Deck 43: Multivariable Linear Systems

Question 1

Solve the system of linear equations and check any solution algebraically.? $$\left\{ \begin{aligned}5 x - 3 y + 2 z & = 3 \\2 x + 4 y - z & = 7 \\x - 11 y + 4 z & = 3\end{aligned} \right.$$ ?

A)? $( - 3,7,3 )$
B)No solution
C)? $( 3,7 , - 3 )$
D)? $( - 3,7 , - 3 )$
E)? $( 3,7,3 )$

Answer 1

No solution

Question 2

Find the equation of the circle $x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$ that passes through the points. ?? $( 0,0 ) , ( 0 , - 3 ) , ( 4,0 )$ ?

A)? $x ^ { 2 } + y ^ { 2 } - 4 x + 3 y = 0$
B)? $x ^ { 2 } - y ^ { 2 } - 4 x - 3 y = 0$
C)? $x ^ { 2 } + y ^ { 2 } - 4 x - 3 y = 0$
D)? $x ^ { 2 } + y ^ { 2 } + 4 x + 3 y = 0$
E)? $x ^ { 2 } - y ^ { 2 } - 4 x + 3 y = 0$

Answer 2

? $x ^ { 2 } + y ^ { 2 } - 4 x + 3 y = 0$

Question 3

Use back-substitution to solve the system of linear equations.? $$\left\{ \begin{array} { c c } 2 x + y - 3 z & = 10 \\y + z & = 6 \\z & = 4\end{array} \right.$$ ?

A)? $$( 10,1,4 )$$
B)? $$( - 10,2 , - 4 )$$
C)? $( 10,2 , - 4 )$
D)? $( 10,2,4 )$
E)? $( - 10,2,4 )$

Answer 3

? $( 10,2,4 )$

Question 4

A small corporation borrowed $771,000 to expand its clothing line.Some of the money was borrowed at 8%,some at 9%,and some at 10%.How much was borrowed at each rate if the annual interest owed was $67,500 and the amount borrowed at 8% was four times the amount borrowed at 10%? ​

A)$252,000 at 8% $456,000 at 9%
$63,000 at 10%
B)$252,000 at 9% $456,000 at 8%
$63,000 at 10%
C)$252,000 at 8% $63,000 at 9%
$63,000 at 9%
D)$252,000 at 8% $63,000 at 9%
$63,000 at 10%
E)$252,000 at 8% $63,000 at 9%
$456,000 at 10%

Question 5

Use back-substitution to solve the system of linear equations.? $$\left\{ \begin{array} { c c } x - y + 2 z & = 22 \\3 y - 8 z & = - 9 \\z & = - 9\end{array} \right.$$ ?

A)? $( - 13 , - 27 , - 9 )$
B)? $( 13 , - 27 , - 9 )$
C)? $( - 13,27 , - 9 )$
D)? $( 13 , - 27,9 )$
E)? $( 13,27 , - 9 )$

Question 6

Find the equation of the parabola $y = a x ^ { 2 } + b x + c$ that passes through the points. ?? $( 0,0 ) , ( 4 , - 4 ) , ( 8,0 )$ ?

A)? $\frac { 1 } { 4 }$ x² - 4 y
B)? $\frac { 1 } { 4 }$ x² -2 x
C)?- $\frac { 1 } { 4 }$ x² - 4 x
D)? $\frac { 1 } { 4 }$ x² + 4 x
E)?- $\frac { 1 } { 4 }$ x² + 4 x

Question 7

Solve the system of linear equations and check any solution algebraically.? $$\left\{ \begin{array} { l l } 2 x + y - z & = 5 \\x - 2 y + 2 z & = - 7 \\3 x - y + z & = 3\end{array} \right.$$ ?

A)? $( 5 , - 7,3 )$
B)? $( 5 , - 7 , - 3 )$
C)? $( - 5 , - 7,3 )$
D)No solution
E)? $( - 5 , - 7 , - 3 )$

Question 8

Solve the system of linear equations and check any solution algebraically.? $$\left\{ \begin{array} { l } 5 x + 3 y + 17 z = 0 \\6 x + 4 y + 22 z = 0 \\5 x + 2 y + 19 z = 0\end{array} \right.$$ ?

