From top to bottom: 6, 2, -2, -6
Answer:
33,600
Step-by-step explanation:
1000 × 4.2 = 4200 x 8 = 33,600
Options:
a) If corresponding pairs of sides and corresponding pairs of angles of two triangles are congruent, then the triangles can be matched up exactly using rigid motions.
b) If two triangles can be matched up exactly using rigid motions, then the corresponding pairs of sides and corresponding pairs of angles of the triangles are congruent.
c) Two triangles can be matched up exactly using rigid motions if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
d) If corresponding pairs of sides and corresponding pairs of angles of two triangles are not congruent, then the triangles are not congruent.
Answer:
c) Two triangles can be matched up exactly using rigid motions if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
Step-by-step explanation:
For both pairs of triangles, what you proved is how to use rigid motions (i.e. rigid transformations) to make congruent shapes.
When rigid transformation is applied to a shape, the image (i.e. result) of the transformation produces an exact shape (i.e. equal corresponding angles and corresponding sides), meaning that the side lengths and the angles of the preimage (before transformation) and the image (after transformation) is unaltered.
<em>Option (c) is true</em>
B. They are both congruent and similar
Step-by-step explanation:
In order to graph this system of equations, you have to put the equations in terms of y so that you can graph it by hand.
For the first equation:
Subtract x on both sides so that it reads to be 
For the second equation:
Subtract 3x on both sides and divide by -1 to make the y positive. Remember that when you divide, the sign 
always flips:
So the two equations you have to graph now are and 
.
In order to graph, start from your y-intercept for each of the equations and go vertical/horizontal based on the coefficient of your equation. For instance, for your first equation, you would go down -1 and to the right 1. Repeat until your whole equation is graphed. For the second equation your coefficient is 3, so you would go up 3 from -4 and to the right 1. Repeat.
Once you have your equations graphed, you need to find where the two graphs both have solutions. To do this, pick any point from the graph and plug it into the x and y of one equation. If the equation equals itself, then that area is the solution of the graph for that equation. Make sure to do this for both equations. Once you find the area in which both equations have solutions for each other, that is the area that needs to be shaded.
Here is what your graph should look like:
