Ask a New Question
Menu

1.An expression for the length of the rectangle in terms of the width would be ________

2. The formula for the area of a rectangle is _______

3. Using trial and error, if the area is 96 m^2, then the length and width are _________

options:
1. L = 24 & w =4
2. L = 2w - 4
3. area = L x w
4. w = 2L - 4
5. area = 1 over (L x w)
6. area 2L + 2w
7. L = 4 & w = 24
8. L = 2 & w = 8
9. L = 8 & w = 12
10. L = 4 - 2w

3 answers

  1. An expression for the length of the rectangle in terms of the width would be L = 2w - 4 (Option 2).

  2. The formula for the area of a rectangle is area = L x w (Option 3).

  3. Using trial and error, if the area is 96 m², then the length and width are L = 8 & w = 12 (Option 9).

Match the equation with its solution(s).

1. 3i + 2i − 7 = 18
2. 3i + 5 = 2i − 7
3. 3i + 5 = 3i + 7
4. 3(2i − 7) = 15
5. 3(2i + 7) = 6i + 21

options:

1. No solution
2. i = 6
3. i = 5
4. i = 2
5. i = 7
6. i = 11
7. i = -12
infinite solutions

Let's solve each equation step by step and match them with their solutions.

  1. Equation: \( 3i + 2i - 7 = 18 \)
    Solution: Combine like terms: \( 5i - 7 = 18 \)
    Add 7 to both sides: \( 5i = 25 \)
    Divide by 5: \( i = 5 \)
    Match: i = 5 (Option 3)

  2. Equation: \( 3i + 5 = 2i - 7 \)
    Solution: Subtract \( 2i \) from both sides: \( i + 5 = -7 \)
    Subtract 5 from both sides: \( i = -12 \)
    Match: i = -12 (Option 7)

  3. Equation: \( 3i + 5 = 3i + 7 \)
    Solution: Subtract \( 3i \) from both sides: \( 5 = 7 \)
    This is a contradiction, so there is no solution.
    Match: No solution (Option 1)

  4. Equation: \( 3(2i - 7) = 15 \)
    Solution: Expand: \( 6i - 21 = 15 \)
    Add 21 to both sides: \( 6i = 36 \)
    Divide by 6: \( i = 6 \)
    Match: i = 6 (Option 2)

  5. Equation: \( 3(2i + 7) = 6i + 21 \)
    Solution: Expand: \( 6i + 21 = 6i + 21 \)
    This is an identity, which means it has infinite solutions.
    Match: infinite solutions (Option 8)

Summary of Matches:

  1. \( 3i + 2i - 7 = 18 \) → i = 5 (Option 3)
  2. \( 3i + 5 = 2i - 7 \) → i = -12 (Option 7)
  3. \( 3i + 5 = 3i + 7 \) → No solution (Option 1)
  4. \( 3(2i - 7) = 15 \) → i = 6 (Option 2)
  5. \( 3(2i + 7) = 6i + 21 \) → infinite solutions (Option 8)