The hanger image below represents a balanced equation, 6
21
Find the value of d that makes the equation true.
MY
d=

The value of d that balances the equation is d=15

Step-by-step explanation:

Equations

We are given an image with a hanger that represents a balanced equation.

If the equation is balanced, then the 'weights' of each side should be equal.

On the right side, there is 21 and on the left side, there are 6 and d.

Adding both, we have 6+d on the left side.

Equating both sides:

6 + d = 21

To find d, we subtract 6 on both sides:

d = 21 - 6

d = 15

The value of d that balances the equation is d=15

  The locations of A' and B' are A'(0, 4) and B'(4, 0); lines f and f' are parallel.

Step-by-step explanation:

Dilation about the origin multiplies each coordinate value by the dilation factor. A(0, 2) becomes A'(0, 4) when dilated by a factor of 2. Likewise, B(2, 0) becomes B'(4, 0).

Dilation does not change the direction of lines, so all dilated image lines are parallel to the corresponding original lines.