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College algebra final milestone latest update 2024
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College algebra final milestone latest update 2024
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Nursedocs@2024 uytdresas What is the value of the following expression? • 16 • -18 • -2 • 0 RATIONALE To solve this expression, evaluate the exponent for each term. Start with the first term, Any number taken to the power of zero equals 1. So is equal to 1. Evaluate the next term, . When the exponent is 1, the value of the term is the same as its base, so 2 to the first power remains 2. Next, evaluate the term which is the same as ( -3) (-3). Negative 3 times negative 3 equals positive 9. The last term, , indi cates that -2 is multiplied by itself three times. equals -8 because when a negative number is multiplied by itself an odd number of times, the answer remains negative. Finally, evaluate the addition and subtraction from left to right with 1 minus 2. 1 minus 2 is -1. Next, add -1 and 9. NURSEDOCS Nursedocs@2024 uytdresas -1 plus 9 is 8. Finally add 8 and -8. 8 plus -8 is the same as 8 minus 8, or 0. CONCEPT Introduction to Exponents 2 To collect data on the signal strengths in a neighborhood, Tracy must drive from house to house and take readings. She has a graduate student, Dave, to assist her. Tracy figures it would take her eight hours to complete the task working alone, and that it wou ld take Dave 12 hours if he completed the task by himself. How long will it take Tracy and Dave to complete the task together? • 7.2 hours • 6.0 hours • 4.8 hours • 3.6 hours RATIONALE We can use the relationship between work, rate, and time to build equations to solve this problem. To begin, we need to identify the relationship for Tracy and Dave, separately. Tracy's rate is 1 task in 8 hours. We do not know the time it will take them to work on the project together, so we will just denote the time as t. When we multiply the rate and time together, we get Tracy's work at (notice how the units for hours cancel). We can repeat this process for Dave. Dave's rate is 1 task in 12 hours. We do not know the time it will take them to work on the projec t together, so we will just denote the time as t. When we multiply the rate and time NURSEDOCS Nursedocs@2024 uytdresas together, we get Dave's work at . Now we can create a rational equation by adding Tracy and Dave's work together. The work is 1 task, so their combined work is equal t o 1 task. In the rational equation, t is the amount of time it takes Tracy and Dave to complete the task together. With rational equations, we can add them together once they have common denominators. A simple way to find common denominators is to multi ply the denominators of the fractions together. Make sure that you are doing this to all terms to ensure they all end up with the same denominator. Next, evaluate the multiplication. Now we have three fractions with common denominators. Once we have this, we can solve for t using the expressions in the numerator. To solve for t, first combine like terms. 12t plus 8t is equal to 20t. Finally divide both sides by 20 to solve for t. It will take Tracy and Dave 4.8 hours to complete the task toge ther. CONCEPT Rational Equations Representing Work and Rate 3 What is the solution set for the following inequality? 4x – 3 + 6x > 5x + 7 • x < 2 • x < 0.8 • x > 0.8 • x > 2 NURSEDOCSThe benefits of buying summaries with Stuvia:
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