College Algebra - Final Milestone with Answers!

College Algebra - Final Milestone with Answers. You passed this Milestone 23 questions were answered correctly. 2 questions were answered incorrectly. 1 Which of the following equations is correctly calculated? • -2 × -7 = -14 • 81 ÷ -9 = -9 • -36 ÷ 4 = 9 • 4 × 12 = -48 RATIONALE This is correct. The quotient of a positive and negative number is always negative. This is incorrect. The product of two negative numbers is always positive. The correct product is 14. CONCEPT Multiplying and Dividing Positive and Negative Numbers 2 Select the solution to the following system of equations: • • correct • • RATIONALE This is incorrect. The quotient of a positive and a negative number is always negative. The correct quotient is -9. This is incorrect. The product of two positive numbers is always positive. The correct product is 48. When we add the two equations, the term will cancel, leaving . Now we can solve for by dividing both sides by . Dividing by gives a solution of . Once we divide both sides by , we get a solution of . We can solve for by plugging in for in either equation. Let's use the second equation . Once is plugged in for , evaluate and solve for . Here, by multiplying by , the result contains a term, which will cancel when combined with the second equation. Now, we can add the two equations together. Before you can add equations, sometimes you must multiply entire equations by a scalar value for the method to work as intended. For this system, we can multiply the second equation by . Subtracting a negative is the same as adding a postive . Next, subtract from both sides. On the right side, minus equals . Now we can solve for by dividing both sides by . CONCEPT Solving a System of Linear Equations using the Addition Method 3 Perform the following operations and write the result as a single number. [4 + 8 × (5 – 3)] ÷ 5 + 6 • 10 correct • 10.8 • 2 • 1.8 RATIONALE This is the solution to the system of equations. Following the Order of Operations, we must first evaluate everything in parentheses and grouping symbols. When there are brackets or braces, evaluate the innermost operations first. Here, we must evaluate 5 minus 3 first. 5 minus 3 is 2. There are still operations inside grouping symbols to evaluate. Multiplication comes before addition, so we must evaluate 8 times 2 next. CONCEPT Introduction to Order of Operations 4 Consider the quadratic function . What do we know about the graph of this quadratic equation, based on its formula? • The vertex is and it opens upward. • The vertex is and it opens downward. • The vertex is and it opens upward. 8 times 2 is 16. Next, we add 4 and 16 to complete the operations inside parentheses. 4 plus 16 is 20. Now there is just division and subtraction. Division comes before subtraction in the Order of Operations, so we divide 20 by 5 next. 20 divided by 5 is 4. Lastly, add 4 and 6. 4 plus 6 is 10.