A)? $( - 5,6 , - 5 )$
B)? $( - 5,6,5 )$
C)? $( 5,6 , - 5 )$
D)? $( 5,6,5 )$
E)? $( 0,0,0 )$

Question 9

Solve the system of linear equations and check any solution algebraically.? $$\left\{ \begin{array} { l } 6 y + 4 z = - 24 \\3 x + 3 y = 21 \\2 x - 3 z = 22\end{array} \right.$$ ?

A)? $( - 4,0 , - 11 )$
B)? $( - 11,0 , - 4 )$
C)? $( 11,0 , - 4 )$
D)? $( - 4,0,11 )$
E)? $( 11 , - 4,0 )$

Question 10

Solve the system of linear equations and check any solution algebraically.? $$\left\{ \begin{array} { c c } x + y + z & = 16 \\2 x - y + z & = 18 \\3 x - z & = 19\end{array} \right.$$ ?

A)? $( 8 , - 3 , - 5 )$
B)? $( - 8 , - 3,5 )$
C)? $( 8,3,5 )$
D)? $( - 8 , - 3 , - 5 )$
E)? $( 8 , - 3,5 )$

Question 11

Solve the system of linear equations and check any solution algebraically.? $$\left\{ \begin{array} { l } 2 x + 2 z = 14 \\5 x + 3 y = 16 \\3 y - 4 z = 16\end{array} \right.$$ ?

A)? $( - 28 , - 52 , - 35 )$
B)? $( 28 , - 52 , - 35 )$
C)? $( - 28,52,35 )$
D)? $( 28 , - 52,35 )$
E)? $( 28,52,35 )$

Question 12

Find the equation of the parabola $y = a x ^ { 2 } + b x + c$ that passes through the points. ?? $( 0,5 ) , ( 1,6 ) , ( 2,5 )$ ?

A)? $x ^ { 2 } + 2 x + 5$
B)? $- x ^ { 2 } - 2 x - 5$
C)? $- x ^ { 2 } - 2 x + 5$
D)? $- x ^ { 2 } + 2 x + 5$
E)? $- x ^ { 2 } + 2 x - 5$

Question 13

Determine whether the ordered triple is a solution of the system of equations.? $$\left\{ \begin{aligned}4 x + y - z & = 0 \\- 8 x - 6 y + z & = - \frac { 7 } { 4 } \\3 x - y & = - \frac { 9 } { 4 }\end{aligned} \right.$$ ? $$\left( \frac { - 1 } { 2 } , \frac { 3 } { 4 } , \frac { - 5 } { 4 } \right)$$ ? ?

A)Yes
B)No

Question 14

Use back-substitution to solve the system of linear equations. ?? $$\left\{ \begin{array} { c l } 2 x - y + 5 z & = 24 \\y + 2 z & = 9 \\z & = 7\end{array} \right.$$ ?

A)? $$( - 8 , - 5,7 )$$
B)?? $$( - 8,5,7 )$$
C)?? $( - 8 , - 5 , - 7 )$
D)?? $( - 7 , - 5,7 )$
E)?? $( - 8 , - 5 , - 5 )$

Question 15

Determine whether the ordered triple is a solution of the system of equations. ?
?? $$\left\{ \begin{array} { c l } 6 x - y + 2 z & = 26 \\4 x - 3 z & = 26 \\2 x + 5 z & = 0\end{array} \right.$$ ?? $$( 5,0 , - 2 )$$ ?

A)No
B)Yes

Question 16

Determine whether the ordered triple is a solution of the system of equations.? $$\left\{ \begin{array} { l } 3 x + 4 y - z = 16 \\5 x - y + 2 z = 26 \\2 x - 3 y + 7 z = 30\end{array} \right.$$ ?? $$( 4,2,4 )$$ ?

A)No
B)Yes

Question 17

Solve the system of linear equations and check any solution algebraically.? $$\left\{\begin{array} { l } 3 x + 3 y = 0 \\6 x + 3 y - z & = 0 \\12 x + 3 y + 3 z & = 0\end{array}\right.$$ ?

A) $( - 3,6,12 )$ ?
B)?(0,0,0)
C)? $( - 3,6 , - 12 )$
D)? $( 3,6,12 )$
E)? $( 3,6 , - 12 )$

Question 18

Find the equation of the circle $x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$ that passes through the points. ?? $( 0,0 ) , ( 0,12 ) , ( 6,6 )$ ?

