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mathematics
basic technical mathematics
Basic Technical Mathematics 12th Edition Allyn J. Washington, Richard Evans - Solutions
Find the function f (x) = ax2 + bx + c, if f(1) = −3, f(−3) = −35, and f(3) = −11.
Solve the given systems of equations graphically. y = 2x - 4 y = -x + 3
Solve the given systems of equations by the method of elimination by addition or subtraction. v + 2 = 2v + 4t = 9 1 7
Solve each system of equations by sketching the graphs. Use the slope and the y-intercept or both intercepts. Estimate the result to the nearest 0.1 if necessary. S s - 4t = 8 2st +4
Solve the given systems of equations by use of determinants. 51 +6w 41 7w 31+w7h = 1 3h = 6 2h = -3
Solve the given systems of equations by determinants. 4r = R 4r + 3R 17 3
Solve the given systems of equations by the method of elimination by addition or subtraction. 3x - y = 5 Зу - 9x 9х = -15
Find the slope of the line that passes through the given points.(5, −3), (−2, −5)
Solve the given systems of equations by use of determinants. 3r+st r+t2s 2 = 0 4rs + t = 3
Three oil pumps fill three different tanks. The pumping rates of the pumps (in L/h) are r1, r2, and r3, respectively. Because of malfunctions, they do not operate at capacity each time. Their rates can be found by solving the following system of equations: n + 2 + 3 12 r₁ + 2r₂ =
Solve the given systems of equations by determinants. 12t + 9y = 14 6t = 7y - 16
Solve the given systems of equations graphically. y + 3x = y = 2x - 3 6
Solve each system of equations by sketching the graphs. Use the slope and the y-intercept or both intercepts. Estimate the result to the nearest 0.1 if necessary. y = 4x - 6 2x = y - 4
Find the slope of the line that passes through the given points.(−3, 4), (−7, −4)
Solve each system of equations by sketching the graphs. Use the slope and the y-intercept or both intercepts. Estimate the result to the nearest 0.1 if necessary. y = -x + 3 2y = 6 - 4x
Solve the given systems of equations graphically. 4A 3A + 2B B = 6 12
Find the slope of the line that passes through the given points.(0.4, 0.5), (−0.2, 0.2)
Solve the given systems of equations by the method of elimination by addition or subtraction. 2x - 3y 3x + 2 = 2y 4 = 0
Solve the given systems of equations by determinants. = 3x - y = 3 4x = 3y + 14
The forces acting on a certain girder, as shown in Fig. 5.42, can be found by solving the following system of equations:Find the forces, in newtons. 0.707 F₁ - 0.800F₂ 0.707 F₁+ 0.600F₂ - F₂ 3.00F₂ 3.00F3 = 0 = 10.0 €20.0
Solve the given systems of equations by use of determinants. 2x - 2y + 3z = 5 2x + y 2z = −1 3z + y - 4x = 0
Solve each system of equations by sketching the graphs. Use the slope and the y-intercept or both intercepts. Estimate the result to the nearest 0.1 if necessary. P-6=6v би v = 3-3p V
Solve the given systems of equations graphically. 2x - 5y = 10 3x + y = 6
Solve the given systems of equations by use of determinants. 2u2v + 3w = 0 3u + v + 4w = 21 -u - 3v + 7w = 15
Solve the given systems of equations by the method of elimination by addition or subtraction. 3i₁ + 5 = -4i₂ 3i₂ = 5i₁ 5i₁ - 2
Using Kirchhoff’s laws (see the chapter introduction; the equations can be found in most physics textbooks) with the electric circuit shown in Fig. 5.43, the following equations are found. Findthe indicated currents (in A) I1, I2, and I3. 1.01, +3.0(1₁13) = 12 2.07₂ +4.0(1₂+13) = 12 1.01,
Find the slope of the line that passes through the given points.(−2.8, 3.4), (1.2, 4.2)
Solve each system of equations by sketching the graphs. Use the slope and the y-intercept or both intercepts. Estimate the result to the nearest 0.1 if necessary. x - 4y = 6 2y = x + 4
Solve the given systems of equations graphically. 7x = 2y + 14 y = 4x + 4 -
Solve the given systems of equations by either method of this section. 2x - y = 5 6x + 2y = -5
Solve the systems of equations. it is necessary to set up the appropriate equations. All numbers are accurate to at least three significant digits.Find angles A, B, and C in the roof truss shown in Fig. 5.44. Fig. 5.44 A A+B T 2B C B
Solve the given systems of equations by use of determinants. 3x - 7y + 3z = 6 3x + 3y + 6z = 1 5x5y + 2z = 5
Sketch the line with the given slope and y-intercept.m = 3, (0, 1)
Solve each system of equations by sketching the graphs. Use the slope and the y-intercept or both intercepts. Estimate the result to the nearest 0.1 if necessary. x + y = 3 3x - 2y = 14
Solve each system of equations by sketching the graphs. Use the slope and the y-intercept or both intercepts. Estimate the result to the nearest 0.1 if necessary. - 2r₁ + 2r₂ = 7 4r₁ - 2r₂ 2r₂ = 1
