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mathematics
precalculus
Precalculus 9th edition Michael Sullivan - Solutions
Carletta has $10,000 to invest. As her financial consultant, you recommend that she invest in Treasury bills that yield 6%, Treasury bonds that yield 7%, and corporate bonds that yield 8%. Carletta wants to have an annual income of $680, and the amount invested in corporate bonds must be half that
A dietitian at Palos Community Hospital wants a patient to have a meal that has 78 grams (g) of protein, 59 g of carbohydrates, and 75 milligrams (mg) of vitamin A. The hospital food service tells the dietitian that the dinner for today is salmon steak, baked eggs, and acorn squash. Each serving of
A dietitian at General Hospital wants a patient to have a meal that has 47 grams (g) of protein, 58 g of carbohydrates, and 630 milligrams (mg) of calcium. The hospital food service tells the dietitian that the dinner for today is pork chops, corn on the cob, and 2% milk. Each serving of pork chops
Find the function f(x) = ax3 + bx2 + cx + d for which f(-2) = -10, f(-1) = 3, f(1) = 4 and f(3) = 15.
Find the function f(x) = ax3 + bx2 + cx + d for which f(-3) = -112, f(-1) = -2, f(1) = 4 and f(2) = 13.
Find the function y = ax2 + bx + c whose graph contains the points (1, -1), (-3, -1), and (-2, 14).
Find the function y = ax2 + bx + c whose graph contains the points (1, 2), (-2, -7), and (2, -3).
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. — 4х + у %3D 5 2х — у + z — w %3D 5 z + w = 4
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 4х + у + z — w%3D 4 х — у + 2z + Зw %3D 3
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. х — Зу + z %3D 1 2х — у — 4z %3D 0 х — Зу + 2z %3D 1 х — 2у 3D 5
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. z %3D 3 2х + 3у — — г%3D 0 %3D 0 х — у- —х + у + х + у+ 3z %3D 5
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 2x + y - z = 4 -x + y + 3z = 1 4
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. y + z = 5 (3х + 2у — 2z %3D0 х-
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. x + 2y - z = 3 2x - y + 2z = 6 х — Зу + 3z %3D 4 ||
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. x + 2y + z = 1 2x - y + 2z = 2 3x + y + 3z = 3
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. x + y + z + w = -x + 2y + z = 2x + 3y + z – w = 4 6. -2x + y – 2z + 2w = -1
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. х + у +z + w %3D 2х — у +z %3D0 Зх + 2у + z — w %3 х — 2у — 2z + 2w 3D —1 4
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. х + у %3D 1 2х — у+z3D 1 y х + 2у + z 3 3
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 2 Зх + у — %3D 3 2х — у+ %3D 1 8. 4х + 2y 3
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. х + 4у — 3z %3D —8 Зх — у+ 3z %3D 12 х+ у+ 62 %3D 1
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. x + 2y – z = -3 2x – 4y + z = -7 4 -2x + 2y – 3z
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. -4 y + z = 2х — Зу + 4z3D —15 5х + у — 2z %3 12 ||
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. х+ у — z %3D 6 Зх — 2у + z%3D —5 х + Зу — 2z %3D 14
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. Зх — 2у + 2z %3D 7x — Зу + 2z %3D — 1 -1 2х — Зу + 4z %3D
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. Зх — 2y + 2z 7x — Зу + 2z %3D — 1 2х — Зу + 4z 3D 0 3D
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 2х — Зу — z %3D 0 Зх + 2у + 2z 3D 2 х + 5у + 3z 3D 2
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. —х + у + %3D —1 —х + 2у — 3z 3D —4 Зх — 2у — 7z %3D 0
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 2х — Зу — z 3 0 —х + 2у + z%3D5 Зх — 4у — z %3 1
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 2х — 2у — 2z %3D 2 2х + Зу + %3D 2 Зх + 2у %3D 0
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 2x — 2х + 2у + %3D —7 Зх — 4у — 3z 3D 7
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. х — 2у + 3z - 4 2х + у+ z3 —3х + 2у — 2z %3D —10
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 2х + у %3D -4 -2y + 4z Зх — 2z %3D —11
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. х — у%3D 6 2х — 32 %3D 16 2y + z = 4
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. Зх — 5у %3D 3 15х + 5у %3D 21
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. + y = -2 x - 2y = 8
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 2х + 3у %3D 6 х — у 2
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. y = 7 9х — Зу %3D 21 Зх
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. x + 2y = 4 2x + 4y = 8 %3D
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. Зх + 3у %3D 3 4х + 2у %3D 3
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 2х — 4у 3D —2 Зх + 2у %3D 3 -2
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. х + 2у %3 5 = 3
Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. Jx + y = 8 \x - y = 4
The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x, y; or x, y, z; or x1 , x2 , x3 , x4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give
The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x, y; or x, y, z; or x1 , x2 , x3 , x4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give
The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x, y; or x, y, z; or x1 , x2 , x3 , x4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give
The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x, y; or x, y, z; or x1 , x2 , x3 , x4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give
The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x, y; or x, y, z; or x1 , x2 , x3 , x4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give
The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x, y; or x, y, z; or x1 , x2 , x3 , x4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give
The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x, y; or x, y, z; or x1 , x2 , x3 , x4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give
The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x, y; or x, y, z; or x1 , x2 , x3 , x4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give
The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x, y; or x, y, z; or x1 , x2 , x3 , x4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give
The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x, y; or x, y, z; or x1 , x2 , x3 , x4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give
The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x, y; or x, y, z; or x1 , x2 , x3 , x4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give
The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x, y; or x, y, z; or x1 , x2 , x3 , x4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give
Write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix. Rị = -r2 + r r2 + r3 4 -3 -1 3 -5 4 6. R3 = -3 -6 6.
