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Question 2 A) Assuming an equation with one side as a squared variable expression and the other side as a numeric expression, which of the following statements is correct? (1 point) Responses Statement #1: If the numeric expression is zero, there are two solutions. Statement #1: If the numeric expression is zero, there are two solutions. Statement #2: If the numeric expression is zero, there is one solution. Statement #2: If the numeric expression is zero, there is one solution. Statement #3: If the numeric expression is zero, there are no solutions. Statement #3: If the numeric expression is zero, there are no solutions. Question 3 A) Solve x2=100 by inspection. There are two real solutions. Enter your solutions below. (2 points) { $$, $$} Question 4 A)Solve the following quadratic equation using square roots: −9+(x−3)2−4=−4 (1 point) Responses {16, -10} {16, -10} {2, -8} {2, -8} {8, -2} {8, -2} Question 5 A)Find the values of x that make the following equation equal zero: (x+4)(x−2)=0 .(1 point) Responses x=−4 and x=2 x is equal to negative 4 and x is equal to 2 x=2 and x=4 x is equal to 2 and x is equal to 4 x=−2 and x=4 x is equal to negative 2 and x is equal to 4 Question 6 A) Solve the factored quadratic equation (19x−3)(9+x)=0 . Type answers as whole numbers or in simplest fraction form. (2 points) The solution set is x= {$$, $$} Question 7 A)Solve the quadratic equation 84x2+16x=0 by factoring out the GCF.(1 point) Responses The solutions are x=0 and x=4 The solutions are x is equal to 0 and x is equal to 4 The solutions are x=−421 and x=0 The solutions are x is equal to negative 4 over 21 and x is equal to 0 The solutions are x=−4 and x=−421 The solutions are x is equal to negative 4 and x is equal to negative 4 over 21 Question 8 A) Use the tables to answer the question. Jamal Step 1: Set equation = 0. x2+4x−12=0 Step 2: Write quadratic equation as the product of two factors. (x+6)(x−2)=0 Step 3: Set each factor equal to 0. x+6=0 and x−2=0 Step 4: Solve each equation. x=−6 and x=2 George Step 1: Begin with the equation. x2+4x−5=7 Step 2: Write quadratic equation as the product of two factors. (x+5)(x−1)=7 Step 3: Set each factor equal to 0. x+5=0 and x−1=0 Step 4: Solve each equation. x=−5 and x=1

1 answer

Let’s go through each question one by one.

Question 2 A

To determine which statement is correct regarding the situation where a squared variable expression equals a numeric expression, we focus on the scenario where the numeric expression is zero:

  • Statement #1: If the numeric expression is zero, there are two solutions. (False – there can be at most one solution)

  • Statement #2: If the numeric expression is zero, there is one solution. (True – \( x^2 = 0 \) gives \( x = 0 \))

  • Statement #3: If the numeric expression is zero, there are no solutions. (False)

Correct Answer: Statement #2: If the numeric expression is zero, there is one solution.

Question 3 A

To solve \( x^2 = 100 \) by inspection, we take the square root of both sides:

  • \( x = \sqrt{100} = 10 \)
  • \( x = -\sqrt{100} = -10 \)

Solutions: {10, -10}

Question 4 A

To solve the equation \( -9 + (x - 3)^2 - 4 = -4 \):

  1. Simplify the equation: \[ (x - 3)^2 - 9 = -4 \] \[ (x - 3)^2 = 5 \]

  2. Take the square root of both sides: \[ x - 3 = \pm \sqrt{5} \]

  3. The solutions are: \[ x = 3 + \sqrt{5} \text{ and } x = 3 - \sqrt{5} \]

None of the provided answer choices match the exact solutions derived.

If you assume approximate numbers to match the answer choices:

  • \( 3 + \sqrt{5} \approx 5.236 \)
  • \( 3 - \sqrt{5} \approx 0.764 \)

None of the provided options seem correct based on the mathematical solution derived.

Question 5 A

To find the values of \( x \) from \( (x + 4)(x - 2) = 0 \):

Set each factor to zero:

  1. \( x + 4 = 0 \) → \( x = -4 \)
  2. \( x - 2 = 0 \) → \( x = 2 \)

Answer: x = -4 and x = 2

Question 6 A

To solve the factored quadratic equation \( (19x - 3)(9 + x) = 0 \):

Set each factor to zero:

  1. \( 19x - 3 = 0 \) → \( 19x = 3 \) → \( x = \frac{3}{19} \)
  2. \( 9 + x = 0 \) → \( x = -9 \)

Solution set: \( x = { \frac{3}{19}, -9 } \)

Question 7 A

To solve the quadratic equation \( 84x^2 + 16x = 0 \) by factoring out the GCF:

  1. The GCF is \( 4x \): \[ 4x(21x + 4) = 0 \]

  2. Setting factors to zero:

    • \( 4x = 0 \) → \( x = 0 \)
    • \( 21x + 4 = 0 \) → \( 21x = -4 \) → \( x = -\frac{4}{21} \)

Solutions: The solutions are \( x = 0 \) and \( x = -\frac{4}{21} \)

Question 8 A

Jamal and George's steps seem largely correct, with Jamal solving \( x^2 + 4x - 12 = 0 \) correctly and finding \( x = -6 \) and \( x = 2 \).

George's steps, however, set the quadratic equation incorrectly. The equation \( x^2 + 4x - 5 = 7 \) should be rearranged to \( x^2 + 4x - 12 = 0 \).

Thus, Jamal’s solution is correct, while George has errors leading to incorrect factorization and solutions.

Final Notes: Ensure each answer aligns contextually based on further instructions or requirements for format.