sat exam

Since we have all coefficients of 3 raised to the n, we have: 3(3^n) Using our exponent rules, we have: 3^(n + 1)

A. 2 B. 3 C. 4 D. 5 E. 6 We have 3 conditions that all must be met: Whole number Prime Number 20 * number is divisible by 6 The are all whole numbers One A, B, and D are prime, so we eliminate C and E 20(2) = 40 which is not divisible by 6 - Eliminate Answer A 20(5) = 100 which is not...

a. b^(y + 1) b. b^(y + 2) c. b^(y + 3) d. b^2y e. b^3y Multiply each side by b: 3b = b^y * b 3b = b^(y + 1) answer A.

Multiply the 2's together: 2 x 2 x 2 = 8 Multiply the 10 with exponent terms together: 10^3 x 10^6 * 10^12 = 10^(3 + 6 + 12) = 10^21 Group both results: 8 x 10^21

If 2x + y = 7 and y + 2z = 23, what is the average of x, y, and z? A. 5 B. 7.5 C. 15 D. 12.25 Add both equations to get all variables together: 2x + y + y + 2z = 23 + 7 2x + 2y + 2z = 30 We can divide both sides by 2 to simplify: (2x + 2y + 2z)/2= 30/2 x + y + z = 15 Notice: the average of...

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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

Which of the following is equivalent to 9^3/4? a) 9^1/3 b) 9 ^ 1/4 c) sqrt(3) d) 3 * sqrt(3) Since 9 is 3^2, we have 3^(3*2/4) which is 3^6/4 Since 6/4 is 3/2, we have: 3^(3/2) Since 3/2 is 1 + 1/2, we have: 3^1*sqrt(3) 3*sqrt(3) or option D.

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 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

A local radio station sells time slots for programs in 20-minute intervals. If the station operates 24 hours per day, what is the total number of 20-minute time slots the radio station can sell for Thursday and Friday? Thursday and Friday = 2 days With 24 hours per day, we have 24 * 2 = 48...

Aaron is staying at a hotel that charges $99.95 per night plus tax for a room. A tax of 8% is applied to the room rate, and an additional onetime untaxed fee of $5.00 is charged by the hotel. Which of the following represents Aaron’s total charge, in dollars, for staying x nights? The Room cost...

If (x - 1)/3 = k and k = 2, what is the value of x? If k = 2, we have: (x - 1)/3 = 2 Cross multiply: x - 1 = 3 * 2 x - 1 = 6 Type this equation into the search engine, we get: x = 7