Answer:
5 1/3 gallons
Step-by-step explanation:
Equation: 8 1/6 - 2 5/6
8-2=6
1/6-5/6= -4/6
6-4/6=5 2/6
Simplify:
5 1/3 gallons
Answer:
91/216
Step-by-step explanation:
The probability of getting a 4 in the first three rolls is 1 minus the probability of not getting a 4 on any of the rolls.
P(at least one 4) = 1 − P(no 4s)
P(at least one 4) = 1 − (5/6)³
P(at least one 4) = 91/216
Alternatively, you can calculate it this way.
The probability of getting a 4 on the first roll is 1/6.
The probability of getting a 4 on the second roll is (5/6) (1/6) = 5/36.
The probability of getting a 4 on the third roll is (5/6) (5/6) (1/6) = 25/216.
The probability of any of the three events is 1/6 + 5/36 + 25/216 = 91/216.
Answer:
It is a perfect square expression.
It factors to (x+2)^2
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Explanation:
The general format for a perfect square is
(a+b)^2 = a^2 + 2ab + b^2
Which can be seen through the use of the FOIL rule.
Compare x^2+4x+4 with a^2+2ab+b^2, and we have these three equivalences:
- x^2 = a^2 .... first terms
- 4x = 2ab .... middle terms
- 4 = b^2 .... last terms
Since x^2 = a^2, we can apply the square root to both sides to get a = x. Similarly, 4 = b^2 leads to b = 2. We could get b = -2, but that would mean 2ab = 2x*(-2) = -4x instead of 4x. So we'll stick with b = 2 instead.
Because a = x and b = 2, we then can say:
(a+b)^2 = a^2 + 2ab + b^2
(x+2)^2 = x^2 + 2*x*2 + 2^2
(x+2)^2 = x^2 + 4x + 4
Showing that x^2+4x+4 factors to (x+2)^2.
Answer:
A) x = 2
Step-by-step explanation:
I am not sure but I think this means...
2x + 5 = 3x - 3
5 = 3x - 3 + 2x
5 + 3 = 3x + 2x
8 = 5x
8/5 or 1.6 = x
Diagrams make explanations a lot easier so I created one, see bottom for the picture.
As GHF are all midpoints, that means the lines that connect them are half of the opposite sides.
CD = 2HF
DE = 2GF
CE = 2GH
As HF is 2x CD, and CD = 24:
HF = CD ÷ 2
HF = 24 ÷ 2 = 12
As DE = 2x GF and DF is 9:
DE = 2 x 9
DE = 18
As CE = 2x GH and GH = 7:
CE = 2 x 7
CE = 14
Hope this helps!
