Let us prove that angle 1 is complementary to angle 3 step by step.
1. We have been given that angle 1 is complementary to angle 2.
2. Since we know that complementary angles add up to 90 degrees, therefore, by the definition of complementary 
.
3. We have been also given that line segment BD bisects 
.
4. By the definition of bisect 
.
5. Angles are congruent if their measures, in degrees, are equal, therefore, by angle congruence postulate 
.
6.
Upon substituting in above equation we will get,
Therefore, by substitution property of equality .
Hence, proven that angle 1 is complementary to angle 3.
Answer: 40/81
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Work Shown:
B = selecting 1 blue
R = selecting 1 red
P(B) = 5/9, since there are 5 blue out of 5+4 = 9 total
P(R) = 4/9, since there are 4 red out of 9 total
P(2 blue) = P(B)*P(B) = (5/9)*(5/9) = 25/81
P(2 red) = P(R)*P(R) = (4/9)*(4/9) = 16/81
The last two equations are valid because we are sampling with replacement. Each selection is independent.
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P(2 same color) = P(2 blue OR 2 red)
P(2 same color) = P(2 blue) + P(2 red)
P(2 same color) = 25/81 + 16/81
P(2 same color) = (25+16)/81
P(2 same color) = 41/81
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P(2 different color) = 1 - P(2 same color)
P(2 different color) = 1 - 41/81
P(2 different color) = 81/81 - 41/81
P(2 different color) = (81-41)/81
P(2 different color) = 40/81
Answer:
A is (20, -35)
B is (-15, 45)
Step-by-step explanation:
Hope this helps you out :)
Have a great day
-Kendra <3
We can use point-slope form (since we have the slope, and 1 ordered pair)
point-slope form is y-y1=m(x-x1)
x=-5
y=4
m=3
y-(4)=3(x-(-5)
