AnswersAlgebraic ReasoningModeling with Matrices

Modeling with Matrices — Quiz Answers

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A test is worth 100 points. The test is made up of 40 items. Each item is worth either 2 points or 3 points. Which matrix equation and solution represent the situation?

A
the 2 by 3 matrix row 1, 1 1 40 row 2, 2 3 100 There are 20 items worth 2 points each and 20 items worth 3 points each.
B
the 2 by 3 matrix row 1, 1 1 40 row 2, 2 3 100 There are 10 items worth 2 points each and 30 items worth 3 points each.
C
the 2 by 3 matrix row 1, 1 2 40 row 2, 1 3 100 There are 10 items worth 2 points each and 30 items worth 3 points each.
D
the 2 by 3 matrix row 1, 1 2 40 row 2, 1 3 100 There are 20 items worth 2 points each and 20 items worth 3 points each.
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A trail mix is made up of peanuts that cost p dollars per pound and dried fruit that costs d dollars per pound. A blend of 1 half pound of peanuts and 3 fourths pound of dried fruit costs 6 point 5 0 dollars A blend of 3 fourths pound of peanuts and 1 fourth pound of dried fruit costs 4 point 5 0 dollars Which matrix equation can be used to solve for the cost of 1 pound of peanuts and the cost of 1 pound of dried fruit?

A
the 2 by 2 matrix, row 1, column 1, 1 half column 2, 3 fourths row 2, column 1, 3 fourths column 2, 1 fourth the 2 by 1 column matrix p d is equal to the 2 by 1 column matrix 6 point 5 0 4 point 5 0
B
the 2 by 2 matrix, row 1, column 1, 1 half column 2, 3 fourths row 2, column 1, 3 fourths column 2, 1 fourth the 2 by 1 column matrix p d is equal to the 2 by 1 column matrix 4 point 5 0 6 point 5 0
C
the 2 by 2 matrix, row 1, column 1, 1 half column 2, 3 fourths row 2, column 1, 3 fourths column 2, 1 fourth the 2 by 1 column matrix d p is equal to the 2 by 1 column matrix 6 point 5 0 4 point 5 0
D
the 2 by 2 matrix, row 1, column 1, 1 half column 2, 3 fourths row 2, column 1, 3 fourths column 2, 1 fourth the 2 by 1 column matrix d p is equal to the 2 by 1 column matrix 4 point 5 0 6 point 5 0
3

A chemist has a container of 12 percent peroxide solution and a container of 20 percent peroxide solution. She needs to mix the two solutions to create 100 mL of a 14 percent solution. If x represents the amount of 12 percent peroxide solution and y represents the amount of 20 percent peroxide solution she needs, which matrix equation can determine the amount of each solution she needs to make the 14 percent solution?

A
the 2 by 2 matrix row 1, 1 1 row 2, 0 point 1 2 0 point 2 the 2 by 1 column matrix x y is equal to the 2 by 1 column matrix 14 100
B
the 2 by 2 matrix row 1, 0 point 1 2 0 point 2 row 2, 1 1 the 2 by 1 column matrix x y is equal to the 2 by 1 column matrix 0 point 1 4 100
C
the 2 by 2 matrix row 1, 1 1 row 2, 0 point 1 2 0 point 2 the 2 by 1 column matrix x y is equal to the 2 by 1 column matrix 0 point 1 4 100
D
the 2 by 2 matrix row 1, 0 point 1 2 0 point 2 row 2, 1 1 the 2 by 1 column matrix x y is equal to the 2 by 1 column matrix 14 100
4

Indira has 18 coins valued at 4 point 2 0 dollars She has only quarters and dimes. Which augmented matrix can be used to determine the number of quarters and dimes in the collection?

