Answer:
D. 11.8 cm
Step-by-step explanation:
This triangle is a 30°-60°-90° triangle. There is a shortcut to find the lengths of the sides of a 30°-60°-90° triangle. The longest side is the hypotenuse. The longest side is double the shortest side or, the shortest side is half the longest side. Here the longest side is 5, so the short leg (shortest side) is 2.5
The other shortcut is that the longer leg is the
short leg×sqroot3
Here, the short leg is 2.5, so the long leg is 2.5×sqroot3
Perimeter is all the sides added together.
5 + 2.5+ 2.5×sqrt3
Do the times first.
5 + 2.5 + 4.3
= 11.8
Answers:
x = -8/5 or x = 8/5
Sum of the first ten terms where all terms are positive = 4092
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Explanation:
r = common ratio
- first term = 4
- second term = (first term)*(common ratio) = 4r
- third term = (second term)*(common ratio) = (4r)*r = 4r^2
The first three terms are: 4, 4r, 4r^2
We're given that the sequence is: 4, 5x, 16
Therefore, we have these two equations
Solve the second equation for r and you should find that r = -2 or r = 2 are the only possible solutions. If r = -2, then 5x = 4r solves to x = -8/5. If r = 2, then 5x = 4r solves to x = 8/5.
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To find the sum of the first n terms, we use this geometric series formula
Sn = a*(1 - r^n)/(1 - r)
We have
- a = 4 = first term
- r = 2, since we want all the terms to be positive
- n = 10 = number of terms to sum up
So,
Sn = a*(1 - r^n)/(1 - r)
S10 = 4*(1 - 2^10)/(1 - 2)
S10 = 4*(1 - 1024)/(-1)
S10 = 4*(-1023)/(-1)
S10 = 4092
The slope should be
m= 2/3 (2 over 3)