Remark
It is easier in this case to state the irrational ones and then talk about the rationals.
sqrt(2) * sqrt(3) is irrational. The square root of 6 fills your calculator's window with many numbers and there is no pattern to them. Sqrt(6) cannot be expressed as a fraction or a repeating decimal which is also a fraction.
The last one is also irrational for the same reason. 3*pi cannot be expressed as either a repeating decimal or a fraction.
All the others are rational. The one you might have trouble with is the first one.
0.12 repeating is actually found by letting x = 0.12121212121212121212...Then
100 x = 12.121212121212121212 ...
<u> x = 0.121212121212121212..</u>. Subtract
99 x = 12
x = 12/99
So the mixed fraction you get is 3 12/99 which is 309/99
When you multiply that by 1.4 it does not change the fact that you still get a fraction. It turns out to be 721 / 165. The method is similar to the one used to get 12 / 99. I don't think you need to know the exact answer. You need only need to know that the first one is rational.
Choice 2 is rational because 9 and 25 are perfect squares. sqrt(9) = 3
Sqrt(25) = 5.
3*5 = 15.
Answer
One Two are four are all rational.
Answer:
Question Answer
What is the length of a segment when the coordinates of its endpoints are (-4,5) and (-6,9)? 4.5
What is the length of a segment when the coordinates of its endpoints are (-4,5) and (-6,9)? 10.8
Step-by-step explanation:
Given:
First side(A): 2B - 7
Second side(B): B
Third side(C): B + 4
Plug in values:
A + B + C = 80
2B - 7 + B + B + 4 = 80
If you look at the coefficients only, you can rewrite the equation like this:
2B + B + B - 7 + 4 = 80
This means that 4B - 7 + 4 = 80
=4B - 3 = 80
= 4B = 80 + 3
B = 83/4, so you can either write B as 83/4 or as 20.75.
Checking your work:
A: 2(20.75) - 7 = 34.5
B: 20.75
C: 4 + 20.75 = 24.75
34.5 + 20.75 + 24.75 = 80cm.
Hope this helped.
The vertex to this quadratic equation is 2