Solve the given systems of equations by use of determinants. 18x + 24y + 4z = 46 63x+6y15z = -75 -90x + 30y - 20z = -55
Solve the given systems of equations graphically. 5v = 15 - 3t t = 6v 12 -
Solve the given systems of equations by either method of this section. 3x + 2y = 4 6x - 6y = 13
Solve the given systems of equations by determinants. 2x-3y - 4 = 0 Зу 3x + 2 = 2y
Solve the given systems of equations graphically. 3M + 4N = 6 2M - 3N = 2
Solve the systems of equations. it is necessary to set up the appropriate equations. All numbers are accurate to at least three significant digits.Under certain conditions, the cost per mile C of operating a car is a function of the speed v (in mi/h) of the car, given byC = av2 + bv + c. If C = 28
Solve the given systems of equations by either method of this section. 6x + 3y + 4 = 0 5y + 9x + 6 = 0
Solve the given systems of equations by determinants. 3i₁ + 5 = −4i₂ 31₂ 5i₁ - 2 =
Solve the given systems of equations graphically. 5x + 2y = 5 4x8y = 6
Solve the given systems of equations by use of determinants. p+ 2q + 2r = 0 2p+6q3r 4p - 3q + 6r = -1 - 8
Solve the given systems of equations by either method of this section. 1 + 6q = 5p 3p 4q = 7
Sketch the line with the given slope and y-intercept.m = 0, (0, 5)
Solve each system of equations by sketching the graphs. Use the slope and the y-intercept or both intercepts. Estimate the result to the nearest 0.1 if necessary. 2x - 3y = -5 3x + 2y = 12
Solve the given systems of equations by use of determinants. 9x + 12y + 2z = 23 21x + 2y 5z = -25 - 6y 18x4z = -11
Solve the systems of equations. it is necessary to set up the appropriate equations. All numbers are accurate to at least three significant digits.In an election with three candidates for mayor, the initial vote count gave A 200 more votes than B, and 500 more votes than C. An error was found, and
Solve the given systems of equations by using an appropriate algebraic method. x + 2y = 5 x + 3y = 7
Solve the given systems of equations by either method of this section. 15x + 10y = 11 20x25y = 7
Sketch the line with the given slope and y-intercept.m = −4, (0, −2)
Solve the given systems of equations by determinants. All numbers are approximate. 0.3x 0.7y= 0.4 - 0.2x + 0.5y = 0.7
Solve each system of equations to the nearest 0.001 for each variable by using a calculator. x = 4y + 2 3y = 2x + 3
Solve the systems of equations. it is necessary to set up the appropriate equations. All numbers are accurate to at least three significant digits.A person invests a total of $22,500 in three different mutual funds, A, B and C. The yields after one year were 5.00%, 6.00%, and 6.50% for funds A, B,
Solve the given systems of equations by determinants. All numbers are approximate. 250R + 225Z = 400 375R675Z = 325
Solve the given systems of equations by using an appropriate algebraic method. 2x - y = 7 x + y = 2
The three points (x1, y1), (x2, y2), and (x3, y3) are collinear (they lie on a single straight line) ifuse this fact to decide if the given points are colliner.(−2, 1), (2, 3), (6, 5) xi Х yı X2 Уг X3 Уз 1 1
Solve the given systems of equations by either method of this section. 2x + 6y = -3 -6x 18y = 5 =
Sketch the line with the given slope and y-intercept.m = 1/2, (0, 0)
Use the determinant at the right. Answer the questions about the determinant for the changes given in each exercise.How does the value change if the first two rows are interchange 24 1 365 = 35 798
Solve the systems of equations. it is necessary to set up the appropriate equations. All numbers are accurate to at least three significant digits.A university graduate school conferred 420 advanced academic degrees at graduation. There were 100 more MA degrees than MS and PhD degrees combined, and
Solve each system of equations to the nearest 0.001 for each variable by using a calculator. 1.2x 2.4y = 4.8 3.0x = -2.0y + 7.2 -
The three points (x1, y1), (x2, y2), and (x3, y3) are collinear (they lie on a single straight line) ifuse this fact to decide if the given points are colliner.(−8, 20), (−3, 6), (1,−8) xi Х yı X2 Уг X3 Уз 1 1
Solve the given systems of equations by using an appropriate algebraic method. 4x + 3y = -4 y = 2x - 3
Sketch the line with the given slope and y-intercept.m = 2/3, (0, -2)
Solve the given systems of equations by determinants. All numbers are approximate. 40s - 30t = 60 20s 40t -50
Solve each system of equations to the nearest 0.001 for each variable by using a calculator. 4.0x3.5y = 1.5 1.4y+ 0.2x = 1.4
Use the determinant at the right. Answer the questions about the determinant for the changes given in each exercise.What is the value if the second row is replaced with the first row (the first row remains unchanged—the first and second rows are the same)? 24 1 365 = 35 798
