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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 quart 25 gallons of antifreeze at $6.50 per gallon 24 tires at an average price of $49.75 per tire 4 batteries at a total price of $140 various 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 3 Operations on Matrices

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row rows 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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Barnett/Ziegler/Byleen Finite Mathematics 11e 5 Example: Addition Solution 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

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6 Example: Subtraction Solution Now, we will subtract the same two matrices Subtract corresponding entries as follows: =

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Matrix Addition Example:

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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 Example:

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To add matrices, we add the corresponding elements. They must have the same dimensions. A + B

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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.

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ADDITIVE INVERSE OF A MATRIX:

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Find the additive inverse:

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Scalar Multiplication: We multiply each # inside our matrix by k.

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Barnett/Ziegler/Byleen Finite Mathematics 11e 18 Matrix Equations Example: Find a, b, c, and d so that Solution: Subtract the matrices on the left side: Use the definition of equality to change this matrix equation into 4 real number equations: a - 2 = 4b + 1 = 3c + 5 = -2d - 6 = 4 a = 6b = 2 c = -7d = 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 womens 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?

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