A)? $x ^ { 2 } - y ^ { 2 } + 12 y = 0$
B)? $x ^ { 2 } - y ^ { 2 } - 12 y = 0$
C)? $- x ^ { 2 } + y ^ { 2 } - 12 y = 0$
D)? $x ^ { 2 } + y ^ { 2 } - 12 y = 0$
E)? $x ^ { 2 } + y ^ { 2 } + 12 y = 0$

Question 19

Use back-substitution to solve the system of linear equations.? $$\left\{ \begin{array} { c c c } 4 x - 3 y - 2 z & = & 21 \\6 y - 5 z & = & 5 \\z & = & - 7\end{array} \right.$$ ?

A)? $( - 2 , - 5 , - 7 )$
B)? $( - 2,5,7 )$
C)? $( - 5,7 , - 2 )$
D)? $( - 2 , - 5,7 )$
E)? $( - 5 , - 7 , - 2 )$

Question 20

Find the equation of the circle $x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$ that passes through the points. ?? $( 0,0 ) , ( 6,6 ) , ( 12,0 )$ ?

A)? $x ^ { 2 } + y ^ { 2 } + 12 x = 0$
B)? $x ^ { 2 } + y ^ { 2 } - 12 x = 0$
C)? $x ^ { 2 } - y ^ { 2 } - 12 x = 0$
D)? $x ^ { 2 } - y ^ { 2 } + 12 x = 0$
E)? $- x ^ { 2 } + y ^ { 2 } - 12 x = 0$

Question 21

The perimeter of a triangle is 110 feet.The longest side of the triangle is 21 feet longer than the shortest side.The sum of the lengths of the two shorter sides is 12 feet more than the length of the longest side.Find the lengths of the sides of the triangle. ​

A)50 ft,33 ft,28 ft
B)49 ft,34 ft,28 ft
C)49 ft,33 ft,50 ft
D)49 ft,33 ft,28 ft
E)49 ft,35 ft,28 ft

Question 22

Find the value of x,y and z in the figure.​ ​ where a = 6,b = 14
​

A)​x = 33°,y = 94°,z = 53°
B)​x = 33°,y = 53°,z = 94°
C)​x = 94°,y = 94°,z = 53°
D)x = 33°,y = 53°,z = 53°
E)​x = 60°,y = 60°,z = 60°

Question 23

Solve the system of linear equations.? $$\left\{ \begin{array} { c c c } x + y + z & = 2 \\x - y + 2 z & = - 13 \\- 4 y - z & = - 33\end{array} \right.$$

A)? $( - 7,8,1 )$
B)? $( 8 , - 7,1 )$
C)? $( 7 , - 8,3 )$
D)?? $( - 8,7,3 )$
E)?? $( - 4,6,0 )$

Question 24

A mixture of 7 pounds of fertilizer A,21 pounds of fertilizer B,and 8 pounds of fertilizer C provides the optimal nutrients for a plant.Commercial brand X contains equal parts of fertilizer B and fertilizer C.Commercial brand Y contains one part of fertilizer A and two parts of fertilizer B.Commercial brand Z contains two parts of fertilizer A,five parts of fertilizer B,and two parts of fertilizer C.How much of each fertilizer brand is needed to obtain the desired mixture? ​

A)Brand X = 12 lb Brand Y = 15 lb
Brand Z = 9 lb
B)Brand X = 12 lb Brand Y = 9 lb
Brand Z = 9 lb
C)Brand X = 12 lb Brand Y = 15 lb
Brand Z = 15 lb
D)Brand X = 12 lb Brand Y = 9 lb
Brand Z = 15 lb
E)Brand X = 9 lb Brand Y = 15 lb
Brand Z = 12 lb

Question 25

Find the value of x,y and z in the figure.​ ​ where a = 3
​

A)​x = 60°,y = 60°,z = 57°
B)​x = 60°,y = 63°,z = 57°
C)​x = 63°,y = 63°,z = 57°
D)​x = 57°,y = 63°,z = 60°
E)​x = 60°,y = 60°,z = 60°

Question 26

Perform the row operation and find the equivalent system. Add Equation 1 to Equation 2.? $$\left\{ \begin{array} { c c c } x - 4 y + 5 z & = 9 & \text { Equation 1 } \\- x + 5 y - 9 z & = 8 & \text { Equation 2 } \\4 x - 5 z & = 0 & \text { Equation 3 }\end{array} \right.$$ ?