Write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix. R1 = -2r2 + r R3 = 2r, + r3 -2 5 -3 1 2 -5 6 -2 1 4 -4
Write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix. 1 -3 -4 R2 = -6r1 + r2 6. 6 -5 -6 6. R3 = rị + r3 4 -1 4-
Write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix. 1 -3 2 R2 = -2r¡ + r2 -6 R3 = 3r1 + r3 2 -5 3 -4 -3 -6 4
Write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix. 1 -3 R2 = 4r1 + r2 3 -5 -5 3r1 + r3 -4 -5 -3 4 R3 = 3r1 + r3 -3 -2 4.
Write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix. 1 -3 4 3 -5 6 -3r1 + r2 3 R2 R3 = 5r, + r3 3 4 -5
Write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix. -3 -3 -2r, + r2 R2 2 -5 -4
Write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix. R2 = -2rị + r2 -2 5 -3 2 -5
Write the augmented matrix of the given system of equations. y + 2z - w = х + 3у — 4z + 2w %3D 2 - 5z 5 х- 2 Зх — у — 52 — w%3D -1
Write the augmented matrix of the given system of equations. х — у — z3D 10 2х + у + 2z %3D —1 —3х + 4y 4х — 5у + z3 Z.
Write the augmented matrix of the given system of equations. 2х + Зу — 4z %3 х — 52 + 2 %3D 0 х + 2у — 3z % -2
Write the augmented matrix of the given system of equations. х+ у — z %3D 2 3х — 2у 3D 2 y 5х + 3у — z %3D1
Write the augmented matrix of the given system of equations. y - z = 0 х+ у%3D 5 2х — 32 3D 2 5х — у — %3D 0
Write the augmented matrix of the given system of equations. y + z = 10 Зх + 3у %3D 5 + y + 2z = 2
Write the augmented matrix of the given system of equations. 4 3 3 X- 4 3 4
Write the augmented matrix of the given system of equations. 0.03y = 0.06 |0.13.x + 0.10y = 0.20 0.01.x 0.20
Write the augmented matrix of the given system of equations. 9х — у %3D 0 = 0 Зх y – 4 = 0
Write the augmented matrix of the given system of equations. 2х + 3у — 6 %3D 0 4х — бу + 2%3D 0
Write the augmented matrix of the given system of equations. Зх + 4у 3D 7 4х — 2у 3D 5
Write the augmented matrix of the given system of equations. х — 5у %3D 5 4х + Зу 3D 6
The notation refers to the entry in the __________ row and column_________of a matrix.
True or False.The matrix is in row echelon form. 3 1 -2 1
The matrix used to represent a system of linear equations is called a(n)________matrix.
Use the information given in Problem 79. Suppose that a third group purchased 3 deluxe hamburgers, 2 large fries, and 4 large colas for $10.95. Now is there sufficient information to determine the price of each food item? If so, determine each price.
Three painters, Beth, Bill, and Edie, working together, can paint the exterior of a home in 10 hours (hr). Bill and Edie together have painted a similar house in 15 hr. One day, all three worked on this same kind of house for 4 hr, after which Edie left. Beth and Bill required 8 more hr to finish.
