The answers are A, B and D.
Answer:
The length of the shorter piece = 3 ft
The length of the longer piece = 10 ft
Step-by-step explanation:
According to the question;
- Total length of the string is 13 ft
- Longer piece is 4ft longer than twice the shorter piece;
Therefore;
- Assuming the shorter piece is x ft
- Then, the longer piece will be (2x + 4) ft
Thus;
Longer piece + shorter piece = 13 ft
x ft + (2x + 4) ft = 13 ft
3x + 4 = 13
3x = 9
x = 3 ft and
2x + 4 = 10 ft
Therefore;
The length of the shorter piece = 3 ft
The length of the longer piece = 10 ft
Simplifying
3m = 5(m + 3) + -3
Reorder the terms:
3m = 5(3 + m) + -3
3m = (3 * 5 + m * 5) + -3
3m = (15 + 5m) + -3
Reorder the terms:
3m = 15 + -3 + 5m
Combine like terms: 15 + -3 = 12
3m = 12 + 5m
Solving
3m = 12 + 5m
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '-5m' to each side of the equation.
3m + -5m = 12 + 5m + -5m
Combine like terms: 3m + -5m = -2m
-2m = 12 + 5m + -5m
Combine like terms: 5m + -5m = 0
-2m = 12 + 0
-2m = 12
Divide each side by '-2'.
m = -6
Simplifying
m = -6
Answer:
Reflecting a point across the y-axis -> changes the sign of the x-coordinate
Reflecting a point across both axes -> changes the sign of both coordinates
Reflecting a point across the x-axis -> changes the sign of the y-coordinate
Step-by-step explanation:
Reflections:
- The rule to reflect a point across the y-axis is (-x, y), meaning that the x-coordinate's sign changes.
- Reflecting a point across both axes is the same thing as rotating it 180 degrees, so the rule is (-x, -y). This means that both coordinates' signs change.
- Reflecting a point across the x-axis is (x, -y), meaning that the y-coordinate's sign changes.