A)? $- y + 4 z = 17$
B)? $- 4 y + z = 17$
C)? $- 4 y - z = 17$
D)? $y + 4 z = 17$
E)? $y - 4 z = 17$

Question 27

Use back-substitution to solve the system of linear equations.? $$\left\{ \begin{array} { c c c } - 3 x - 9 y - 7 z & = 0 \\4 y + 2 z & = - 8 \\z & = & 6\end{array} \right.$$

A)? $( 1,6 , - 5 )$
B)? $( - 5,1,6 )$
C)? $( 3 , - 5,6 )$
D)? $( 1 , - 5,6 )$
E)? $( 6 , - 5,1 )$

Question 28

Determine whether the statement is true or false. ​
If a system of three linear equations is inconsistent,then its graph has one points common to all three equations.
​

A)False
B)True

Question 29

Find values of x,y,and ? that satisfy the system.These systems arise in certain optimization problems in calculus,and ? is called a Lagrange multiplier.? $$\left\{ \begin{array} { c } 5 x - 5 x \lambda = 0 \\- 2 y + \lambda = 0 \\y - x ^ { 2 } = 0\end{array} \right.$$ ?

A)? $x = \pm \frac { \sqrt { 2 } } { 2 } , y = \frac { 1 } { 2 } , \lambda = - 1 \text { or } x = 0 , y = 0 , \lambda = 0$
B)? $x = \pm \frac { \sqrt { 2 } } { 2 } , y = \frac { 1 } { 2 } , \lambda = 1 \text { or } x = 0 , y = 1 , \lambda = 1$
C)? $x = \pm \frac { \sqrt { 2 } } { 2 } , y = \frac { 1 } { 2 } , \lambda = 1 \text { or } x = 0 , y = 0 , \lambda = 0$
D)? $x = \pm \frac { \sqrt { 2 } } { 2 } , y = - \frac { 1 } { 2 } , \lambda = 1 \text { or } x = 0 , y = 0 , \lambda = 0$
E)? $x = - \frac { \sqrt { 2 } } { 2 } , y = \frac { 1 } { 2 } , \lambda = 1 \text { or } x = 0 , y = 0 , \lambda = 0$

Question 30

Find values of x,y,and ? that satisfy the system.These systems arise in certain optimization problems in calculus,and ? is called a Lagrange multiplier.? $\left\{\begin{array}{ll}2 x+\lambda & =0 \\2 y+\lambda & =0 \\x+y-10 & =0\end{array}\right.$ ?

A)x = 5?,y = -10,? = -10
B)?x = 5,y = 5,? = 5
C)x = -10,y = 5,? = -10
D)x = 5,y = -10,? = 5
E)x = 5,y = 5,? = -10

Question 31

?Determine which one of the ordered triples below is a solution of the given system of equations. $$\left\{ \begin{array} { l l } 5 x + 7 y - 7 z & = 11 \\2 x - 3 y - z & = - 18 \\3 x - 4 y + z & = - 41\end{array} \right.$$

A)? $( - 2 , - 4 , - 6 )$
B)? $( - 2 , - 4 , - 7 )$
C)? $( - 6,2 , - 9 )$
D)? $( - 9,2 , - 6 )$
E)? $( 2,6,9 )$

Question 32

A health insurance company advertises on television,on radio,and in the local newspaper.The marketing department has an advertising budget of $45,000 per month.A television ad costs $1,000,a radio ad costs $200 ,and a newspaper ad costs $500 .The department wants to run 70 ads per month,and have as many television ads as radio and newspaper ads combined.How many of each type of ad can the department run each month? ​

A)Television = 35 ads Radio = 25 ads
Newspaper = 10 ads
B)Television = 20 ads Radio = 25 ads
Newspaper = 10 ads
C)Television = 25 ads Radio = 10 ads
Newspaper = 35 ads
D)Television = 35 ads Radio = 30 ads
Newspaper = 10 ads
E)Television = 35 ads Radio = 10 ads
Newspaper = 25 ads

Question 33

The perimeter of a triangle is 170 feet.The longest side of the triangle is 5 feet shorter than twice the shortest side.The sum of the lengths of the two shorter sides is 36 feet more than the length of the longest side.Find the lengths of the sides of the triangle.
​

A)67 ft,67 ft,36 ft
B)68 ft,67 ft,36 ft
C)-68 ft,67 ft,36 ft
D)69 ft,67 ft,36 ft
E)67 ft,67 ft,67 ft

Question 34

Solve the system of linear equations and check any solution algebraically.? $$\left\{ \begin{array} { c } x + 4 z = 1 \\x + y + 10 z = 10 \\2 x - y + 2 z = - 5\end{array} \right.$$ ?

