College Algebra (MAC-2233) Lessons:        Pre-Assessment Exam            Final Exam (Proctored)            Page 1    2   3

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Page 3

Explanation
x = dimes
x + 3 = quarters
 
0.10x + 0.25(x + 3) = 3.20
0.10x + 0.25x + 0.75 = 3.20
0.35x + 0.75 = 3.20
0.25x = 2.45
x = 7 = dimes
x + 3 = quarters
7 + 3 = quarters
The answer is 10.
 
Let’s check the answer.
Remember we have 7 dimes and 10 quarters (3 more quarters than dimes).
.10(7) + .25(10) = 3.20
.70 + 2.50 = 3.20
3.20 = 3.20

Explanation
As we look at the answer, we can see that we need to solve a quadratic equation,
and not solve for x. So, we will put the equation into quadratic form.

Add 32 to both sides of the equation.            (3x+5)² + 32 = 0
Simplify (3x + 5)² + 32       Rewrite (3x + 5)²    as (3x + 5) (3x + 5)
We are left with (3x+5) (3x+5) + 32 = 0
Expand (3x+5) (3x+5)
using the FOIL Method 3x(3x) + 3x ⋅ 5 + 5(3x) + 5 ⋅ 5 + 32 = 0
Simplify and combine like terms. 9x² + 30x + 25 + 32 = 0
Add 25 and 32        9x² + 30x + 57 = 0
Now, solve the Quadratic Equation like we did earlier.
9x² + 30x + 57 = 0              

 

Explanation

The easiest way to graph this equation is to pick zero as the starting point.
Then we use -3 in the y-intercept form as we are given -3 in the equation,
so the first pair we plot would be (0,-3).
 
Solution 2(0) – 3 = -3
 
Then we can use 1 as the second starting point and evaluate 1 in the equation to
find the ordered pair. So, we know the equation is y = 2x – 3
we use 2x – 3 to find the second ordered pair.
 
Solution
2(1) – 3 = -1
 
Now we can graph the equation.
(0,-3) > 2(0) – 3 = -3
(1,-1) > 2(1) – 3 = -1

 

Explanation
t = time
We would write this equation as so:
48t = 54(t – 2)
Simplify
48t = 54t – 108
Subtract 54t from both sides.
-6t = -108
Divide both sides by -6.
t = 18
 
Let’s check the answer (please note Car B drove 2 hours less)
 
48t = 54 x (t – 2)
48(18) = 54 x (18 – 2)
48(18) = 54(16)
864 = 864

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College Algebra (MAC-2233) Lessons:        Pre-Assessment Exam                  Final Exam (Proctored)            Page 1    2    3

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More Lessons  1    2    3    4    5    6    7    8    9   10   11   12   13    14    15    16    17    18    19    20    21    22    23    24    25  

 

Explanation

|x| + 2 = 10
Subtract 2 from both sides.
|x| = 8
Remove the absolute value term from the equation, so this means the answers can be:
8 or -8
Since the multiple-choice answer is -8, the answer is -8.

Explanation

|x| + 2 = 10
Subtract 2 from both sides.
|x| = 8
Remove the absolute value term from the equation, so this means the answers can be:
8 or -8
Since the multiple-choice answer is -8, the answer is -8.

Explanation

11x – 13 = 31
Add 13 to both sides.
11x = 44
Divide both sides by 11
x = 4

Explanation
5x = 2.5
Divide both sides by 5.
x = 0.5

Explanation
The leading coefficient is the leading term,
and the degree is 3 because it is the greatest exponent.

Explanation
-6x = 24
Divide both sides by -6
x = -4

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College Algebra (MAC-2233) Lessons:        Pre-Assessment Exam                  Final Exam (Proctored)            Page 1    2    3
More Lessons  1    2    3    4    5    6    7    8    9   10   11   12   13    14    15    16    17    18    19    20    21    22    23    24    25  

 

Explanation

We simply flip the second fraction, multiply, and simplify!

So, ÷
 =
 by dividing 72 by 12
72 / 12 = 6

Explanation

2/10 + 4/10 = 6/10 Simplify by dividing by 2 = 3/5
 
5/6 – 1/6 = 4/6 = Simplify by dividing by 2 = 2/3
 
2/9 + 4/9 = 6/9 = Simplify by dividing by 3 = 2/3
 
8/12 – 2/12 = 6/12 = Simplify by dividing by 6 = 1/2

Explanation
To write  as a fraction with a common denominator multiply by
To write  as a fraction with a common denominator multiply b
 
·  +  -  ·
Now we combine all the terms
+  -
We are left with  -
Now we need another denominator so we what do is
We multiple both sides by .
( -  =         -
Now we need to multiply  by
We are left with  -
Now we have common denominators, so we can combine the top
(the bottom keeps 12y as the denominator)
  -  =

Explanation
x + 0.2 = 0.7
x + 0.2 – (0.2) = 0.7 + (-0.2)
x = 0.7 – 0.2
x = 0.5

Explanation
x + 12 = -27
x + 12 - (12) = -27 + (-12)
x = -27 + -12 = -39
x = -39

Explanation
5x = 2.5
5x / (5) = 2.5 / (5)
2.5 / 5 = 0.5

Explanation
2x + 8 = 20
2x + 8 – (8) = 20 – (8)
2x = 12
12 / 2 = 6

Explanation
Without graphing the equation, we know the value of x = -3 because
there are no other values for x with this problem, so we would plug in the
value of x and solve for y.

y = 4(-3) – 5
y = -12 -5
-12 + -5 = -17
x = -3, y = -17
(-3, -17)

Explanation
-2y³(-6y³)
-2 x -6 = 12
-y³ x -y³ = y⁶
Now combine.
12y