Question

Which expressions are equivalent to [22c 33d]? Choose 3 answers:

1) [(-2c-3d)(-11)]
2) [2(11c-3/2d)]
3) [(66c 99d) × 1/3]
4) [-1 × (-22-33d)]
5) [11 × (2c+3d)]

Answer 1

After evaluating the provided options, the equivalent expressions to [22c 33d] are [(-2c-3d)(-11)], [(66c 99d) × 1/3], and [11 × (2c+3d)], which corresponds to options 1), 3), and 5).

Step-by-step explanation:

The student has asked which expressions are equivalent to [22c 33d]. We determine the equivalent expressions by factoring, distributing, or comparing after simplifying. Let's evaluate the given options:

1. [(-2c-3d)(-11)] - Multiplying each term in the parentheses by -11 will result in the expression equivalent to [22c + 33d].
2. [2(11c-3/2d)] - Distributing the 2 inside the parentheses will not result in the exact terms 22c and 33d, so this expression is not equivalent.
3. [(66c + 99d) × 1/3] - Multiplying each term in the parentheses by 1/3 will also result in the expression equivalent to [22c + 33d].
4. [-1 × (-22c-33d)] - This expression has a typographical error; assuming it should be [-1 × (-22c + 33d)], multiplying each term inside the parentheses by -1 will make it equivalent to [22c + 33d].
5. [11 × (2c+3d)] - Multiplying 11 by each term in the parentheses will result in the expression equivalent to [22c + 33d].
6. Based on these calculations, the expressions equivalent to [22c + 33d] are options 1), 3), and 5).