Angle 1 and angle 2 are supplementary. angle 1 measures 3x and angle 2 measures 2x + 10. what does x equal?
1 answer:
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Answer:
-4
Step-by-step explanation:
x³ + cx + 4 divided by x + 2 has a remainder of 4, so:
(x³ + cx + 4) / (x + 2) = ax² + bx + d + 4 / (x + 2)
Multiply both sides by x + 2:
x³ + cx + 4 = (ax² + bx + d) (x + 2) + 4
Distribute:
x³ + cx + 4 = ax²(x + 2) + bx(x + 2) + d(x + 2) + 4
x³ + cx + 4 = ax³ + 2ax² + bx² + 2bx + dx + 2d + 4
x³ + cx + 4 = ax³ + (2a + b)x² + (2b + d)x + 2d + 4
Match the coefficients.
a = 1
2a + b = 0
2b + d = c
2d + 4 = 4
Solving, a = 1, b = -2, and d = 0. So c = -4.
We can also solve this using long division (see picture).
Answer:
Equation:
f(x) = (x + 3)^2
Graph: see image
Step-by-step explanation:
Translation just means shift or slide. To show a LEFT shift in the equation, go in close to the x, inside the parenthesis with the x, for LEFT shift, insert +3.
Left and right shifts might be the opposite of what you may think. Minus a number shifts right and plus a number shifts left.
For the graph, see image. The answer is the green curve.
