Combine the like terms to create an equivalent expression:−3z−z
2 answers:
Answer:
-4z
Step-by-step explanation:
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Note that, -3z and -z are like terms. This means we can combine them right off the bat, which gives us .
. -4z is our final answer.
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Answer: Choice A
A trapezoid has only 1 pair of parallel sides, but a parallelogram has 2.
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Explanation:
These terms are just things you memorize. A diagram of two examples is shown below. The example shows a non-rectangular parallelogram, but you could go with rectangles or squares if you wanted to.
This is a tough one. the general form of a parabola is 
, where h and k are the coordinates of the vertex and p is the distance from the vertex to the focus. In order to get our parabola into this form and solve for p (which will give us our focal point), we have to complete the square. Set the parabola equal to 0, then move over the constant to get this equation: 
. In order to complete the square, the leading coefficient on the squared term has to be a +1. Ours is a 
, so we have to factor that out of the x terms. When you do that you end up with 
. Now we can complete the square by taking half the linear term, squaring it, and adding it to both sides. Our linear term is 16, so half of 16 is 8 annd 8 squared is 64. HOWEVER, on the left side, that is still hanging out in front, which means that when we add in 64, we are actually adding in 
which is -4. Now here's what we have: 
which simplifies to 
. Creating the perfect square binomial on the left was the point of this (to give us our vertex), so when we do that we have 
. Now just for simplicity, we will take baby steps. Move the -6 back over by addition and set it back equal to y: 
. Now we will work on getting into standard form. Move the 6 back over by the y (baby steps, remember) to get 
. Multiply both sides by -16 to get our "p" on the right: 
. We need to use our "4p" part of the standard form to find the p, which is the distance from the vertex to the focus. 4p=-16, and p = -4. That means that the focus is 4 units below the vertex. Let's figure out what the vertex is. From our equation, the vertex is ( -8, 6), and since this is an upside-down opening parabola, the focus will be aligned with the x-coordinate of the vertex. So our focus lies 4 units below 6 (6 is the y coordinate of the vertex which indicates up and down movement), so our focus has coordinates of (-8, 2), the first choice above. Told you it was a tough one! These conics are quite challenging!
Given:
The vertices of a polygon QRST are T(-2, 3), Q(1, 5), R(3, -1) and S(0, 0).
To find:
The vertices for .
Solution:
The rule represents refection of polygon QRST across the x-axis.
If a figure is reflected across the x-axis, then
Using this rule, we get
Therefore, the vertices for are T'(-2, -3), Q'(1, -5), R'(3, 1) and S'(0, 0).