A
the 2 by 3 matrix row 1, 1 0 point 2 5 4 point 2 0 row 2, 1 0 point 1 0 18
B
the 2 by 3 matrix row 1, 1 1 18 row 2, 0 point 2 5 0 point 1 0 4 point 2 0
C
the 2 by 3 matrix row 1, 1 0 point 2 5 18 row 2, 1 0 point 1 0 4 point 2 0
D
the 2 by 3 matrix row 1, 1 1 4 point 2 0 row 2, 0 point 2 5 0 point 1 0 18
6

For a client, a landscaper purchases 3 oak trees and 4 maple trees for 380 dollars For his own home, the landscaper purchases 2 oak trees and 5 maple trees for 370 dollars Which augmented matrix represents the situation?

A
the 2 by 3 matrix row 1, 3 2 380 row 2, 4 5 370
B
the 2 by 3 matrix row 1, 4 5 380 row 2, 3 2 370
C
the 2 by 3 matrix row 1, 2 5 380 row 2, 3 4 370
D
the 2 by 3 matrix row 1, 3 4 380 row 2, 2 5 370
7

Janelle is five years younger than Louisa. In three years, Janelle will be half Louisa’s age. If j represents Janelle’s age now and l represents Louisa’s age now, which matrices represent the situation?

A
the 2 by 2 matrix, row 1, column 1, 1 column 2, negative 1 row 2, column 1, 1 column 2, negative 1 half the 2 by 1 column matrix j l is equal to the 2 by 1 column matrix row 1 5 row 2 negative 3 halves
B
the 2 by 2 matrix, row 1, column 1, 1 column 2, negative 1 row 2, column 1, 1 column 2, negative 1 half the 2 by 1 column matrix j l is equal to the 2 by 1 column matrix row 1 5 row 2 negative 3
C
the 2 by 2 matrix, row 1, column 1, 1 column 2, negative 1 row 2, column 1, 1 column 2, negative 1 half the 2 by 1 column matrix j l is equal to the 2 by 1 column matrix row 1 negative 5 row 2 negative 3 halves
D
the 2 by 2 matrix, row 1, column 1, 1 column 2, negative 1 row 2, column 1, 1 column 2, negative 1 half the 2 by 1 column matrix j l is equal to the 2 by 1 column matrix row 1 negative 5 row 2 negative 3
8

Jeremy’s fruit stand sells peaches and watermelons. In the first hour the fruit stand is open, 12 bushels of peaches and 5 watermelons are sold for a total of 150 dollars In the second hour, 15 bushels of peaches and 8 watermelons are sold for a total of 198 dollars A bushel of peaches costs p dollars, and a watermelon costs w dollars. Which matrix equation represents the situation?

A
the 2 by 2 matrix row 1, 5 12 row 2, 8 15 the 2 by 1 column matrix p w is equal to the 2 by 1 column matrix 150 198
B
the 2 by 2 matrix row 1, 12 5 row 2, 15 8 the 2 by 1 column matrix p w is equal to the 2 by 1 column matrix 150 198
C
the 2 by 2 matrix row 1, 5 8 row 2, 12 15 the 2 by 1 column matrix p w is equal to the 2 by 1 column matrix 150 198
D
the 2 by 2 matrix row 1, 12 15 row 2, 5 8 the 2 by 1 column matrix p w is equal to the 2 by 1 column matrix 150 198
9

A test is worth 100 points. The test is made up of 40 items. Each item is worth either 2 points or 3 points. Which matrix equation and solution represent the situation?

A
the 2 by 3 matrix row 1, 1 1 40 row 2, 2 3 100 There are 10 items worth 2 points each and 30 items worth 3 points each.
B
the 2 by 3 matrix row 1, 1 2 40 row 2, 1 3 100 There are 20 items worth 2 points each and 20 items worth 3 points each.
C
the 2 by 3 matrix row 1, 1 1 40 row 2, 2 3 100 There are 20 items worth 2 points each and 20 items worth 3 points each.
D
the 2 by 3 matrix row 1, 1 2 40 row 2, 1 3 100 There are 10 items worth 2 points each and 30 items worth 3 points each.

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