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mathematics
precalculus

Questions and Answers of Precalculus

An application of Kirchhoff’s Rules to the circuit shown results in the following system of equations: Find the currents I1 , I2 , I3 and I4. I = 13 + I2 24 – 611 – 313 = 0
A Florida juice company completes the preparation of its products by sterilizing, filling, and labeling bottles. Each case of orange juice requires 9 minutes (min) for sterilizing, 6 min for filling,
To manufacture an automobile requires painting, drying, and polishing. Epsilon Motor Company produces three types of cars: the Delta, the Beta, and the Sigma. Each Delta requires 10 hours (hr) for
An application of Kirchhoff’s Rules to the circuit shown results in the following system of equations: Find the currents I1 , I2 , I3 and I4. -4 + 8 – 212 = 0 8 = 514 + I1 4 =
A landscape company is hired to plant trees in three new subdivisions. The company charges the developer for each tree planted, an hourly rate to plant the trees, and a fixed delivery charge. In one
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
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
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
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
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 +
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
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 —
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
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
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 ,
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 ,
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 ,
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 ,
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 ,
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 ,
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 ,
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 ,
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 ,
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 ,
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 ,
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 ,
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
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
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 +
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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

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