Although the exact values of m and n are not known, it can be determined that the difference of m and n is always positive. This is true because subtracting a negative number is the same as adding the positive. Since n < 0, subtracting the negative n will always be a net addition to the value of m, which is a positive number to begin with. Therefore, answer choice A is correct.

Since ¹⁄₄ inch on the blueprint represents an actual length of 1 foot, 1 inch on the blue print represents an actual length of 4 feet. When the room is 3 inches by 4¹⁄₄ inches on the blueprint, it is actually 4(3) feet by 4(4¹⁄₄) feet. Because the room is rectangular, the area is equal to length times width, so the area is 4(3) × 4(4¹⁄₄)= 12 × 17 = 204 square feet.

To find the next term in the geometric sequence, recall that when looking at a geometric sequence, the nth term can be written (for some base number b) as bn. This sequence is decreasing in magnitude, thus the absolute value of b is less than 1. It also alternates signs, which indicates that b is negative. At this point, mathematical intuition might suggest trying b = −¹⁄₃, and then calculating for what value of n the terms in the given sequence correspond (see table).

To find the value of the expression 2x³ − x² + 3x + 5 for x = −2, simply substitute −2 into the expression wherever there is an x, as follows:
2(−2)³ − (−2)² + 3(−2) + 5
2(−8) − (4) + 3(−2) + 5
2(−8) − 4 + (−6) + 5
Recall that when taking negative numbers to odd powers, they retain their negative sign; however, when negative numbers are taken to even powers, they become positive. Thus the expression 2(−8) − 4 + (−6) + 5 is equivalent to −16 − 4 − 6 + 6 = 21.

If the length of the chord XY is 8, then the length of the segment XZ is 4. The right triangle XCZ has a hypotenuse of 5 (equal to the radius), leg of 4, and second leg equal to the length of segment CZ. To find the length of segment CZ you can use the Pythagorean Theorem for a right triangle (c² = a² + b² where c is the hypotenuse and a and b are legs):
5² = 4² + CZ²
CZ² = 5² − 4²
CZ² = 25 − 16
CZ² = 9
CZ = 3

If t is the speed of the truck, then twice the speed of the truck can be written as 2t. If the speed of the car exceeded twice the speed of the truck by 15 mph, the car’s speed was 2t + 15.

To find half of 9 feet 6 inches, recall that there are 12 inches in a foot. Therefore, 9 feet 6 inches is equal to 9(12) + 6 = 114 inches. Half of 114 inches is 57 inches, which is equivalent to 4 feet 9 inches [4(12) + 9 = 57].

To determine the ratios, it is helpful to assign numerical values to the lengths of the segments. In this case, since the ratio of AB to BC is 1:4, let AB have a length of 1 and BC have a length of 4. Since AC = AB + BC, it can be given a length of 5. Therefore, the ratio of lengths AB to AC is 1:5.

To solve this problem, divide the number of those people in favor of constructing a new high school by the total number of people polled and simplify, as follows:
44 ÷ (44 + 58 + 8) = 44/110 = 2/5