Math exam help
1.
Which of the following is the correct matrix representation of the October Inventory of small and large t-shirts and pants?
| Inventory for August | Inventory for September | Inventory for October | ||||
| Small | Large | Small | Large | Small | Large | |
| T-Shirts | 2 | 3 | 4 | 6 | 7 | 8 |
| Pants | 1 | 4 | 3 | 5 | 5 | 6 |
Answer
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1.
If find -2A.
Answer
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If and
find A – B.
Answer
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1.
If find 2A.
Answer
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1.
Matrix A has dimensions 2 x 3. Matrix B has dimensions 3 x 6. These two matrices can be multiplied to find the product AB.
Answer True False
1.
Evaluate
Answer
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| Does not exist. |
1.
Evaluate
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| Does not exist |
1.
Evaluate
Answer
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| Does not exist. |
1.
Find the determinant of
Answer
| 14 | ||
| -14 | ||
| 1 | ||
| -1 |
1.
Find the determinant of
Answer
| -48 | ||
| -56 | ||
| 56 | ||
| 48 |
1.
What is the determinant of the following matrix?
Answer
| -10 | ||
| -14 | ||
| -20 | ||
| -25 |
1.
What is the determinant of the following matrix? Does the matrix have an inverse?
Answer
| 5; no | ||
| 5; yes | ||
| 1; no | ||
| 1; yes |
1.
Is the following system consistent or inconsistent?
8x + y + 4 = 0
y = -8x – 4
Answer
| consistent | ||
| inconsistent |
1.
Is the following system consistent or inconsistent?
7x + 6 = -2y
-14x -4y + 2 = 0
Answer
| consistent | ||
| inconsistent |
1.
Is the following system consistent or inconsistent?
-2x – 2y = 6
10x + 10y = -30
Answer
| consistent | ||
| inconsistent |
1.
Is the following system consistent or inconsistent?
2y = x – 7
-2x – 6y = -14
Answer
| consistent | ||
| inconsistent |
1.
Is the following system consistent or inconsistent?
y = 2x + 5
-2x + y = -2
Answer
| consistent | ||
| inconsistent |
If a system has exactly one solution it is called _______________.
Answer
| consistent | ||
| inconsistent | ||
| independent | ||
| dependent |
1.
Does the following system of equations have a solution?
Answer
| Yes | ||
| No |
1.
What is the approximate solution of the following system of equations?
Answer
| (2, -7) | ||
| (-7, 2) | ||
| (7, 2) | ||
| (-7, -2) |
1.
Solve the following system of equations by using the substitution method. 3y – 2x = 11 y + 2x = 9
Answer
| (2, 5) | ||
| (-2, -5) | ||
| (4, 5) | ||
| Inconsistent |
1.
Solve the following system of equations by using the substitution method. y = -3x + 5 5x – 4y = -3
Answer
| (-1, -2) | ||
| (2, 1) | ||
| (3, 4) | ||
| (1, 2) |
1.
Solve the following system of equations by using the elimination method. x – y = 11 2x + y = 19
Answer
| (1, 10) | ||
| (-1, -1) | ||
| (12, 2) | ||
| (10, -1) |
1.
Solve the following system of equations by using the elimination method. -4x – 2y = -12 4x + 8y = -24
Answer
| (5, 3) | ||
| (-6, -6) | ||
| (3, 1) | ||
| (6, -6) |
1.
Solve the following system of equations using matrices. 3x – 2y = 31 3x + 2y = -1
Answer
| (5, -8) | ||
| (3, 5) | ||
| (-3, 9) | ||
| (2, 8) |
1.
Solve the following system of equations using matrices. 4x + 5y = -7 3x – 6y = 24
Answer
| (1, 4) | ||
| (2, -3) | ||
| (5, 6) | ||
| (3, 4) |
1.
The sum of two numbers is 7. Four times the first number is one more than 5 times the second. Find the two numbers.
Answer
| 2 and 1 | ||
| 4 and 3 | ||
| 5 and 7 | ||
| 2 and 3 |
1.
Which of the following is a solution to the following system of inequalities?
Answer
| (2, 2) | ||
| (0, 1) | ||
| (-1, 0) | ||
| (4, -4) |
1.
Which of the following is a solution to the following system of inequalities?
Answer
| (1, 1) | ||
| (-4, 0) | ||
| (3, 2) | ||
| (5, 0) |
1.
One possible solution of this system of inequalities is (1, 4).
Answer
| TRUE | ||
| FALSE |
1.
What is the system of equations that describes the following graph?
Answer
| x + 3y > 4; 3x – y > 2 | ||
| x + 3y < 4; 3x – y > 2 | ||
| x + 3y < 4; 3x – y < 2 | ||
| x + 3y = 4; 3x – y ≥ 2 |
1.
What is the system of equations that describes the following graph?
Answer
| x + y < 3; x – y > -2; y ≥ 0 | ||
| x + y > 3; x – y < -2; x ≥ 0 | ||
| x + y < 3; x – y > -2; y ≤ 0 | ||
| x + y < 3; x – y > -2; x ≥ 0 |
1.
