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college algebra graphs and models
College Algebra 7th Edition Robert F Blitzer - Solutions
Graph each system of equations and find any solutions. Check your answers. Identify the system as consistent or inconsistent. If the system is consistent, state whether the equations are dependent or independent. -2x + y = 2 -x+y=0
Let A be the given matrix. Find A-1. 2-2 05 0 0 1 8
Use a determinant to find the area of the shaded region. 3 (0,0) 1 (1.4) 3 (4,2) X
Graph the solution set to the system of inequalities. x + 2y = 4 2x - y ≥ 6
If possible, find AB and BA. -13 4-[2-48] 3]. = 40 A B = 1 -1 2 03
If possible, solve the system. -X + 2z = -9 -13 = 13 у + 42 = 3x + y У
Let A be the given matrix. Find A-1. 202 150 -1 0 2
Perform each row operation on the given matrix by completing the matrix on the right. 1 -1 2 7 12 -20 R2 + R 0 5 R - R → 1 T - 2
If possible, find AB and BA. -1 A = 2 -1 5 6 1-4 B-[133] 7 -7 =
Graph each system of equations and find any solutions. Check your answers. Identify the system as consistent or inconsistent. If the system is consistent, state whether the equations are dependent or independent. 2x - 2y = 4 -2x - 2y = 4
If possible, find AB and BA. 0 1 34 02 B = -1 0 20-1 14 2
If possible, solve the system. x + y + z = 2x -1 9- = = + 2y+32 = 0
Use a determinant to find the area of the shaded region. ((-3,3) (-1.-3) (2,3)
If possible, find AB and BA. 2 4 -1 -2 0 -5 6 9 B = 1 -1 -1 20
Let A be the given matrix. Find A-1. 3 -1 -1 3-1 3 -1
If possible, solve the system. x = y + 1/2 x + 2y = 32 3z = x + 3y + 2z = -4 20 0
Graph the solution set to the system of inequalities. 3x y ≤ 3 x + 2y = 2
Perform each row operation on the given matrix by completing the matrix on the right. 1-2 3 6 145 5 5 32 2
Evaluate f(3, 4) if f(x, y) = x2 + y2
Use a determinant to find the area of the shaded region. (1,3) (0,0) (3,2) (5,4) ➤X
Graph the solution set in the xy-plane. (a) y ≤-2 (c) x + 2y < -2 2x-3y> -3 (b) 3x - 4y > 12 (d) x² - 2y ≤ 4 2-x² ≥y zy
Graph the solution set to the system of inequalities. 3x + 2y < 6 x + 3y ≤ 6
Graph each system of equations and find any solutions. Check your answers. Identify the system as consistent or inconsistent. If the system is consistent, state whether the equations are dependent or independent. 3x - y = 0 -3x - y = 0
Use Gaussian elimination with backward substitution to solve the system of linear equations. Write the solution as an ordered pair or an ordered triple whenever possible. x + 2y = 3 -x - y = 7
If possible, find AB and BA. 5 3 B = -3 4
If possible, solve the system. ²x + x + y = x-2y+z= y + z -8
Let A be the given matrix. Find A-1. 2-3 5-63 20 3
Determine if B is the inverse matrix of A by evaluating AB and BA. 64 - [31 2 -2.5 -3 4 B =
Graph each system of equations and find any solutions. Check your answers. Identify the system as consistent or inconsistent. If the system is consistent, state whether the equations are dependent or independent. 2x + y = 3 -2x - y = 4
Use a determinant to find the area of the shaded region. (-1.3) (-4,1) (-1, -3) 1 (2.2) (4,0) X
Use Gaussian elimination with backward substitution to solve the system of linear equations. Write the solution as an ordered pair or an ordered triple whenever possible. 2x + 4y = 10 x-2y=-3
Graph each system of equations and find any solutions. Check your answers. Identify the system as consistent or inconsistent. If the system is consistent, state whether the equations are dependent or independent. x - 4y = 4 2x8y = 4
Determine if B is the inverse matrix of A by evaluating AB and BA. A [1 L01 2 1 2 10-1 B = -1 0 2 2 -1 -1 -1 -1
Graph the solution set to the system of inequalities. 4x + 3y = 12 2x+6y= 4
The variable z varies jointly with the square of x and the square root of y. If z = 7.2 when x = 3 and y = 16, find z when x = 5 and y = 4.
