|Q1. Verify that the values of the variables listed are solutions of the system of equations.
x = 0, y = -5, z =-4
b. not a solution
Q2. Perform the indicated operation, whenever possible. –
Q3. Solve the system using the inverse method.
a. x = -36, y = -38, z = -14
b. x = -14, y = 88, z = -32
c. x = -60, y = 82, z = -34
d. x = 8, y = 24, z = 10
Q4. Solve the system of equations.
a. x = 0, y = 1, z = 0
b. x = 1, y =1, z = 1
c. x = 0, y = 1, z = -1
d. x = 0, y = 0, z = 1
Q5. A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 8 slices of pizza and 4 soft drinks for $29.40. The second group bought 7 slices of pizza and 6 soft drinks for $30.30. How much does one slice of pizza cost?
a. $2.26 per slice of pizza
b. $2.76 per slice of pizza
c. $2.33 per slice of pizza
d. $1.83 per slice of pizza
Q6. Perform the indicated operations and simplify.
Let A =, B = , and C = . Find AB + BC.
Q7. Find the inverse of the matrix.
a. No inverse
Q8. Jenny receives $1270 per year from three different investments totaling $20,000. One of the investments pays 6% , the second one pays 8%, and the third one pays 5%. If the money invested at 8% is $1500 less than the amount invested at 5%, how much money has Jenny invested in the investment that pays 6%?
Q9. Perform the indicated operation, whenever possible. +
Q10. Verify that the values of the variables listed are solutions of the system of equations.
x = 5, y = 5
a. not a solution
Q11. Solve the system.
a. inconsistent (no solution)
b. (-9, 0)
c. (0, 0)
d. y = – – 9, where x is any real number
Q12. Rob bought 2 pairs of shorts, 3 shirts and a pair of shoes for $146.64. Jessie bought 3 pairs of shorts, 5 shirts and 2 pairs of shoes for $256.35. Allen bought a pair of shorts and 4 shirts for $104.07. What is the price of a pair of shorts? Express answer rounded to two decimal places.
Q13. A movie theater charges $8.00 for adults and $5.00 for children. If there were 40 people altogether and the theater collected $272.00 at the end of the day, how many of them were adults?
a. 16 adults
b. 10 adults
c. 29 adults
d. 24 adults
Q14. Solve the system using the inverse method.
a. x = 1, y = -2
b. x = -2, y = 1
c. x = -1, y = 2
d. x = 2, y = -1
Q15. Use the elimination method to solve the system.
a. x = 11, y = -11
b. x = -2, y = 9
c. x = 9, y = -9
d. x = -9, y = 9
Q16. Write the partial fraction decomposition of the rational expression.
d. + +
Q17. Use the properties of determinants to find the value of the second determinant, given the value of the first.
Given> = 3, find the value of >.
Q18. An 8-cylinder Crown Victoria gives 18 miles per gallon in city driving and 21 miles per gallon in highway driving. A 300-mile trip required 15.5 gallons of gasoline. How many whole miles were driven in the city?
a. 153 miles
b. 168 miles
c. 147 miles
d. 132 miles
Q19. A retired couple has $190,000 to invest to obtain annual income. They want some of it invested in safe Certificates of Deposit yielding 7%. The rest they want to invest in AA bonds yielding 10% per year. How much should they invest in each to realize exactly $17,200 per year?
a. $120,000 at 7% and $70,000 at 10%
b. $130,000 at 7% and $60,000 at 10%
c. $130,000 at 10% and $60,000 at 7%
d. $140,000 at 10% and $50,000 at 7%
Q20. Find the inverse of the matrix.