What is the system of equations that describes the following graph?
Answer
| x + y < 3; x – y ≥ 2 | ||
| 2x + 3y ≥ 1; x – y ≥ 2 | ||
| 2x – y ≥ 13; x + y = 2 | ||
| x + y ≥ 32; x – y = 2 |
1.
What is the system of equations that describes the following graph?
Answer
| y ≥ 0; x ≤ 3 | ||
| x > 0; y < 3 | ||
| x ≥ 0; y ≤ 3 | ||
| x ≤ 0; y ≥ 3 |
1.
What is the system of equations that describes the following graph?
Answer
| x + 2y ≥ 4; x ≥ 2 | ||
| x + 2y ≥ 4; y ≥ 2 | ||
| x + 2y > 4; y > 2 | ||
| x + 2y > 4; x > 2 |
1.
What is the system of equations that describes the following graph?
Answer
| x + y ≤ 1; x – y ≥ 4 | ||
| x + y > 1; x – y ≥ 4 | ||
| x + y ≤ 1; x – y < 4 | ||
| x + y ≤ 1; x – y > 4 |
1.
What is the system of equations that describes the following graph?
Answer
| x > 2; x ≥ -5; y ≤ 6; y > -1 | ||
| x ≤ 2; x < -5; y > 6; y ≥ -1 | ||
| x ≤ 2; x ≥ -5; y ≤ 6; y ≥ -1 | ||
| x ≤ 2; x ≥ -5; y ≤ 6; y ≤ -1 |
1.
Solve 3x – y + 2z = 6 -x + y = 2 x – 2z = -5
Answer
| (-1, -3, -3) | ||
| (1, 3, 3) | ||
| (1, -3, -3) | ||
| (1, 3, -3) |
1.
Solve x + y = 9 y + z = 7 x – z = 2
Answer
| Infinite number of solutions | ||
| no solutions | ||
| (9, 7, 2) | ||
| (3, 6, 1) |
1.
Solve x + 3y + z = 1 2x – y – z = 6 5x + y + z = 1
Answer
| (1, 6, 1) | ||
| (1, 2, -6) | ||
| (2, 1, -4) | ||
| (-1, -2, 6) |
1.
Solve 4x + y – 2z = 0 2x – 3y + 3z = 9 -6x – 2y + z = 0
Answer
| (0, 9, 0) | ||
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| (0, -9, 0) | ||
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1.
Solve x – 2y – 3z = 3 3x + y + z = 12 3x – 2y – 4z = 15
Answer
| (0, 0, -1) | ||
| (3, 12, 15) | ||
| (3, 9, -6) | ||
| (-3, -9, 6) |
1.
Solve 4x + y + z = 1 8x – 4y – 7z = 2 5y – 9z = 3
Answer
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1.
Solve x + 3y + 4z = 0 x – 2z = 8 y + z = 3
Answer
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1.
In her wallet, Ms. Thompson has one-dollar, five-dollar, and ten-dollar bills, totally $171. She has the same number of five-dollar bills as one-dollar and ten-dollar bills put together. If she has 30 bills in all, how many bills of each denomination does she have?
Answer
| 11 one-dollar bills, 10 five-dollar bills, 9 ten-dollar bills | ||
| 6 one-dollar bills, 17 five-dollar bills, 8 ten-dollar bills | ||
| 11 one-dollar bills, 16 five-dollar bills, 8 ten-dollar bills | ||
| 6 one-dollar bills, 15 five-dollar bills, 9 ten-dollar bills |
1.
Twice the first number is eleven more than the sum of the other two numbers. The sum of twice the first number and three times the third number is one more than the second number. The second number is equal to the sum of the first number and the third number. Find the three numbers.
Answer
| 1st number = -6, 2nd number = 3.5, 3rd number = 2.5 | ||
| 1st number = 8, 2nd number = 4, 3rd number = 1 | ||
| 1st number = -8, 2nd number = -4, 3rd number = -1 | ||
| 1st number = 6, 2nd number = 3.5, 3rd number = -2.5 |
1.
What is the correct matrix for the inventory of boots in sizes 10 and 12.
| Boots | Flats | Sneakers | ||||
| Blue | Gray | Blue | Gray | Blue | Gray | |
| Shoes Size 10 | 3 | 5 | 9 | 10 | 1 | 4 |
| Shoes Size 12 | 2 | 0 | 2 | 7 | 4 | 0 |
Answer
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1.
Evaluate
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1.
Evaluate
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1.
Matrix A has dimensions 3 x 2. Matrix B has dimensions 3 x 2. A x B will have dimensions 3 x 2.
Answer
| TRUE | ||
| FALSE |
1.
Evaluate
Answer
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1.
Evaluate
Answer
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1.
Find the determinant of
Answer
| 0 | ||
| 6 | ||
| -10 | ||
| -5 |
1.
