[III] Opinions Presented in the Open-Ended Question Responses
Practice Open-Ended Question (10 mins )
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Transcript of Practice Open-Ended Question (10 mins )
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Practice Open-Ended Question (10 mins)
“Keeping Records at the Gas Station”
Juan has a part-time job at a gas station. Part of his responsibility is to keep track of the sales of stock items. During one week last July he sold the following:
160 quarts of oil at an average price of $1.45 per quart25 gallons of antifreeze at $6.50 per gallon24 tires at an average price of $49.75 per tire4 batteries at a total price of $140various auto supply accessories at a total price of
$245.75
A.) What was the total income from the sale of all these items?
B.) What percent of sales did the accessories represent?
C.) If Juan received a 5% commission on total sales, and a salary of $100 a week, how much did Juan earn that week?
D.) If Juan is offered another job for a salary of $150 a week without commission, should he quit his current job? Why or why not? Support your answer.
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HSPA Prep Lesson 3Operations on Matrices
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row
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A matrix is a rectangular array of numbers. We subscript entries to tell their location in the array
Matrices are identified by
their size.
Matrices and Row Operations
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columnthj
rowthiaij
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5Barnett/Ziegler/Byleen Finite Mathematics 11e
Example: AdditionSolution
Add the matrices
Solution: First note that each matrix has dimensions of 3x3, so we are able to perform the addition. The result is shown at right:
Adding corresponding entries, we have 4 3 1 1 2 3
0 5 2 6 7 95 6 0 0 4 8
3 1 46 2 75 10 8
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Example: SubtractionSolution
Now, we will subtract the same two matrices
Subtract corresponding entries as follows:
4 3 1 1 2 30 5 2 6 7 95 6 0 0 4 8
4 ( 1) 3 2 1 30 6 5 ( 7) 2 95 0 6 ( 4) 0 8
5 5 26 12 115 2 8
=
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Matrix Addition
2 4 1 05 0 2 11 3 3 3
Example:
3 47 12 0
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Scalar Multiplication
To do this, multiply each entry in the matrix by the number outside (called the scalar). This is like distributing a number to a polynomial.
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Scalar Multiplication
2 44 5 01 3
Example:
8 1620 04 12
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To add matrices, we add the corresponding elements. They must have the same dimensions.
5 0 6 34 1 2 3
A B
A + B
5 6 0 34 2 1 3
1 36 4
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2 1 3 0 0 02.)
1 0 1 0 0 0
2 1 31 0 1
When a zero matrix is added to another matrix of the same dimension, that same matrix is obtained.
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To subtract matrices, we subtract the corresponding elements. The matrices must have the same dimensions.1 2 1 13.) 2 0 1 3
3 1 2 3
1 1 2 ( 1)2 1 0 33 2 1 3
0 33 35 4
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4 1 6 51.)
6 3 7 3
1 3 2 2 1 52.)
4 0 5 6 4 3
2 613 0
1 4 72 4 8
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ADDITIVE INVERSE OF A MATRIX:1 0 2
3 1 5A
1 0 23 1 5
A
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Find the additive inverse:
2 1 56 4 3
2 1 56 4 3
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Scalar Multiplication:
1 2 31 2 34 5 6
k
We multiply each # inside our matrix by k.
1 2 31 2 34 5 6
k k kk k kk k k
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3 01.) 3
4 5
9 012 15
2
1 22.) 5 4 1
0 5
xy
x
2
5 10 520 5 50 25 5
xy
x
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18Barnett/Ziegler/Byleen Finite Mathematics 11e
Matrix EquationsExample: Find a, b, c, and d so that
2 1 4 35 6 2 4
a bc d
Solution: Subtract the matrices on the left side:2 1 4 35 6 2 4
a bc d
Use the definition of equality to change this matrix equation into 4 real number equations:a - 2 = 4 b + 1 = 3 c + 5 = -2 d - 6 = 4 a = 6 b = 2 c = -7 d = 10
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On your own:
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Practice Open-Ended (10 mins)
Discounts & Sales Tax
Sports Authority is having a sale. Every item in the store is discounted, however the discounts vary throughout the store!
1.) An jacket in the women’s clothing department is regularly priced at $60 and is on sale for $42.
Determine the percent discount rate for this
item.
2.) Find the total cost for a Nike tennis racket that is regularly priced at $125 and is on sale for
15% off. (*include a 6% sales tax.)
3.) If all of the sneakers are on sale at the % discount rate in #2, and the sales price for a pair of Nike sneakers is $85 (not including tax), what was the original price of the sneakers?