The correct answer is 97. The intersecting lines form a triangle, and the angle with measure of x° is an exterior angle of this triangle. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles of the triangle. One of these angles has measure of 23° and the other, which is supplementary to the angle with measure 106°, has measure of 180° − 106° = 74°. Therefore, the value of x is 23 + 74 = 97.

The correct answer is 2.The given expression can be rewritten as \(\frac{2x+6}{(x+2)^{2}}-\frac{2x+4}{(x+2)^{2}}\), which is equivalent to\(\frac{2x+6-2x+4}{(x+2)^{2}}\), or \(\frac{2}{(x+2)^{2}}\). This is in the form \(\frac{a}{(x+2)^{2}}\); therefore, a = 2.

The correct answer is \(\frac{21}{4}\), or 5.25. Use substitution to create a one-variable equation that can be solved for x. The second equation gives that y = 2x. Substituting 2x for y in the first equation gives ¹⁄₂(2x + 2x)=\(\frac{21}{2}\). Dividing both sides of this equation by ¹⁄₂ yields (2x + 2x) = 21. Combining like terms results in 4x = 21. Finally, dividing both sides by 4 gives x = \(\frac{21}{4}\)= 5.25. Either 21/4 or 5.25 can be gridded as the correct answer.

The correct answer is ⁶⁄₅, or 1.2. To solve the equation 2(p + 1) + 8(p − 1) = 5p, first distribute the terms outside the parentheses to the terms inside the parentheses: 2p + 2 + 8p − 8 = 5p. Next, combine like terms on the left side of the equal sign: 10p − 6 = 5p. Subtracting 10p from both sides yields −6 = −5p. Finally, dividing both sides by −5 gives p = ⁶⁄₅ = 1.2. Either 6/5 or 1.2 can be gridded as the correct answer.

The correct answer is 4. The equation 60h + 10 ≤ 280, where h is the number of hours the boat has been rented, can be written to represent the situation. Subtracting 10 from both sides and then dividing by 60 yields h ≤ 4.5. Since the boat can be rented only for whole numbers of hours, the maximum number of hours for which Maria can rent the boat is 4.

Since gasoline costs $4 per gallon, and since Alan’s car travels an average of 25 miles per gallon, the expression \(\frac{4}{25}\) gives the cost, in dollars per mile, to drive the car. Multiplying \(\frac{4}{25}\) by m gives the cost for Alan to drive m miles in his car. Alan wants to reduce his weekly spending by $5, so setting \(\frac{4}{25}\) m equal to 5 gives the number of miles, m, by which he must reduce his driving.

Choices A, B, and C are incorrect. Choices A and B transpose the numerator and the denominator in the fraction. The fraction \(\frac{25}{4}\) would result in the unit miles per dollar, but the question requires a unit of dollars per mile. Choices A and C set the expression equal to 95 instead of 5, a mistake that may result from a misconception that Alan wants to reduce his driving by 5 miles each week; instead, the question says he wants to reduce his weekly expenditure by $5.

The graph of y = −f(x) is the graph of the equation y = −(2^x + 1), or y = −2^x− 1. This should be the graph of a decreasing exponential function. The y-intercept of the graph can be found by substituting the value x = 0 into the equation, as follows: y = −2⁰ − 1 = −1 − 1 = −2. Therefore, the graph should pass through the point (0, −2). Choice C is the only function that passes through this point.

Choices A and B are incorrect because the graphed functions are increasing instead of decreasing. Choice D is incorrect because the function passes through the point (0, −1) instead of (0, −2).

When n is increased by 1, t increases by the coefficient of n, which is 1.

Choices A, C, and D are incorrect and likely result from a conceptual error when interpreting the equation.

Since 9 can be rewritten as 3² , 9^3⁄₄ properties of exponents, this can be written as 3 ^sup>3⁄₂, which can further be rewritten as 3^3⁄₂ (3^1⁄₂), an expression that is equivalent to 3√3.

Choices A is incorrect; it is equivalent to 9^1⁄₃. Choice B is incorrect; it is equivalent to 9^1⁄₄. Choice C is incorrect; it is equivalent to 3^1⁄₂.

The volume of right circular cylinder A is given by the expression πr²h, where r is the radius of its circular base and h is its height. The volume of a cylinder with twice the radius and half the height of cylinder A is given by π(2r)²(¹⁄₂)h, which is equivalent to 4πr¹⁄₂(¹⁄₂)h = 2πr²h.Therefore, the volume is twice the volume of cylinder A, or 2 × 22 = 44.

Choice A is incorrect and likely results from not multiplying the radius of cylinder A by 2. Choice B is incorrect and likely results from not squaring the 2 in 2r when applying the volume formula. Choice D is incorrect and likely results from a conceptual error.