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)   Apr 21, 2021