Question

answer all 24 questions in this part. each correct answer will receive 2 credits. no partial credit will be allowed. utilize the information provided for each question to determine your answer. note that diagrams are not necessarily drawn to scale. for each statement or question, choose the word or expression that, of those given, best completes the statement or answers the question. record your answers on your separate answer sheet. 48 use this space for computations. 1 which expression is equivalent to (100x^2 - 16)? (1) ((50x - 8)(50x + 8)) (2) ((50x - 8)(50x - 8)) (3) ((10x - 4)(10x + 4)) (4) ((10x - 4)(10x - 4)) 2 josie has $2.30 in dimes and quarters. she has two more dimes than quarters. which equation below can be used to determine (x), the number of quarters she has? (1) (0.35(2x + 2) = 2.30) (2) (0.25(x + 2) + 0.10x = 2.30) (3) (0.25x + 0.10(x + 2) = 2.30) (4) (0.25x + 0.10(x - 2) = 2.30) 3 if (g(x) = -2x^2 + 16), then (g(-3)) equals (1) (-20) (2) (-2) (3) (34) (4) (52) 4 what are the zeros of (f(x) = x^2 - 8x - 20)? (1) (10) and (2) (2) (10) and (-2) (3) (-10) and (2) (4) (-10) and (-2)

Explanation:

Question 1

Step1: Recognize the difference of squares

The expression \(100x^2 - 16\) is a difference of squares, which has the form \(a^2 - b^2=(a - b)(a + b)\). Here, \(a = 10x\) (since \((10x)^2=100x^2\)) and \(b = 4\) (since \(4^2 = 16\)).

Step2: Factor using difference of squares

So, \(100x^2-16=(10x - 4)(10x + 4)\)? Wait, no, wait. Wait, \(100x^2=(50x)^2\) and \(16 = 8^2\)? Wait, no, \(100x^2=(10x)^2\), \(16 = 4^2\). Wait, but also \(100x^2-16 = 4(25x^2 - 4)=4((5x)^2-2^2)=4(5x - 2)(5x + 2)\), but the options are:

(1) \((50x - 8)(50x + 8)\): \((50x)^2-8^2=2500x^2 - 64
eq100x^2 - 16\)

(2) \((50x - 8)(50x - 8)\): \((50x - 8)^2=2500x^2-800x + 64
eq100x^2 - 16\)

(3) \((10x - 4)(10x + 4)\): \((10x)^2-4^2=100x^2 - 16\). Wait, but also, \(100x^2-16=(10x - 4)(10x + 4)\)? Wait, no, wait, \(100x^2-16=(10x - 4)(10x + 4)\) or \(4(5x - 2)(5x + 2)\). But among the options, option (3) is \((10x - 4)(10x + 4)\)? Wait, no, the options:

Wait, the original options:

(1) \((50x - 8)(50x + 8)\)

(2) \((50x - 8)(50x - 8)\)

(3) \((10x - 4)(10x + 4)\)

(4) \((10x - 4)(10x - 4)\)

Wait, \(100x^2-16=(10x)^2-4^2=(10x - 4)(10x + 4)\), but also, \(100x^2-16 = 4(25x^2 - 4)=4(5x - 2)(5x + 2)\). But the options given:

Wait, maybe I made a mistake. Wait, \(100x^2-16=(10x - 4)(10x + 4)\) is correct? Wait, \((10x - 4)(10x + 4)=100x^2+40x - 40x - 16=100x^2 - 16\). Yes. But also, \(100x^2-16=(50x - 8)(50x + 8)\)? \((50x)^2-8^2=2500x^2 - 64
eq100x^2 - 16\). So the correct option is (3).

Step1: Define variables

Let \(x\) be the number of quarters. Then the number of dimes is \(x + 2\) (since she has two more dimes than quarters).

Step2: Calculate total value

The value of quarters is \(0.25x\) (since each quarter is \$0.25) and the value of dimes is \(0.10(x + 2)\) (since each dime is \$0.10). The total value is \$2.30. So the equation is \(0.25x+0.10(x + 2)=2.30\), which is option (3).

Step1: Substitute \(x=-3\) into \(g(x)\)

Given \(g(x)=-2x^2 + 16\), substitute \(x=-3\) into the function.

Step2: Compute the value

\(g(-3)=-2(-3)^2+16=-2(9)+16=-18 + 16=-2\)

Answer:

(3) \((10x - 4)(10x + 4)\)

Question 2