Progressively Harder Math Multiple Choice

Dividing both numbers by three gives the simplified answer of ²⁷/₁₃.

-5 * -6 equals 30, as the negatives cancel. Then, 30 - 7 equals 23.

Division is equal to multiplying by a reciprocal, so ⁸/₅ divided by ¹²/₇ is the same as ⁸/₅ multiplied by ⁷/₁₂. Then, just multiply across, 8 * 7 = 56, 5 * 12 = 60. Finally, divide 4 out of both to simplify, leaving ¹⁴/₁₅.

First, distribute, resulting in 5x + 10 = 8. Then, subtract 10 from both sides, leaving 5x = -2. Finally, divide by 5, leaving x = -2/5.

The slope can be determined for any graph without a y-intercept by dividing y-distance by x-distance for any point on the graph. On the correct answer, (3, 2) is a point, which results in a slope of 2/3.

The ratio of arc length to circumference is directly proportional to the ratio of degrees in the angle to total degrees. Therefore, where arc length is s, 14π/s = 360/60, which simplifies to s = 7π/3.

Since two of the sides are equal, the triangle is isosceles. Therefore, the third side, 8, is perpendicular to and bisected by the height of the triangle. This creates two congruent right triangles, both of which have the side of 4 and the hypotenuse of 5. Therefore, the missing side, the height, is 3 by the Pythagorean Theorem. Then, according the the triangle area formula, the entire carpet has an area of (3)(8)(¹/₂), which simplifies to 12. Then, 12 times $2.02 per square foot is $24.24.

The power rule allows finding derivatives by multiplying the coefficient of each term by the exponent of the term, then subtracting one from the exponent. Do note that constants are multiplied by x⁰, and therefore are eliminated when using the power rule. Then, applying the power rule to each individual term results in 10x⁹ + 112x⁶ - 8x - 2x^-3.

When factored, this rational function is ^{x + 1}/_{(x + 1)(x - 1)}.Then, it shares the common factor (x + 1) in both the numerator and the denominator, which, when set equal to zero, equals -1. Therefore, there is a hole at x = -1. Then, the remaining factor in the denominator is (x - 1), which when set to zero results in the vertical asymptote of x = 1.

Each column in the first matrix is multiplied by its corresponding row in the second matrix. 0 * 4 = 0, -5 * 1 = -5, 11 * -2 = -22. 0 + -5 + -22 = -27.

First, the rational function must be factored into the form ^{(x + 4)(x - 1)(x + 2)}/_{(x + 4)(x - 2)}. Then, (x + 4) cancels out, leaving ^{(x - 1)(x + 2)}/_{(x - 2)}. Plugging in -4 results in -5/3, therefore the limit is -5/3.

e to an imaginary power rotates a radius of 1 around the complex plane. In this case, the power is the arctangent of ³/₄, which indicates that the angle is the same as a right triangle with the ratio of 3 : 4 from its opposite side to its adjacent side. On the complex plane, this results in ⁴/₅ + ³/₅i. Multiplied by the 5 in front of the e, this gives the final answer of 4 + 3i. Alternatively, from a purely formulaic perspective, e^θi = cos(θ) + i * sin(θ), in which case substitution yields the same answer.