Answer:
For a table for x and y values for this absolute value equation, it would look like this:
x --- y
3 --- (-5)
4 --- (-1)
5 --- 3
6 --- (-1)
7 --- (-5)
Step-by-step explanation:
When you are building a table for an absolute value graph, you start with the base formula for absolute value equations:
y = a|x-h| + k
In this equation (h, k) is the vertex and therefore the middle point. From there we go two numbers in each direction for our x values. And for every change in x, y changes by a factor of a.
Diagram of two triangles
The two triangles are similar because they are both right triangles, meaning that one angle is 90° and the other two are acute (less than 90°).
The diagram on the left is missing its hypotenuse - the variable <em>c</em><em>.</em><em> </em>The hypotenuse is opposite of the right angle. The diagram on the right side is missing one of its legs.
Note: The hypotenuse is the <em>longest</em><em> </em>side of a right triangle.
Word Problen
The legs are 21 blocks and 20 blocks because they are by the right angle. Use the Pythagorean theorem to find the diagonal path's length, which is the hypotenuse.
Standard form of Pythagorean theorem.
Equation with the legs substituted and the missing hypotenuse value - <em> </em><em>c</em><em>.</em>
Square the legs and add.
Take the square root and simplify. The square root of 841 is 29 and -29, but distance is positive.
Thus the diagonal distance is 29 blocks.
Check by substituting.
Answer: Choice B
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A more in depth look
Choice A is true because the points are going downward as you read from left to right. The points aren't all on the same line but they are close to one. We can cross choice A off the list.
Choice B is false. So this is the answer. The fact that the points are close to the same line indicates that the r value is close to -1 rather than 0. If the points were randomly scattered about, or if they fell on a curve such as a parabola, then the linear correlation coefficient r would be (closer to) zero.
Choice C is true. The explanatory variable is the independent variable x. We can cross choice C off the list.
Choice D is true. The points are fairly close to the same straight line. It's not perfect but it's good enough. We can cross choice D off the list.
Answer:
The answer is "the negative signs were switched"
