ACCUPLACER Next Generation Quantitative Reasoning Algebra and Statistics Version 4 Questions

Explanation

The average of two numbers is their sum divided by 2. We are given that the average of g and 100 is 75. This can be written as the equation (g+100)/2​=75. To find the value of g+100, we can multiply both sides of the equation by 2. This gives us g+100=75×2, which simplifies to g+100=150. Thus, the value of g+100 is 150.

Explanation

The shaded region in the graph is bounded by two solid lines. We can determine the inequality for each boundary line. The first line passes through the origin (0,0) and the point (1,3). The slope of this line is 3−0​/1-0=3, so its equation is y=3x. The shaded region is below this line, which means the inequality is y≤3x. The second line passes through the origin (0,0) and the point (−1,3). The slope of this line is 3−0​/-1-0=−3, so its equation is y=−3x. The shaded region is above this line, which means the inequality is y≥−3x. The combination of these two inequalities is −3x≤y≤3x. While the provided options do not exactly match this derived inequality, the option −x≤y≤3x contains the correct upper boundary (y≤3x) and is the most plausible intended answer, assuming there is a typo in the slope of the lower boundary.

Explanation

The inequality −5≤a≤5 means that the integer values for a can range from -5 to 5. The inequality 1<b<5 means that the integer values for b can be 2, 3, or 4. To find the least integer value of the fraction a/b​, we must find pairs of a and b from their respective sets that produce an integer result, and then select the smallest of those results.

Explanation

To solve the inequality −1≤4x−5, we must isolate the variable x. First, add 5 to both sides of the inequality to get 4≤4x. Then, divide both sides by 4 to find the value of x, which gives us 1≤x. This inequality can also be written as x≥1, which means x can be any number that is greater than or equal to 1. On a number line, this is represented by a solid circle at 1 (to show that 1 is included in the solution set) with shading extending to the right. The other graphs are incorrect as they do not accurately represent this solution.

Explanation

The equation of a line can be written in slope-intercept form, y=mx+b, where m is the slope and b is the y-intercept. By looking at the graph, we can see that the line crosses the y-axis at (0,−1), so the y-intercept is b=−1. To find the slope, we can use two points on the line, such as (0,−1) and (3,0). The slope is m=rise/run​=(0−(−1))/3-0​=1/3​. Substituting these values into the slope-intercept form gives us the equation y=1/3​x−1.