M101 7.1-7.3 practice SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the sstem b substitution. 1) - 2 = -16 2-2 = -22 1) 2) 4-5 = 8 9 + 3 = 75 2) Solve the sstem b elimination. 3) + 3 = 8-2 + 4 = -16 3) 4) -7 + 7 = -49 3-2 = 22 4) 1
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Draw a sketch of the two graphs described, with the indicated number of points of intersection. 5) A parabola and a circle; three points 5) A) B) C) D) 2
6) A parabola and a hperbola; four points 6) A) B) C) D) 3
7) An ellipse and a hperbola; four points 7) A) B) C) D) 4
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the sstem graphicall. Do not use a calculator. 8) - = 0 2 - = -4 8) 9) 2 + 2 = 5 - = -1 9) Solve the nonlinear sstem of equations. 10) 2 + 2 = 61 - = 1 10) 11) 2-2 = 39 - = 3 11) Solve the problem. Round to an appropriate number of significant digits. 12) A contractor mies concrete from bags of pre-mi for small jobs. How man bags with 4% cement should he mi with 6 bags of 7% cement to produce a mi containing 5% cement? 12) 5
13) A theatre sells two tpes of tickets to their plas; children's tickets and adult tickets. For toda's performance the have sold a total of 1035 tickets. Also, the have sold 4 times as man children's tickets as adult tickets. How man children's tickets have the sold? 13) Solve the problem. 14) A rectangular plot has area 126 d 2 with a perimeter of 46 d. What is the length of the longest side? 14) 15) Bob fenced in a rectangular garden in his ard. The length of the rectangle is 4 feet longer than the width and the perimeter is 56 feet. What is the width of the rectangle? 15) Use the substitution-of-variable technique to solve the sstem analticall. 16) -9 + 1 = - 19 8 16) -8-2 = - 7 4 17) 4 + 9 = 11 2 17) 8-7 = 41 6 Answer the question. 18) When using the substitution or elimination method to solve a sstem of two equations, ou end up with an equation stating 0 = 7. What does this indicate to ou about the sstem of equations? 18) 19) If the graphs of a sstem of two equations are a line and a parabola, what are the possible numbers of solutions (with real coordinates) of this sstem? 19) 20) If the graphs of a sstem of two equations are a circle and a parabola, what are the possible numbers of solutions (with real coordinates) of this sstem? 20) Solve the sstem analticall. 21) - + 2z = -3 4 + z = -1 + 2 + z = 1 21) 22) - + z = -4 + + z = 0 + - z = -6 22) 23) 2-5 - 3z = -1 6-5 + 6z = 4 10 + 3z = 3 23) 6
Solve the sstem in terms of the arbitrar variable listed. 24) ; 3 + + z = 5 4 + 5 - z = -8 24) 25) ; 2-5 + z = 11 3 + - 6z = 1 25) 26) ; + - 2z = 8 3 + z = - 6 26) Solve the problem. 27) A $64,000 trust is to be invested in bonds paing 8%, CDs paing 6%, and mortgages paing 10%. The bond and CD investment together must equal the mortgage investment. To earn a $5520 annual income from the investments, how much should the bank invest in bonds? 27) Use a sstem of equations to solve problem. 28) Find the equation of the parabola = a 2 + b +c that passes through the points (-2, 0), (0, -6), and (3, 2). 28) 29) Suppose that the position of a particle moving along a straight line is given b s(t) = at 2 + bt + c, where t is time in seconds and a, b, and c are real numbers. If s(0) = -2, s(1) = -2, and s(2) = -10, find a, b, and c. Then find s(10). 29) Write the augmented matri for the sstem. 30) 5 + 2 = 39 7 = 14 30) 31) 5 + 8 + 2z = 48 8 + 6 + 3z = 56 4 + 6 + 8z = 50 31) Write the sstem of equations associated with the augmented matri. Do not solve. 32) 9-8 2-4 -7 9 32) 7
The augmented matri is in row-echelon form and represents a sstem of linear equations. Solve the sstem using back-substitution. 33) 1-5 -5 33) 0 0 8 34) 1 2-3 -2 0 1 4 5 0 0 1 3 34) Solve the sstem. 35) 3 + 5 = 19 5 = -10 35) 36) 8 - + 4z = 86 6 + 8-3z = 58-4 - 2 + z = -36 36) Solve the problem. 37) A chemist has prepared two acid solutions, one of which is 4% acid b volume, another 11% acid. How man cubic centimeters of each should the chemist mi together to obtain 50 cm 3 of 6.66% solution? 38) John has a jarful of quarters and nickels. There are 108 coins in the jar. The value of the coins is $16.80. How man of each tpe of coin are there? 37) 38) 39) Anne and Nanc use a metal allo that is 26.6% copper to make jewelr. How man ounces of a 25% allo must be mied with a 29% allo to form 70 ounces of the desired allo? 39) Provide an appropriate response. 40) Suppose that ou are solving a sstem of three linear equations b the row echelon method and obtain the following augmented matri. 40) 1 11-13 -22 0 0 0 0 0 4-8 -4 What conclusion can ou draw about the solutions of the sstem? 8