Answer: x = 30' , y = 45'
hope this helps
Step-by-step explanation:
U is 90' it's a right triangle
well simple VRT you already know 2 angles which is 60' and 90'
R = 60'
V = 90'
T = x
you know that a triangle = 180'
so you do
180 - 60 - 90 = x
30 = x
if you want to do y
then you already know that U is 90' on both sides.
since you also know S,
S = 45'
U = 90'
V = y
180 - 90 - 45 = y
45 = y
Answer:
The slope of line A is C. 2
Step-by-step explanation:
You can check the slope by dividing the rise (how many units up) and the run (how many units across). This line has a rise of rise of 4 and a run of 2. Diving 4 by 2 gives you a slope of 2.
Answer:
D: I and IV only.
Step-by-step explanation:
We can go through each statement and examine its validity.
I) All congruent triangles are similar.
For congruent triangles, all of its corresponding sides and angles are congruent.
Since all angles are congruent, this fulfills the AA Similarity criterion. Thus, I is true.
II) All similar triangles are congruent.
Congruence guarantees similarity, but similarity does not guarantee congruence.
Two triangles need only two congruent angles to guarantee similarity, while two congruent angles does guarantee congruence. II is false.
III) All right triangles are similar.
Triangles are similar through the AA criterion. One angle of a right triangle must be 90, so this leaves 90 for the two remaining angles. Since these two angles can be anything that sum to 90, we are not guaranteed similarity. For example, 20 - 70 - 90 and 30 - 60 - 90 triangles. They are both right triangles, but are not similar. III is false.
IV) All isosceles right triangles are similar.
Again, since we have a right triangle, one angle is 90, which leaves two remaining angles that must sum to 90.
However, since it is isosceles, the two remaining angles must measure the same. Only one solution exists then: both angles must be 45.
Since all angles must be 45 - 45 - 90, it fulfills the AA Criterion. Thus, all isosceles right triangles are similar. IV is true.
The correct statements are I and IV.
Answers:
Part 1 (the ovals)
Domain = {-6,-1,1,5,7}
Range = {-4,-1,2,4}
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Part 2 (the table)
Domain = {1,-3,-2}
Range = {-2,5,1}
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Part 3 (the graph)
Domain = {1, 2, 3, 4, 5, 6}
Range = {-1, 0, 1, 2, 3, 6}
===============================================
Explanation:
Part 1 (the ovals)
The domain is the set of input values of a function. The input oval is the one on the left.
All we do is list the numbers in the input oval to get this list: {-6,-1,1,5,7}
The curly braces tell the reader that we're talking about a set of values.
So this is the domain.
The range is the same way but with the output oval on the right side
List those values in the right oval and we have {-4,-1,2,4}
Which is the range. That's all there is to it.
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Part 2 (The tables)
Like with the ovals in part 1, we simply list the input values. The x values are the input values. Notice how this list is on the left side to indicate inputs.
So that's why the domain is {1, -3, -2}. Optionally you can sort from smallest to largest if you want. Doing so leads to {-3, -2, 1}
The range is {-2,5,1} for similar reasons. Simply look at the y column
Side Note: we haven't had to do it so far, but if we get duplicate values then we must toss them.
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Part 3 (the graph)
Using a pencil, draw vertical lines that lead from each point to the x axis. You'll notice that you touch the x axis at the following numbers: 1, 2, 3, 4, 5, 6
So the domain is the list of those x values (similar to part 2) and it is {1, 2, 3, 4, 5, 6}
Erase your pencil marks from earlier. Draw horizontal lines from each point to the y axis. The horizontal lines will arrive at these y values: -1, 0, 1, 2, 3, 6
So that's why the range is {-1, 0, 1, 2, 3, 6}