Find the determinant of
Answer
| 0 | ||
| 20 | ||
| -10 | ||
| -20 |
1.
The following system of equations is consistent.
Answer
| TRUE | ||
| FALSE |
The following system of equations has a solution.
Answer True False
1.
What is the solution to this system of equations?
Answer
| (-4, 4) | ||
| (4, -4) | ||
| (2, 4) | ||
| (4, 2) |
1.
Solve y = 2x – 4 by the substitution method. 7x – 5y = 14
Answer
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1.
Solve 4x + 3y = 13 by the substitution method. x + y = 4
Answer
1.
Solve 9x + 2y = 2 by the elimination methods. 21x + 6y = 4
Answer
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1.
Solve –x + 2y = 12 using the elimination method. x + 6y = 20
Answer
1.
Solve 2x + y = 3 using matrices. 3x – 2y = 8
Answer
| (2, 1) | ||
| (1, 1) | ||
| (4, -5) | ||
| (2, -1) |
1.
Solve 3x – 7y = 25 using matrices. 5x – 8y = 27
Answer
| (25, 27) | ||
| (27, 25) | ||
| (-1, -4) | ||
| (4, 1) |
1.
The degree measure of one of two complementary angles is 30 less than twice that of the other. What are the degree measures of the angles? (Remember that complimentary angles add to be 90 degrees)
Answer
| 45 degrees and 45 degrees | ||
| 30 degrees and 60 degrees | ||
| 27 degrees and 63 degrees | ||
| 40 degrees and 50 degrees |
1.
Which of the following is NOT a solution to the system of inequalities?
Answer
| (2, -2) | ||
| (2, 0) | ||
| (1, 0) | ||
| (4, -1) |
1.
What is the system of inequalities associated with the following graph?
Answer
| y > -2 x + y ≥ 1 | ||
| y < -2 x + y > 1 | ||
| y < -2 x + y ≥ 1 | ||
| y < -2 x + y < 1 |
1.
Solve 3x – y + 2z = 9 using matrices. x – 2y – 3z = -1 2x – 3y + z = 10
Answer
| (9, -1, 10) | ||
| (1, 2, 2) | ||
| (1, 2, -2) | ||
| (1, -2, 2) |
Solve 3x – 2y + z = -5 using matrices. -2x + 3y – 3z = 12 3x – 2y – 2z = 4
Answer
| (1, 0, -3) | ||
| (1, -3, 0) | ||
| (0, 1, -3) | ||
| (0, -3, 1) |
1.
Joe has a total of 14 pennies, dimes and quarters in his pocket, which total $1.52. The number of dimes and quarters combined is equal to the number of pennies. How many of each coin does Joe have?
Answer
| 7 pennies, 5 dimes, 2 quarters | ||
| 7 pennies, 2 dimes, 5 quarters | ||
| 5 pennies, 7 dimes, 2 quarters | ||
| 2 pennies, 7 dimes, 5 quarters |
1.
Evaluate
Answer
1.
Evaluate
Answer
1.
If matrix A has dimensions 3 x 2 and matrix B has dimensions 3 x 2, can matrix A and matrix B be multiplied?
Answer
| yes | ||
| no |
1.
If matrix A has dimensions 2 x 5 and matrix B has dimensions 5 x 5, can matrix A and matrix B be multiplied?
Answer
| yes | ||
| no |
Evaluate
Answer
1.
Evaluate
Answer
1.
Find the determinant of
Answer
1.
Find the determinant of
Answer
1.
Solve y – 3x = 5 by the substitution method. y + x = 3
Answer
1.
Solve 3x – 5y = 15 by the substitution method. y = 2x + 4
Answer
1.
Solve 3x – 2y = 1 using the elimination method. 4y = 6x – 2
Answer
1.
Solve x – 3y = -17 using the elimination method. -x + 8y = 52
Answer
1.
Solve 4x + 5y = 40 using matrices. x – y = 1
Answer
1.
Solve 5x – 6y = 50 using matrices. -x + 5y = -48
Answer
1.
Find the value of two numbers if their sum is 12 and their difference is 4.
Answer
1.
What is the system of inequalities associated with the following graph?
Answer
| x – y ≥ -3 5x – y ≤ -3 | ||
| x – y ≥ -3 5x + y ≤ -3 | ||
| x – y ≥ 3 5x – y ≤ 3 | ||
| x + y ≥ -3 5x – y ≤ -3 |
1.
What is the system of inequalities associated with the following graph?
Answer
| 3x + y ≥ -3 x + 2y ≤ 4 | ||
| -3x – y ≥ -3 x + 2y ≤ 4 | ||
| 3x + y ≥ -3 x – 2y ≥ 4 | ||
| 3x – y ≤ 3 x – 2y ≥ 4 |
Solve x – 3y + z = 10 using matrices. x + y – 3z = -10 -3x – y + z = 2
Answer
1.
Which matrix represents the image of the triangle with vertices at (-2, 0), (1, 5), and (4, -8) when reflected over the line, y = -x?
Answer
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