A)? $( 4,10 , - 2 )$
B)? $( - 4,10,2 )$
C)? $( - 4,10 , - 2 )$
D)? $( 4,10,2 )$
E)No solution

Question 35

You work as a disc jockey at your college radio station.You are supposed to play 44 songs within two hours.You are to choose the songs from the latest rock,dance,and pop albums.You want to play twice as many rock songs as pop songs and four more pop songs than dance songs.How many of each type of song will you play? ​

A)Rock =24 Dance = 8
Pop =8
B)Rock =24 Dance = 8
Pop =12
C)Rock =12 Dance = 8
Pop = 24
D)Rock =12 Dance = 8
Pop =12
E)Rock =24 Dance = 12
Pop =12

Question 36

A small corporation borrowed $800,000 to expand its line of toys.Some of the money was borrowed at 8%,some at 9%,and some at 10%.How much was borrowed at each rate if the annual interest owed was $67,400 and the amount borrowed at 8% was five times the amount borrowed at 10%? ​

A)$575,000 at 8%
$110,000 at 9%
$115,000 at 10%
B)$575,000 at 8%
$115,000 at 9%
$115,000 at 9%
C)$575,000 at 9%
$110,000 at 8%
$115,000 at 10%
D)$575,000 at 8%
$115,000 at 9%
$110,000 at 10%
E)$575,000 at 8%
$115,000 at 9%
$115,000 at 10%

Question 37

Solve the system of linear equations. $$\left\{ \begin{array} { l l } - x + 2 y - 5 z & = - 24 \\2 x + 5 z & = 25 \\4 x + 4 y + 3 z & = 21\end{array} \right.$$

A)? $( - 5,5,2 )$
B)? $( - 2,3,5 )$
C)? $( 5,2 , - 5 )$
D)? $( 5 , - 2,3 )$
E)? $( 5 , - 2,0 )$

Question 38

A chemist needs 10 liters of a 25% acid solution.The solution is to be mixed from three solutions whose concentrations are 10%,20%,and 50%.How many liters of each solution will satisfy each condition? Use 2 liters of the 50% solution. ​

A)7 L of 10%,7 L of 20%,2 L of 50%
B)1 L of 10%,2 L of 20%,7 L of 50%
C)1 L of 10%,7 L of 20%,1 L of 50%
D)1 L of 10%,7 L of 20%,2 L of 50%
E)7 L of 10%,1 L of 20%,2 L of 50%

Question 39

Find values of x,y,and ? that satisfy the system.These systems arise in certain optimization problems in calculus,and ? is called a Lagrange multiplier. ?? $$\left\{ \begin{array} { l } 2 + 2 y + 2 \lambda = 0 \\2 x + 1 + \lambda = 0 \\2 x + y - 96 = 0\end{array} \right.$$ ?

A)?x = 24,y = -49,? = 24
B)?x = -49,y = 48,? = -49
C)?x = 24,y = 48,? = -49
D)x = 24,y = -49,? = -49
E)?x = 24,y = 48,? = 48

Question 40

Find values of x,y,and ? that satisfy the system.These systems arise in certain optimization problems in calculus,and ? is called a Lagrange multiplier.? $\left\{\begin{array}{ll}y+\lambda & =0 \\x+\lambda & =0 \\x+y-18 & =0\end{array}\right.$ ?

