Answer: Choice B) {3, 5, sqrt(34)}
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Explanation:
We can only have a right triangle if and only if a^2+b^2 = c^2 is a true equation. The 'c' is the longest side, aka hypotenuse. The legs 'a' and 'b' can be in any order you want.
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For choice A,
a = 2
b = 3
c = sqrt(10)
So,
a^2+b^2 = 2^2+3^2 = 4+9 = 13
but
c^2 = (sqrt(10))^2 = 10
which is not equal to 13 from above. Cross choice A off the list.
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Checking choice B
a = 3
b = 5
c = sqrt(34)
Square each equation
a^2 = 3^2 = 9
b^2 = 5^2 = 25
c^2 = (sqrt(34))^2 = 34
We can see that
a^2+b^2 = 9+25 = 34
which is exactly equal to c^2 above. This confirms the answer.
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Let's check choice C
a = 5, b = 8, c = 12
a^2 = 25, b^2 = 64, c^2 = 144
So,
a^2+b^2 = c^2
25+64 = 144
89 = 144
which is a false equation allowing us to cross choice C off the list.
<u>Answer:</u>
The correct answer option is H. 4374.
<u>Step-by-step explanation:</u>
We are given the following geometric sequence and we are to find its 8th term:

Here
and common ratio
.
The formula we will use to find the 10th term is:
nth term = 
Substituting the values in the formula to get:
10th term = 
10th term = 4374
Answer:
2.26° per minute
Step-by-step explanation:
11.3 / 5
Answer:
The expression would give the probability that one marble is yellow and the other marble is red is,

Step-by-step explanation:
A bag contains eight yellow marbles, nine green marbles, three purple marbles, and five red marbles. So in total there are 25 marbles.
Hence,
Probability of getting yellow ball = 
Probability of getting red ball = 
Probability that one marble is yellow and the other marble is red is,

Consider the attached ellipse. Let the sun be at the right focus. Then perihelion is at right vertex on the x-axis and aphelion is at the left vertex on the x-axis.
The distances:
- from perihelion to the sun in terms of ellipse is a-c;
- from aphelion to the sun in terms of ellipse is a+c.
Then

Add these two equations:
and subtract first equation from the second:
Note that
thus

The equation for the planet's orbit is
