Milestone Tips Remember that Milestones are open-book. Take the Practice Milestone before taking the Milestone. Take the Milestone at a time and in a place where you can be focused and undisturbed for the entire Milestone time limit. 1 The graph of a linear function passes through the points and . FindIthLe sElopSe oTf thOis fNuncEtion. RATIONALE Since we have two points from a linear function, use the slope formula to find the slope of the line. The slope is the difference in coordinates from the two points divided by the difference in coordinates from the same two points. When plugging in the values it is important to be consistent with which coordinates are subtracted in the calculations. Now that the numbers are plugged in, evaluate the subtraction in both the numerator and the denominator. In the numerator, the difference in coordinates is minus , which is the same as plus , or . In the denominator, the difference in coordinates is minus , which is is CONCEPT the same as plus , or . The slope of the line is 3 over 5. Determining Slope Report an issue with this question Reported. Thanks for your feedback. 2 For the equation 1.75n = 7, what is the value of n? 6 5.25 4 0.25 RATIONALE To find the value of n, we need to isolate it to one side of the equation. We do this by performing inverse operations to both sides of the equation. Since n is being multiplied by 1.75, we will divide both sides by 1.75, because division is the inverse of multiplication. On the left side, n will become isolated once we divide by 1.75. On the right side, we have 7 divided by 1.75. 7 divided by 1.75 is equal to 4. The solution to the equation is n = 4. CONCEPT 2/16 Solving single-step equations Report an issue with this question Reported. Thanks for your feedback. 3 3/16 The Elster family drove 9.25 hours on the first day of their road trip. How many minutes is this equivalent to? 154 minutes 33,300 minutes 555 minutes 9,256 minutes RATIONALE CONCEPT In general, we use conversion factors to convert from one unit to another. A conversion factor is a fraction with equal quantities in the numerator and denominator, but written with different units. We want to convert hours to minutes. We know how many minutes are in 1 hour. We will use this fact to set up a conversion factor. There are 60 minutes in 1 hour so to convert 9.25 hours into minutes, we will multiply by the fraction fraction numerator 60 space m i n u t e s over denominator 1 space h o u r end fraction. Notice how the fractions are set up. The units of hours will cancel, leaving only minutes. Finally we can evaluate the multiplication by multiplying across the numerator and denominator. In the numerator, 9.25 times 60 equals 555. 9.25 hours is equivalent to 555 minutes. Converting Units Report an issue with this question Reported. Thanks for your feedback. 4 Perform the following operations and write the result as a single number. 34 – 18 – (-23) 29 39 75 -7 RATIONALE We can first evaluate the subtraction from left to right. Begin by evaluating 34 minus 18. 34 minus 18 equals 16. Next evaluate 16 minus negative 23. Subtracting a negative is equivalent to adding its opposite: so 16 – (-23) is the same as 16 + 23. 16 plus 23 equals 39. CONCEPT Adding and Subtracting Positive and Negative Numbers Report an issue with this question Reported. Thanks for your feedback. 5 Consider the function . What are the domain and range of this function? RATIONALE A Square root function has the domain restriction that the radicand (the value underneath the radical) cannot be negative. To find the specific domain, construct an inequality showing that the radicand must be greater than or equal to zero. The expression under the radical, , must be greater than or equal to zero. To solve this inequality, add to both sides to undo the subtraction of . This tell us that must be greater than or equal to . In other words, must be less than or equal to . We can write this inequality in the other direction. This is the domain of the function, which means all values must be less than or equal to . To find the range, consider the fact that it is not possible for the input of the function to be a negative number. 4/16 For all x-values less than or equal to 4, the function will have non-negative values for y that only get bigger and bigger as x increases. The range is all values greater than or equal to zero. CONCEPT Finding the Domain and Range of Functions Report an issue with this question Reported. Thanks for your feedback. 6 The population of a small town is decreasing at a rate of 3?ch year. The following table shows a projection of the population, , after years. Years Population 0 8,500 1 8,245 2 7,998 3 7,758 4 7,525 If the population of the small town is currently 8,500 people, how many years will it take for the population to reach 5,500 people? 14.7 years 13.3 years 14.3 years 13.7 years RATIONALE in general, exponential decay is modeled using this equation. We will use information from the problem to find values to plug into this equation. The initial population is , so this is the value for a. The rate of change is so this is our value for b (remember to write this as a decimal). We want to know how many years until the population is , which will be our value for 1 minus is . Next, divide both sides by . y. We need to solve for the time, x. Start by simplifying what's inside the parentheses. We are now left with an exponential expression on the right side. To undo the variable exponent, take the log of both sides. Once we have taken the log of both sides, apply the Power Property of Logs, which allows exponents inside logs to be written as outside factors. Since x is outside the log expression, divide both sides by . x is now isolated. To evaluate, use a calculator to find the value of and . is equal to and is equal to . Finally, divide. CONCEPT It will take 14.3 years for the population to reach 5500. Exponential Decay Report an issue with this question Reported. Thanks for your feedback. 7 Consider the quadratic inequality . What is the solution set? RATIONALE To solve a quadratic inequality, first rewrite it as an equation set equal to zero. Once we have a quadratic equation, we can solve it by factoring. The expression is a basic quadratic equation because it is in the form x squared plus b x plus c and can be factored as left parenthesis x plus p right parenthesis left parenthesis x plus q right parenthesis. Next, identify two integers, product is the constant term, , and whose sum is the x-term coefficient, . p and q, whose Two integers that multiply to and add to are and . Now that we have identified p and q, we can substitute the values int