act exam

If p = log2(x), what is the value of log2(2x^3) in terms of p? A. 6p B. 2p^3 C. 1 + 3p D. 3 + 3p E. 1 + p^3 log2(2x^3) = log2(2) + log2(x^3) log2(2) = 1, so we have: log2(2x^3) = 1 + 3log2(x) Since we're given log2(x) = p, we have: log2(2x^3) = 1 + 3p - Answer C

The ratio of the measures of the 3 angles of a triangle is 1:2:3. What is the measure of the largest angle in degrees? Let the smallest angle be x. Then we have 3 angles based on the ratio: x, 2x, 3x We know the sum of the angles of a triangle equals 180. So we have: x + 2x + 3x = 180 6x = 180...

(4 - a)/(a^2 - 16) (4 - a)/(a + 4)(a - 4) -1(a - 4)/(a + 4)(a - 4) Cancel a- 4 terms -1/(a + 4)

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...