Solve the systems of equations. it is necessary to set up the appropriate equations. All numbers are accurate to at least three significant digits.The computer systems at three weather bureaus have a combined hard-disk memory capacity of 8.0 TB (terabytes). The memory capacity of systems A and C
Solve the given systems of equations by either method of this section. 12V + 108 = -84C 36C+ 48V + 132 = 0
Solve the given systems of equations by determinants. All numbers are approximate. 0.060x+0.048y = -0.084 0.065y 0.13x = 0.078
Solve the given systems of equations by using an appropriate algebraic method. r = -3s - 2 - 2r9s = 2
Solve the given systems of equations by either method of this section. 66x + 66y=-77 33x 132y = 143
Sketch the line with the given slope and y-intercept.m = −9, (0, 20)
Solve the systems of equations. it is necessary to set up the appropriate equations. All numbers are accurate to at least three significant digits.By weight, one fertilizer is 20% potassium, 30% nitrogen, and 50% phosphorus. A second fertilizer has percents of 10, 20, and 70, respectively, and a
Solve the given systems of equations by determinants. All numbers are approximate. 301x - 529y 385x - 741y 1520 2540
Sketch the line with the given slope and y-intercept.m = −0.3, (0, −1.4)
Solve the systems of equations. it is necessary to set up the appropriate equations. All numbers are accurate to at least three significant digits.The average traffic flow (number of vehicles) from noon until 1 p.m. in a certain section of one-way streets in a city is shown in Fig. 5.45. Explain
Solve the given systems of equations by using an appropriate algebraic method. 10i 27v 29 - = 40i 33v + 69
Solve each system of equations to the nearest 0.001 for each variable by using a calculator. 5F - 2T = 7 4T + 3F = 8
Use the determinant at the right. Answer the questions about the determinant for the changes given in each exercise.How does the value change if the elements of the first row are added to the corresponding elements of the second row (the first row remains unchanged)? 24 1 365 = 35 798
Show that the given systems of equations have either an unlimited number of solutions or no solution. If there is an unlimited number of solutions, find one of them. x - 2y3z = 2 x - 4y - 13z = 14 -3x + 5y + 4z = = 0
Solve the given systems of equations by either method of this section. 44 A 115B 5B 227A
Solve the given systems of equations by using an appropriate algebraic method. 3x-6y = 5 2y + 7x = 4
Solve each system of equations to the nearest 0.001 for each variable by using a calculator. x - 5y = 10 2x - 10y = 20
Use the determinant at the right. Answer the questions about the determinant for the changes given in each exercise.How does value change if each element of the first row is multiplied by 2? 24 1 365 = 35 798
Show that the given systems of equations have either an unlimited number of solutions or no solution. If there is an unlimited number of solutions, find one of them. x2y3z = 2 x - 4y - 13z = 14 -3x + 5y + 4z = 2
Find the slope and y-intercept of the line with the given equation and sketch the graph using the slope and y-intercept. A calculator can be used to check your graph.y = −2x + 1
Solve the given systems of equations by determinants. All numbers are approximate. 0.25d + 0.63n = -0.37 -0.61d 1.80n = 0.55 -
In analyzing the forces on the bell-crank mechanism shown in Fig. 5.49, the following equations are found. Find the forces. A 0.60F - B 6.0A 80 0.80F = 0 10F = 0
Solve the given systems of equations by either method of this section. 60x - 40y = 80 2.9x2.0y = 8.0
Solve each system of equations to the nearest 0.001 for each variable by using a calculator. 18х - Зу -Зу 2y = 1 + 12x = 7
Solve the given systems of equations by either method of this section. 2b = 60 - 16 33а = 4b +39
Solve the given systems of equations by determinants. All numbers are approximate. 1.2y + 10.8 -8.4x 3.5x + 4.8y + 12.9 = 0
Show that the given systems of equations have either an unlimited number of solutions or no solution. If there is an unlimited number of solutions, find one of them. 3x + 3y2z = 2 2x = - y + z = 1 x - 5y + 4z -3
Find the slope and y-intercept of the line with the given equation and sketch the graph using the slope and y-intercept. A calculator can be used to check your graph.y = −4x
Solve each system of equations to the nearest 0.001 for each variable by using a calculator. 1.9v = 3.2t 1.2t - 2.6v 2.6v = 6
Solve the given systems of equations by using an appropriate algebraic method. 7x = 2y - 6 7y = 12 - 4x
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