A)?x = 9,y = 9,? = -9
B)?x = 9,y = -9,? = -9
C)?x = 9,y = -9,? = 9
D)?x = 9,y = 9,? = 9
E)?x = -9,y = 9,? = -9

Question 41

Solve the system of linear equations.? $$\left\{ \begin{array} { l l } - 2 x + 3 y - 4 z & = - 19 \\4 x - y - z & = 22 \\4 x + y - z & = 12\end{array} \right.$$

A)? $( 1 , - 4 , - 4 )$
B)? $( 4 , - 5 , - 1 )$
C)? $( - 5 , - 1,4 )$
D)inconsistent
E)? $( - 4,1 , - 4 )$

Question 42

An object moving vertically is at the given heights at the specified times.Find the position equation $s = \frac { 1 } { 2 } a t ^ { 2 } + v _ { 0 } t + s _ { 0 }$ for the object. At t = 1 second,s = 299 feet
At t = 2 seconds,s = 281 feet
At t = 3 seconds,s = 231 feet

A)? $s = - 16 t ^ { 2 } - 30 t + 299$
B)? $s = - 16 t ^ { 2 } - 30 t - 285$
C)? $s = - 32 t ^ { 2 } + 30 t + 299$
D)? $s = - 16 t ^ { 2 } + 30 t + 285$
E)? $s = - 8 t ^ { 2 } + 2 t - 285$

Question 43

Find the equation of the circle $x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$ that passes through the points $( - 4 , - 1 ) , ( - 6 , - 3 ) , ( - 2 , - 3 )$ .

A)? $x ^ { 2 } + y ^ { 2 } + 8 x + 6 y + 29 = 0$
B)? $x ^ { 2 } + y ^ { 2 } + 4 x + 3 y - 4 = 0$
C)? $x ^ { 2 } + y ^ { 2 } + 8 x + 6 y - 4 = 0$
D)? $x ^ { 2 } + y ^ { 2 } + 4 x + 3 y + 21 = 0$
E)? $x ^ { 2 } + y ^ { 2 } + 8 x + 6 y + 21 = 0$

Question 44

Solve the system of linear equations.? $$\left\{ \begin{array} { c l } x + y + z + w & = - 1 \\- 2 x + y + 3 z - w & = 6 \\2 x + 2 z - 2 w & = - 18 \\2 x + 4 y - 4 z + w & = 5\end{array} \right.$$

A)? $( - 5,2 , - 1,3 )$
B)? $( - 5,2,3 , - 1 )$
C)? $( 3,2 , - 1 , - 5 )$
D)inconsistent
E)? $( - 5 , - 1,2,3 )$

Question 45

A residential building contractor borrowed $29,000 to complete a new home.Some of the money was borrowed at 4%,some at 6%,and some at 7%.How much was borrowed at each rate if the annual interest owed was $1,580 and the amount borrowed at 6% is two times more than the amount borrowed at 7%?

A)$11,000 at 4%;$12,000 at 6%;$6,000 at 7%
B)$9,000 at 4%;$14,000 at 6%;$6,000 at 7%
C)$9,000 at 4%;$13,000 at 6%;$7,000 at 7%
D)$10,000 at 4%;$10,000 at 6%;$8,000 at 7%
E)$10,000 at 4%;$14,000 at 6%;$7,000 at 7%

Question 46

Solve the system,if possible.? $$\left\{ \begin{array} { l } 8 x + 5 y + 6 z = 22 \\4 x - 9 y + 2 z = 78 \\7 x - 7 y - 10 z = 57\end{array} \right.$$ ?

A)x = -1,y = 12,z = -2
B)x = 5,y = -6,z = 2
C)x = -5,y = 6,z = -2
D)x = -5,y = 5,z = -2
E)no solution;inconsistent system

Question 47

?Applying Kirchhoff's Laws to the electrical network in the figure,the currents I₁,I₂,and I₃ are the solution of the system $$\left\{ \begin{array} { l l } I _ { 1 } - I _ { 2 } + I _ { 3 } & = 0 \\6 I _ { 1 } + 3 I _ { 2 } & = 11 \\3 I _ { 2 } + 5 I _ { 3 } & = 6\end{array} \right.$$ Find the currents.? $\begin{array} { l } V _ { 1 } = 11 \text { volts, } V _ { 2 } = 6 \text { volts } \\R _ { 1 } = 6 \Omega , R _ { 2 } = 3 \Omega , R _ { 3 } = 5 \Omega\end{array}$ ?

