The answer is that it's a right triangle. One angle is 90°
Answer: 2343 / 256
Explanation
I will do this for you in two forms: 1) adding each term, and 2) using the general formula for the sum of geometric series.
1) Adding the terms:
4
∑ 3 (3/4)^i = 3 (3/4)^0 + 3 (3/4)^1 + 3 (3/4)^2 + 3 (3/4)^3 + 3 (3/4)^4
i=0
= 3 + 9/4 + 27/16 + 81/64 + 243/256 = [256*3 + 27*16 + 64*9 + 4*81 + 243] / 256 =
= 2343 / 256
2) Using the formula:
n-1
∑ A (r^i) = A [1 - r^(n) ] / [ 1 - r]
i=0
Here n - 1 = 4 => n = 5
r = 3/4
A = 3
Therefore the sum is 3 [ 1 - (3/4)^5 ] / [ 1 - (3/4) ] =
= 3 [ 1 - (3^5) / (4^5) ] / [ 1/4 ] = 3 { [ (4^5) - (3^5) ] / (4^5) } / {1/4} =
= (3 * 781) / (4^5) / (1/4) = 3 * 781 / (4^4) = 2343 / 256
So, no doubt, the answer is 2343 / 256
4 + -1 1/3
Turn 4 into an improper fraction.
4/4 is equal to 12/3. We want both 4 and 1 1/3 to have the same denominator so that they could be subtracted from each other.
New question :
12/3 + - 1 1/3
Turn {-1 1/3} into an improper fraction.
(3 × 1) + 1 = 4/3
So, -1 1/3 = -4/3
Our new question :
12/3 + - 4/3
Simplify.
12/3 - 4/3 = 8/3
Turn into a mixed number.
2 2/3
~Hope I helped!~
Answer:
- x > -2
- n ≤ -2 or n ≥ 8
Step-by-step explanation:
<h3>1.</h3>
Add 7x-2 to both sides and collect terms.
2x +2 -6x +7x -2 > -4 -7x +7x -2
3x > -6
x > -2 . . . . . . . divide by 3
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<h3>2.</h3>
Solve these one at a time, and form the union of the answers.
1 +7n ≤ 15 . . . .given
7n ≤ 14 . . . . . . subtract 1
n ≤ 2 . . . . . . . divide by 7
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-2n -2 ≤ -18 . . . given
-2n ≤ -16 . . . . . add 2
n ≥ 8 . . . . . . . . divide by -2
The solution is n ≤ -2 or n ≥ 8.