If possible, find AB and BA. 11 3 -1 2-2 0 4 1-4 0 B-[419] -13 2
Use the concept of the area of a triangle to determine if the three points are collinear. (1, 3), (-3, 11), (2, 1)
Let A be the given matrix. Find A-1. 1 -1 -1 0 5 5-1 -1 0 0 5-1 -1 1 0-1 0 0-1
Graph the solution set to the system of inequalities. x-2y 20 x-3y ≤ 3
Use Gaussian elimination with backward substitution to solve the system of linear equations. Write the solution as an ordered pair or an ordered triple whenever possible. 2x + 3y = 6 x - 2y = -4
If possible, find AB and BA. 2-13 0 10 2-2 3 B = 15 -1 013 -1 2 1
Let A be the given matrix. Find A-1. 3100 1310 0131 0013
Graph each system of equations and find any solutions. Check your answers. Identify the system as consistent or inconsistent. If the system is consistent, state whether the equations are dependent or independent. 3x-y= 7 у -2x + y = -5
Use the concept of the area of a triangle to determine if the three points are collinear. (3, 6), (-1,-6), (5, 11)
Let A be the given matrix. Find A-1. 1 41 1
Graph each system of equations and find any solutions. Check your answers. Identify the system as consistent or inconsistent. If the system is consistent, state whether the equations are dependent or independent. -x + 2y = 3 3x - y = 1
Use Gaussian elimination with backward substitution to solve the system of linear equations. Write the solution as an ordered pair or an ordered triple whenever possible. 2x - y = 1 2x+y = 3
Graph the solution set to the system of inequalities. 2x - 4y = 4 x + y ≤0
Find A- 3B and AB if -2 -5 34 15 7-10 and B = 3 0-2 5-1 4 -2 6-5
If possible, find AB and BA. A 1 -2 0-2 3 2 -14 2 B = -3 0 1 510
Let A be the given matrix. Find A-1. 0 11 11 Lo 1-
Use the concept of the area of a triangle to determine if the three points are collinear. (-2,-5), (4,4), (2.3)
Represent the system of linear equations in the form AX = B. 2x-3y = 7 -3x - 4y = 9
Use Gaussian elimination with backward substitution to solve the system of linear equations. Write the solution as an ordered pair or an ordered triple whenever possible. X x - 3y = -2 2x - y = -4 у=
Five hundred tickets were sold for a play, generating $3560. The prices of the tickets were $5 for children, $7 for students, and $10 for adults. There were 180 more student tickets sold than adult tickets. Find the number of each type of ticket sold.
Complete the following (a) Write the system in the form AX= B. (b) Solve the linear system by computing X = A-1B. x-3y=4 2x - y = 3
Calculate the determinant of each matrix. (a) -23 35 (b) 1-1 3 4-5 0 0 36
Complete the following (a) Write the system in the form AX= B. (b) Solve the linear system by computing X = A-1B. x - 2y + z = 2x + y + 2z = y + z = 0 10 3
Find A-1 if A = 4-5 -3
Graph the solution set to the system of inequalities. 124 D = ₂ + zx
Use the concept of the area of a triangle to determine if the three points are collinear. (4,-5), (-2, 10), (6, -10)
The table shows the total cost of purchasing various combinations of differently priced DVDs. The types of DVDs are labeled A, B, and C.(a) Let a be the cost of a DVD of type A, b be the cost of a DVD of type B, and e be the cost of a DVD of type C. Write a system of three linear equations whose
If possible, find AB and BA. ^-(-1)] 3 -Q B =
One thousand tickets were sold for a baseball game. There were one hundred more adult tickets sold than student tickets, and there were four times as many tickets sold to students as to children. How many of each type of ticket were sold?
