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Name _____________________________
Date ___________________

Algebra
(Answer ID # 0738396)
Solve each system by graphing. Find the vertices of the graph.
1.   7x + 2y    -10
3x - y    -8
4x + 3y    -15
2.   x - 8y    -8
5x + 3y    3
6x - 5y    38
3.   2x - y    -2
3x - 5y    4
x - 4y    -1

Factor. One factor is given.
4.   f(x) = x3 + 1
Factor: x2 - x + 1
5.   f(x) = -4x3 + 8x2 + 396x
Factor: -4x
6.   f(x) = x3 + 9x2 + 15x - 25
Factor: x + 5

Solve each equation by factoring.
7.   x2 + 7x - 18 = 0
8.  
-5

6
x2 - 
22
1

2
x  =  
-8
1

3
x2 - 
11
2

3
9.  
-20x2 + 55x - 35  =  0

Point M is the midpoint between the points P and Q. Find the coordinates of the missing point.
10.  
P
(9  ,  11)

M
(6  ,  
4
1

2
)
11.  
Q
(21  ,  -26)

M
(
14
1

2
  ,  
-17
1

2
)

 

Solve each system of equations using any method.
12.   17x + 10y = 179
21x + 10y = 127
13.   13x + 18y = 112
3x - 5y = 154

Evaluate the expression.
14.  
144i8d7
    
224i7d7b12
15.  
11c7
    
405c11
    
384c10

Solve by factoring.
16.   x2 + 16x + 64 = 0
17.   x2 + 16x + 48 = 0
18.   9x2 - 66x + 121 = 0

Use determinants to calculate the area. Show your work.
19.   Calculate the area of the triangle with the following points:
(-4, -10), (1, -3), (-2, -5)
20.   Calculate the area of the triangle with the following points:
(-5, 0), (0, -4), (4, 5)
21.   Calculate the area of the triangle with the following points:
(-4, 2), (-1, 0), (3, 8)

 

Answer Key

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