Evaluate the expressions when x = 1/2 and y = -3.

1. -4xy
-4 * .5 * -3 = 6

2. 6x - 3y
6(.5) - 3(-3)

3. -5y + 8x + 1
-5(-3) + 8(.5) + 1 = 20

4. -x^2 - y + 2
-0.5^2 - (-3) + 2 = 4.75

5. 2x + 4 (x + .5) + 7
2(.5) + 4 (-3 + .5) + 7 = -2

6. 2(4x - 1)^2 - 3
2(4(.5) - 1)^2 - 3 = -1

looks good to me.

nice work.

1. -4xy: The expression is -4 * (1/2) * (-3) = 6.

2. 6x - 3y: The expression is 6 * (1/2) - 3 * (-3) = 3 + 9 = 12.
3. -5y + 8x + 1: The expression is -5 * (-3) + 8 * (1/2) + 1 = 15 + 4 + 1 = 20.
4. -x^2 - y + 2: The expression is -(1/2)^2 - (-3) + 2 = -1/4 + 3 + 2 = 4.75.
5. 2x + 4 (x + 0.5) + 7: The expression is 2 * (1/2) + 4 * (1/2 + 0.5) + 7 = 1 + 4 + 7 = 12.
6. 2(4x - 1)^2 - 3: The expression is 2 * (4 * (1/2) - 1)^2 - 3 = 2 * (2 - 1)^2 - 3 = 2 * 1^2 - 3 = 2 * 1 - 3 = 2 - 3 = -1.

To evaluate these expressions, we substitute the given values of x and y into the expressions and perform the necessary calculations.

1. -4xy
We substitute x = 1/2 and y = -3:
-4 * (1/2) * -3 = 6

2. 6x - 3y
We substitute x = 1/2 and y = -3:
6 * (1/2) - 3 * (-3) = 9

3. -5y + 8x + 1
We substitute x = 1/2 and y = -3:
-5 * (-3) + 8 * (1/2) + 1 = 20

4. -x^2 - y + 2
We substitute x = 1/2 and y = -3:
-(1/2)^2 - (-3) + 2 = 4.75

5. 2x + 4 (x + .5) + 7
We substitute x = 1/2 and y = -3:
2 * (1/2) + 4 * (1/2 + .5) + 7 = -2

6. 2(4x - 1)^2 - 3
We substitute x = 1/2 and y = -3:
2 * (4 * (1/2) - 1)^2 - 3 = -1

By substituting the values of x = 1/2 and y = -3 into each expression and performing the calculations, we can evaluate the given expressions.