step 1
Find the measure of angle 1
REmember that the sum of the interior angles in any triangle must be equal to 180 degrees
so
In the triangle ABC
90+58+<1=180
148+<1=180
<1=180-148
<1=32 degrees
step 2
Find the measure of angle 2
we know that
<2=<1 -----> bt vertical angles
so
<2=32 degrees
step 3
Find the measure of angle 3
REmember that the sum of the interior angles in any triangle must be equal to 180 degrees
so
In the triangle CDE
32+108+<3=180
140+<3=180
<3=180-140
<3=40 degrees
Answer:
- <u><em>P(M) = 0.4</em></u>
Explanation:
<u>1. Build a two-way frequency table:</u>
To have a complete understanding of the scenary build a two-way frequency table.
Major in math No major in math Total
Major in CS
No major in CS
Total
Major in math No major in math Total
Major in CS
No major in CS
Total 200
- <u>80 plan to major in mathematics:</u>
Major in math No major in math Total
Major in CS
No major in CS
Total 80 200
- <u>100 plan to major in computer science</u>:
Major in math No major in math Total
Major in CS 100
No major in CS
Total 80 200
- <u>30 plan to pursue a double major in mathematics and computer science</u>:
Major in math No major in math Total
Major in CS 30 100
No major in CS
Total 80 200
- <u>Complete the missing numbers by subtraction</u>:
Major in math No major in math Total
Major in CS 30 70 100
No major in CS 100
Total 80 120 200
Major in math No major in math Total
Major in CS 30 70 100
No major in CS 50 50 100
Total 80 120 200
<u>2. What is P(M), the probability that a student plans to major in mathematics?</u>
- P(M) = number of students who plan to major in mathematics / number of students
Using the stated transformation, the graph of g(2x) is given at the end of the answer.
<h3>Horizontal stretch and compression</h3>
An horizontal stretch or an horizontal compression happens when a constant is multiplied at the domain of the function, as follows:
g(x) = f(ax).
The definition of stretch or compression depends on the value of the constant a, as follows:
- If a > 1, it is a compression by a factor of 1/a.
- If a < 1, it is a stretch by a factor of 1/a.
In this problem, the rule is:
f(x) = g(2x).
Meaning that f(x) is an horizontal compression by a factor of 1/2 of g(x), and then the vertices are given as follows:
That is, in each vertex, the x-coordinate was divided by 2, and thus the graph with these vertices is given at the end of the answer.
More can be learned about transformations at brainly.com/question/28725644
#SPJ1
You can find the segment congruent to AC by finding another segment with the same length. So first, you need to find the length of AC.
C - A = AC
0 - (-6) = AC Cancel out the double negative
0 + 6 = AC
6 = AC
Now, find another segment that also has a length of 6.
D - B = BD
2 - (-2) = BD Cancel out the double negative
2 + 2 = BD
4 = BD
4 ≠ 6
E - B = BE
4 - (-2) = BE Cancel out the double negative
4 + 2 = BE
6 = BE
6 = 6
So, the segment congruent to AC is B. BE .
