multiple choice

What fraction lies exactly halfway between 2/3 and 3/4? A) 3/5 B) 5/6 C) 7/12 D) 9/16 E) 17/24 Halfway means taking the average, which is dividing the sum of the fractions by 2 for 2 fractions: 1/2(2/3 + 3/4) 1/2(2/3) + 1/2(3/4) 1/3 + 3/8 We need common denominators, so we type this fraction...

If a, b, and c are positive integers such that a^b = x and c^b = y, then xy = ? A) ac^b B) ac^2b C) (ac)^b D) (ac)^2b E) (ac)^b^2 xy = a^b * c^b We can use the Power of a Product Rule a^b * c^b = (ac)^b Therefore: xy = (ac)^b - Answer C

If f(x) = (3x + 7)^2, then f(1) = ? A) 10 B) 16 C) 58 D) 79 E) 100 f(1) = (3(1) + 7)^2 f(1) = (3 + 7)^2 f(1) = 10^2 f(1) = 100 - Choice E

Given f = cd^3, f = 450, and d = 10, what is c? A) 0.5 B) 4.5 C) 15 D) 45 E) 150 Plugging in our numbers, we get: c(10)^3 = 450 Since 10^3 = 1000, we have: 1000c = 450 Typing this equation into our search engine, we get: c = 0.45 Answer B

On a particular road map, 1/2 inch represents 18 miles. About how many miles apart are 2 towns that are 2 1/2 inches apart on this map? A) 18 B) 22 1/2 C) 36 D) 45 E) 90 Set up a proportion of inches to miles where m is the number of miles for 2 1/2 inches. Note: 1/2 = 0.5 and 2 1/2 = 2.5...

Which of the following is equivalent to the sum of the expression a^2 - 1 and a + 1? A) a^2 + a B) a^3 - 1 C) 2a^2 D) a^3 a^2 - 1 + a + 1 The 1's cancel, so we're left with: a^2 + a - Answer A

If (a - b)/b = 3/7, which of the following must also be true? A) a/b = -4/7 B) a/b = 10/7 C) (a + b)/b = 10/7 D) (a - 2b)/b = -11/7 We can rewrite (a - b)/b as: a/b - b/b = 3/7 Since b/b = 1, we have: a/b - 1 = 3/7 Since -1 = -7/7, we have: a/b - 7/7 = 3/7 Add 7/7 to each side: a/b - 7/7 +...

2 ways to do this: Method 1 If 3r = 18, what is the value of 6r + 3? A) 6 B) 27 C) 36 D) 39 If we type in the equation 3r = 18 into our search engine, we get: r = 6 Take r = 6, and subtitute it into 6r + 3: 6(6) + 3 36 + 3 39 or Answer D Method 2: 6r + 3 = 3r(2) = 3 We're given 3r = 18, so...

If x = 2y/3 and y = 18, what is the value of 2x - 3? A) 21 B) 15 C) 12 D) 10 Substitute the values into the equation: 2(2y/3) - 3 <-- Given x = 2y/3 Simplifying, we have: 4y/3 - 3 Now substitute y = 18 into this: 4(18)/3 - 3 4(6) - 3 24 - 3 21 or Answer A

If 3(c + d) = 5, what is the value of c + d? A) 3/5 B) 5/3 C) 3 D) 5 Divide each side of the equation by 3 to isolate c + d 3(c + d)/3 = 5/3 Cancel the 3's on the left side, we get: c + d = 5/3, or answer B

The expression (5x - 2)/(x + 3) is equivalent to which of the following? A) (5 - 2)/3 B) 5 - 2/3 C) 5 - (2/(x + 3)) D) 5 - (17/(x + 3)) Let's start with an integer x = 2. Plug that into our original expression, and we get: (5(2) - 2)(2 + 3) (10 - 2)/5 8/5 So what we do next is, take x = 2...

Which of the following equations represents a line that is parallel to the line with equation y = -3x + 4? A) 6x + 2y = 15 B) 3x - y = 7 C) 2x - 3y = 6 D) x + 3y = 1 Parallel lines have the same slope, so we're looking for a line with a slope of 3, in the form y = mx + b. For this case, we...

Which of the following is equivalent to 3(2x + 1)(4x + 1)? A) 45x B) 24x^2 + 3 C) 24x^2 + 18x + 3 D) 18x^2 + 6 First, multiply the binomials: We get 8x^2 + 6x + 1 Now multiply this polynomial by 3: 3(8x^2 + 6x + 1) = 24x^2 + 18x + 3, answer C