A)?I₁ = $- \frac { 40 } { 3 }$ amperes;I₂ = $\frac { 91 } { 3 }$ amperes;I₃ = -17 amperes
B)?I₁ = $\frac { 10 } { 9 }$ amperes;I₂ = $\frac { 13 } { 9 }$ amperes;I₃ = $\frac { 1 } { 3 }$ amperes
C)?I₁ = 6 amperes;I₂ = 3 amperes;I₃ = 5 amperes
D)?I₁ = $\frac { 70 } { 33 }$ amperes;I₂ = $- \frac { 19 } { 33 }$ amperes;I₃ = $\frac { 17 } { 11 }$ amperes
E)?I₁ = 70 amperes;I₂ = 91 amperes;I₃ = 21 amperes

Question 48

Solve the system,if possible. ?? $$\left\{ \begin{array} { l } x + y = - 9 \\y + z = - 15 \\2 x - z = 7\end{array} \right.$$ ?

A)x = -9,y = 12,z = 5
B)x = 1,y = -10,z = -5
C)x = -1,y = 10,z = 5
D)x = -9,y = 1,z = 5
E)no solution;inconsistent system

Question 49

Write the partial fraction decomposition of the rational expression.?? $$\frac { 3 } { x ^ { 2 } + 5 x + 4 }$$

A)?1 $\left( \frac { 1 } { x - 1 } - \frac { 1 } { x - 4 } \right)$
B)?1 $\left( \frac { 1 } { x + 1 } - \frac { 1 } { x + 4 } \right)$
C)?1 $\left( \frac { 1 } { x + 4 } - \frac { 1 } { x + 1 } \right)$
D)? $\frac { 3 } { x ^ { 2 } } + \frac { 3 } { 5 x }$ + $\frac { 3 } { 4 }$
E)? $\frac { 3 } { x ^ { 2 } + 5 x + 4 }$

Question 50

In a particular area of the United States,the electric utility company has determined that the average monthly electric bill (in dollars)for homeowners varies with the average monthly temperature (degrees Fahrenheit)as shown in the table below. $$\begin{array} { | l | l | } \hline \begin{array} { l } \text { Average monthly temp. } \\{}^\circ\text {F }\end{array} & \begin{array} { l } \text { Average monthly electric bill } \\\$\end{array} \\\hline 40 & 78 \\\hline 60 & 61 \\\hline 80 & 108 \\\hline\end{array}$$ Find a least squares regression parabola that models the data and use that to estimate the average monthly electric bill in a month with average temperature of 57 ^oF.

A)y = 0.07(57)² - 7.85(57)+ 304 = $84
B)y = 0.06(57)² - 6.85(57)+ 304 = $108
C)y = 0.07(57)² - 5.85(57)+ 304 = $198
D)y = 0.08(57)² - 8.85(57)+ 304 = $59
E)y = 0.08(57)² - 4.85(57)+ 304 = $287

Question 51

Solve the system,if possible. ?? $$\left\{ \begin{array} { l l } x + y + z & = - 20 \\2 x + y + z & = - 30 \\5 x + y - z & = - 46\end{array} \right.$$ ?

A)x = -10,y = -3,z = -7
B)x = 10,y = 3,z = 7
C)x = -2,y = -10,z = 7
D)x = -13,y = -6,z = 7
E)no solution;inconsistent system

Question 52

Find the equation of the parabola $y = a x ^ { 2 } + b x + c$ that passes through the points. $( - 1,4 ) , ( 0,4 ) , ( 1,0 )$ ?

A)? $y = - x ^ { 2 } - 2 x + 4$
B)? $y = - 2 x ^ { 2 } - 2 x - 4$
C)? $y = - 2 x ^ { 2 } + 2 x - 4$
D)? $y = - x ^ { 2 } - 2 x + 3$
E)? $y = - 2 x ^ { 2 } - 2 x + 4$

Question 53

Solve the system,if possible. ​
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Question 54

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { 1 } { x ^ { 2 } + 6 x }$

A)? $\frac { A } { x ^ { 2 } } + \frac { B } { x + 6 }$
B)? $\frac { A } { x } + \frac { B x } { x + 6 }$
C)? $\frac { A } { x } - \frac { B x } { x + 6 }$
D)? $\frac { A } { x } + \frac { B } { x + 6 }$
E)? $\frac { A } { x ^ { 2 } } + \frac { B x } { x + 6 }$