Represent the system of linear equations in the form AX = B. -x + 3y = 10 2х 2x - бу = -1
Graph the solution set to the system of inequalities. x²-y≤0 x² + y² ≤ 6
If possible, find AB and BA. A = [5 -3], B []
Three students buy lunch in the cafeteria. One student buys 2 hamburgers, 2 orders of fries, and 1 soda for $9. Another student buys 1 hamburger, I order of fries, and I soda for $5. The third student buys 1 hamburger and 1 order of fries for $5. If possible, find the cost of each item. Interpret
If a line passes through the points (x1, y1) and (x2, y2), then an equation of this line can be found by calculating the determinant.Find the standard form ax + by = c of the line passing through the given points. 1 det | x y 1 | - . ܐܐ ܕ 1
Use Gaussian elimination with backward substitution to solve the system of linear equations. Write the solution as an ordered pair or an ordered triple whenever possible. -x-2y = 7 -x+ y = -2
Represent the system of linear equations in the form AX = B. x=y=1 -x + 2y = 5
The volume V of an aluminum can is given by V = πr2h, where r is the radius and h is the height. If an aluminum can has a volume of 12 cubic inches and a diameter of 2 inches, find the height of the can to the nearest hundredth of an inch.
In Exercises 83–88, let logb 2 = A and logb 3 = C. Write each expression in terms of A and C. 3/2 logb
Use the formula for compound interest with n compoundings per year to solve this problem. How long, to the nearest tenth of a year, will it take $12,500 to grow to $20,000 at 6.5% annual interest compounded quarterly?
In Exercises 81–100, evaluate or simplify each expression without using a calculator.log 1000
How long, to the nearest tenth of a year, will it take $50,000 to triple in value at 7.5% annual interest compounded continuously?
After a 60% price reduction, you purchase a computer for $440. What was the computer’s price before the reduction?
Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the
In Exercises 81–100, evaluate or simplify each expression without using a calculator.log 107
In Exercises 83–86, determine whether each statement makes sense or does not make sense, and explain your reasoning.My graph of f(x) = 3.2x shows that the horizontal asymptote for f is x = 3.
Write an equation in point-slope form and slope-intercept form of the line passing through (1, −4) and parallel to the line whose equation is 3x - y + 5 = 0.
Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the
In Exercises 83–88, let logb 2 = A and logb 3 = C. Write each expression in terms of A and C.logb 8
In Exercises 81–100, evaluate or simplify each expression without using a calculator.10log 33
What interest rate, to the nearest percent, is required for an investment subject to continuous compounding to triple in 5 years?
Begin by graphing y =|x|. Then use this graph to obtain the graph of y =|x - 2|+ 1.
Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the
In Exercises 81–100, evaluate or simplify each expression without using a calculator.log 108
In Exercises 83–88, let logb 2 = A and logb 3 = C. Write each expression in terms of A and C.logb 6
In Exercises 83–88, let logb 2 = A and logb 3 = C. Write each expression in terms of A and C. 2 log 10%b√27
Use the exponential decay model, A = A0ekt, to solve this exercise. The half-life of polonium-210 is 140 days. How long will it take for a sample of this substance to decay to 20% of its original amount?
Exercises 86–88 will help you prepare for the material covered in the first section.a. Does (4, -1) satisfy x + 2y = 2?b. Does (4, -1) satisfy x - 2y = 6?
According to the U.S. Bureau of the Census, in 2000 there were 35.3 million residents of Hispanic origin living in the United States. By 2010, the number had increased to 50.5 million. The exponential growth function A = 35.3ekt describes the U.S. Hispanic population, A, in millions, t
Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the
In Exercises 83–88, let logb 2 = A and logb 3 = C. Write each expression in terms of A and C.logb 81
In Exercises 81–100, evaluate or simplify each expression without using a calculator.10log 53
Graph x + 2y = 2 and x - 2y = 6 in the same rectangular coordinate system. At what point do the graphs intersect?
Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. In Vex
In Exercises 25–34, begin by graphing f(x) = 2x. Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function’s domain and range. If applicable, use a graphing utility to confirm your
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