One group of customers bought 8 deluxe hamburgers, 6 orders of large fries, and 6 large colas for $26.10. A second group ordered 10 deluxe hamburgers, 6 large fries, and 8 large colas and paid $31.60. Is there sufficient information to determine the price of each food item? If not, construct a
Kelly has $20,000 to invest. As her financial planner, you recommend that she diversify into three investments: Treasury bills that yield 5% simple interest, Treasury bonds that yield 7% simple interest, and corporate bonds that yield 10% simple interest. Kelly wishes to earn $1390 per year in
A Broadway theater has 500 seats, divided into orchestra, main, and balcony seating. Orchestra seats sell for $50, main seats for $35, and balcony seats for $25. If all the seats are sold, the gross revenue to the theater is $17,100. If all the main and balcony seats are sold, but only half the
A movie theater charges $8.00 for adults, $4.50 for children, and $6.00 for senior citizens. One day the theater sold 405 tickets and collected $2320 in receipts. Twice as many children’s tickets were sold as adult tickets. How many adults, children, and senior citizens went to the theater that
A dietitian wishes a patient to have a meal that has 66 grams (g) of protein, 94.5 g of carbohydrates, and 910 milligrams (mg) of calcium. The hospital food service tells the dietitian that the dinner for today is chicken, corn, and 2% milk. Each serving of chicken has 30 g of protein, 35 g of
An application of Kirchhoff’s Rules to the circuit shown results in the following system of equations: Find the currents I1 , I2 and I3. I3 = I1 + I2 8 = 413 + 612 %3D 811 = 4 + 612 4 V 32. 12 V 1Ω
An application of Kirchhoff’s Rules to the circuit shown on page 711 results in the following system of equations: Find the currents I1 , I2 and I3. Iz = I1 + I3 5 - 31, - 51, = 0 10 – 512 – 713 = 0 %3D 13 72 5 V 10 V
In economics, the IS curve is a linear equation that represents all combinations of income Y and interest rates r that maintain an equilibrium in the market for goods in the economy. The LM curve is a linear equation that represents all combinations of income Y and interest rates r that maintain an
In economics, the IS curve is a linear equation that represents all combinations of income Y and interest rates r that maintain an equilibrium in the market for goods in the economy. The LM curve is a linear equation that represents all combinations of income Y and interest rates r that maintain an
Find real numbers a, b, and c so that the graph of the function y = ax2 + bx + c contains the points (-1, -2), (2, 3), and (0, 1).
A doctor’s prescription calls for the creation of pills that contain 12 units of vitamin and 12 units of vitamin E. Your pharmacy stocks two powders that can be used to make these pills: one contains 20% vitamin and 30% vitamin E, the other 40% vitamin and 20% vitamin E. How many units of each
Find real numbers a, b, and c so that the graph of the function y = ax2 + bx + c contains the points (-1, 4), (2, 3), and (0, 1).
A doctor’s prescription calls for a daily intake containing 40 milligrams (mg) of vitamin C and 30 mg of vitamin D. Your pharmacy stocks two liquids that can be used: one contains 20% vitamin C and 30% vitamin D, the other 40% vitamin C and 20% vitamin D. How many milligrams of each compound
The grocery store we use does not mark prices on its goods. My wife went to this store, bought three 1-pound packages of bacon and two cartons of eggs, and paid a total of $13.45. Not knowing that she went to the store, I also went to the same store, purchased two 1-pound packages of bacon and
Pamela requires 3 hours to swim 15 miles downstream on the Illinois River. The return trip upstream takes 5 hours. Find Pamela’s average speed in still water. How fast is the current? (Assume that Pamela’s speed is the same in each direction.)
One group of people purchased 10 hot dogs and 5 soft drinks at a cost of $35.00. A second bought 7 hot dogs and 4 soft drinks at a cost of $25.25. What is the cost of a single hot dog? A single soft drink? We paid $35.00. How much is one hot dog? How much is one soda? We paid $25.25. How much
A restaurant manager wants to purchase 200 sets of dishes. One design costs $25 per set, while another costs $45 per set. If she only has $7400 to spend, how many of each design should be ordered?
The average airspeed of a single engine aircraft is 150 miles per hour. If the aircraft flew the same distance in 2 hours with the wind as it flew in 3 hours against the wind, what was the wind speed?
With a tail wind, a small Piper aircraft can fly 600 miles in 3 hours. Against this same wind, the Piper can fly the same distance in 4 hours. Find the average wind speed and the average airspeed of the Piper. 3 hours 4 hours 600 mi.
A recently retired couple needs $12,000 per year to supplement their Social Security. They have $150,000 to invest to obtain this income. They have decided on two investment options:AA bonds yielding 10% per annum and a Bank Certificate yielding 5%. (a) How much should be invested in each to
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