Answer:
\mathrm{Domain\:of\:}\:x^3+3x^2-x-3\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}
Step-by-step explanation:
Put the first equation in slope-intercept form, or y = mx + b. Start by subtracting y from both sides.
2x - y = -10, subtract 2x from both sides.
-y = -10 - 2x
Divide both sides by negative one.
y = 10 + 2x
To find the slope when the equations are in slope-intercept form you look at the coefficient of x. The first equation has the slope of 2 (which we just found), and the second equation has the slope of -2.
Parallel lines have the same slope and perpendicular lines have opposite reciprocal slopes. Since 2 and -2 are neither of these, your answer is neither.
Answer:
A: -9a
Step-by-step explanation:
Hope that helps!
Answer:
42
Step-by-step explanation:
1/6in made into a decimal is 0.16666... so I rounded it to 0.17.
256 divided by 6.17= 41.9773096 which rounded to the nearest whole number is 42.
Read the problem and answer choices. You want to get from ABCD to EFGH, so you need to figure out how to do that with reflection, translation, and dilation—in that order.
The reflection part is fairly easy. ABC is a bottom-to-top order, and EFG is a top-to-bottom order, so the reflection is one that changes top to bottom. It must be reflection across a horizontal line. The only horizontal line offered in the answer choices is the x-axis. Selection B is indicated right away.
The dimensions of EFGH are 3 times those of ABCD, so the dilation scale factor is 3. This means that prior to dilation, the point H (for example), now at (-12, -3) would have been at (-4, -1), a factor of 3 closer to the origin. H corresponds to D in the original figure, which would be located at (0, -2) after reflection across the x-axis.
So, the translation from (0, -2) to (-4, -1) is 4 units left (0 to -4) and 1 unit up (-2 to -1).
The appropriate choice and fill-in would be ...
... <em>B. Reflection across the x-axis, translation </em><em>4</em><em> units left and </em><em>1</em><em> unit up, dilation with center (0, 0) and scale factor </em><em>3</em><em>.</em>
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You can check to see that these transformations also map the other points appropriately. They do.
