1. Draw, in BLACK, the triangle with vertices (−1, 5), (−6, 3), and (−4, 8). 2. In BLUE, draw the triangle when the BLACK triangle is translated by the function (x, y) → (x, y − 6). 3. In GREEN, draw the triangle when the BLACK triangle is reflected in the y-axis. (You can draw or use coordinates to show the answer)

Step-by-step explanation:

A one-dimensional linear transformation is a function T(x)=ax for some scalar a. To view the one-dimensional case in the same way we view higher dimensional linear transformations, we can view a as a 1×1 matrix. The determinant of the 1×1 matrix is just the number a itself. Although this case is very simple, we can gather some intuition about linear maps by first looking at this case.

An example one-dimensional linear transformation is the function T(x)=3x. We could visualize this function by its graph, which is a line through the origin with slope 3. However, instead, let's view it as a mapping from the real line R back onto the real line R. In this case, we think of the function as x′=T(x), which maps the number x on the x-axis to the new number T(x) on an x′-axis. T takes the number 1 and maps it to 3. T maps 0 to 0 and -1/2 to -3/2. We also use the language that 3 is the image of 1 under the mapping T.

We can summarize this mapping by looking how T maps an interval of numbers. For example, T maps the interval [0,1] to the interval [0,3], as illustrated by the following figure. We colored the interval [0,1] and its image [0,3] with a green to red gradient that illustrates how each point in the interval is mapped by T. A point of a given color in [0,1] is mapped to a point of the same color in the image [0,3].

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1