Question

What is the simplified form of the expression? Show all of your work for credit.

-5 [ 4² ÷ ( 49 - 41) + 6]

Answer 1

[AI-generated answer — Bot GPT 3.5]

First, let's simplify the expression inside the square brackets:

(49 - 41) = 8
4² = 4 * 4 = 16

So, the expression inside the square brackets becomes:
16 ÷ 8 + 6 = 2 + 6 = 8

Now, substitute this value back into the original expression:
-5 * 8 = -40

Therefore, the simplified form of the expression is -40.

Answer 2

Simplify the expression. Show your work.

6xy−7y

Answer 3

[AI-generated answer — Bot GPT 3.5]

To simplify the expression 6xy - 7y, we can factor out the common factor y from both terms:

6xy - 7y = y(6x - 7)

Therefore, the simplified form of the expression is y(6x - 7).

Answer 4

Sarah is making a balloon arc, with pink and yellow balloons, for decorating her brother’s birthday party. For the balloon arc, she needs 4 more pink balloons than twice the yellow balloons. If she has x yellow balloons, then how many pink balloons are needed to finish making the balloon arc? Write an expression she would use to determine the total amount of balloons needed for the arc.

Answer 5

[AI-generated answer — Bot GPT 3.5]

According to the given information, Sarah needs 4 more pink balloons than twice the number of yellow balloons (x).

To determine the total number of balloons needed for the arc, she would use the expression:
2x + 4

This expression represents twice the number of yellow balloons (2x) plus 4 additional pink balloons needed for the arc.

Answer 6

[AI-generated answer — Step-by-Step Bot]

To simplify the given expression, we'll follow the order of operations (PEMDAS/BODMAS) and perform the calculations step by step.

Step 1: Simplify the numerator in the brackets.

-5 [ 4² ÷ ( 49 - 41) + 6]
= -5 [ 4² ÷ ( 8 ) + 6]
= -5 [ 16 ÷ 8 + 6]
= -5 [ 2 + 6]
= -5 [ 8]

Step 2: Perform the multiplication.

-5 [ 8 ] = -40

Therefore, the simplified form of the expression is -40.

Answer 7

[AI-generated answer — Explain Bot]

To find the simplified form of the expression, we need to follow the order of operations (also known as PEMDAS).

1. Start by simplifying any operations inside parentheses.

-5 [ 4² ÷ ( 49 - 41) + 6]

First, solve the expression inside the parentheses:

49 - 41 = 8

So, now the expression becomes:

-5 [ 4² ÷ 8 + 6]

2. Next, perform any exponents:

4² = 4 × 4 = 16

Now the expression becomes:

-5 [ 16 ÷ 8 + 6]

3. After that, perform any multiplications or divisions from left to right:

16 ÷ 8 = 2

Now the expression becomes:

-5 [ 2 + 6]

4. Finally, we perform any additions or subtractions from left to right:

2 + 6 = 8

Now the expression becomes:

-5 * 8

-5 multiplied by 8 is -40.

Therefore, the simplified form of the expression -5 [ 4² ÷ ( 49 - 41) + 6] is -40.