Question

Please help really need a short simple answers

Answer 1

Answers - there are 4 questions so 4 answers below:

1a = square is 3.75 g.

1b = pentagon is infinite # g. It can be called an identity - an equation which is always true, no matter what values are substituted.

2a) 3 + 6 + 6 + 6 + x = 5x + 6

2b) 6 + 6 + 2x = 3 + 3 + 6 + 2x

Step by step

Since the hangers are balanced we can assume the two sides are equal

1a) We can add the known weights for each side and use “x” for the unknown squares and solve

3 + 6 + 6 + 6 + x = 5x + 6
Simplify

21 + x = 5x + 6
Subtract 6 from each side

21 - 6 + x = 5x +6 - 6
Simplify

15 + x = 5x
Subtract x from each side to isolate variable

15 + x - x = 5x - x
Simplify

15 = 4x
Divide both sides by 4 to solve for x

15/4 = 4/4 x

3.75 = x

1b) We can add the known weights for each side and use “x” for the unknown pentagon and solve

6 + 6 + 2x = 3 + 3 + 6 + 2x
Simplify

12 + 2x = 12 + 2x

Since both sides are equal
0 = 0

This means any value will balance so the answer is infinite numbers. This is also called an identity.

Answer 2

The weight of a square is 3.75 grams.

Explanation:

1. Since the hanger is balanced, we know that the two sides are equal

we can make an equation using x for the squares.

first add up the weights we do know on the left side:

3+6+6+6=21

so now we have the first part of the equation

x+21

now find the equation for the right side

5x+6

now set them equal to each other and solve for x

x+21=5x+6

subtract 6 from both sides

x+15=5x

subtract x from both sides

15=4x

divide both sides by 4

x=3.75