Answer:
Figure D. (A)
When you flip the figure across like a mirror, it remains the same shape as the other side. An easy way to determine this is by cutting a line down the middle.
Reflectional symmetry states that if there exists at least one line that divides a figure into two halves such that one-half is the mirror image of the other half.
Edit: Typo!
The vertex of a parabola is the maximum or minimum value, and it’s represented by (x,y). The axis of symmetry is the vertical line that runs through the x axis, and also runs through the vertex. This means that the x value in the vertex (x,y) can represent the axis of symmetry.
Hello there! So, y = mx + b is in slope-intercept form, where m represents the slope, b represents the y-intercept, and y and x remain unfilled. First off, let's solve for the slope. The formula for slope is y2 - y1 / x2 - x1, where you subtract the first x and y coordinates from the second x and y coordinates. So it would be formed like this:
9 - 4 / 6 - (-4)
Let's subtract. 9 - 4 is 5. 6 - (-4) is 10. 5/10 is 1/2 in simplest form. The slope for this equation is 1/2. Now, let's find the y-intercept. We will find that by plugging one of the points into the equation and solving for b. The x and y coordinates will be filled in by that coordinate. Let's use (-4, 4) for this problem. We will also plug in the slope. In this case, the problem will look like this:
4 = (1/2)(-4) + b
Now, let's multiply 1/2 and -4 to get -2. Now, to get b by itself, subtract 2 to both sides to isolate the b. -2 + 2 cancels out. 4 + 2 is 6. b = 6. There. The equation of the line in slope-intercept form is y = 1/2x + 6.
Answer:
Step-by-step explanation:
We are given the following:
and 
a). Recall that a level curve of a function f(x,y) is given by 
where c is a constant. That is, all the points in the set of interest to which the function applied to the points is exactly the value c.
Consider c = 80. So we get
which implies that 
(Graph 1).
We can also consider c=60, which gives us
which implies that 
. (Graph 2)
b)Recall that the gradient of a function f(x,y) is given by
In this case,
Thus, the gradient of T is given by
