Updated: Aug 31, 2021
The equation ax + b = -5x + b has infinitely many solutions, where a and b are constants. What is the value of a?
Maps to Category 10 of the book.
Answer posted on 08/29/2021: Answer is -5.
For an equation to have infinitely many solutions, expressions on both side of the equation must be equal. Since the value of constant b is same on both sides, a must be -5.
Updated: Aug 31, 2021
What is the x-intercept of a line passing through the points (-1, 1.5) and (0, 4)?
Maps to Category 1 of the book.
Answer posted on 08/22/2021: Answer is -1.6 or -4/2.5.
Since x = 0 at y-intercept, the given point (0, 4) is the y-intercept of the line.
Determine the slope, and plug the slope and the y-intercept in the y = mx + b equation.
Slope = (4 - 1.5)/(0-(-1)) = 2.5/1 = 2.5.
Hence, the equation is y = 2.5x + 4.
Since y = 0 at x-intercept, set y = 0 in the above equation and solve for x.
0 = 2.5x + 4 --> 2.5x = -4 --> x = -4/2.5 = -1.6.
Updated: Aug 31, 2021
John scored 88, 92, 96, and 96 in the first four chemistry tests of the school year. If all the tests are out of 100 and are equally weighted, what is the mean score of the four chemistry tests?
Maps to Category 57 of the book.
Answer posted on 08/15/2021: Answer is 93.
mean = sum of numbers/count of numbers.
sum of numbers = 88 + 92 + 96 + 96 = 372.
count of numbers = 4.
mean = 372/4 = 93
