The first set:
3x + 2y = 2 ---1)
5x + 4y = 6 ---2)
From 1), multiply all by 2, 6x + 4y = 4 ---3)
3) - 2),
6x + 4y - (5x + 4y) = 6 - 4
6x + 4y - 5x - 4y = 2
x = 2
Sub in x = 2 into 1),
3(2) + 2y = 2
2y = -4
y = -2
(2 , -2)
The second set:
3x + 2y = 2 ---1)
11x + 8y = 10 ---2)
From 1), multiply all by 4, 12x + 8y = 8 ---3)
3) - 2),
12x + 8y - (11x + 8y) = 8 - 10
12x + 8y - 11x - 8y = -2
x = -2
From this x value alone, we can tell that these two linear systems do NOT have the same solution as they meet at different coordinates.
Hope this helped! Ask me if there's any working from here that you don't understand! :)
The answer is B) 1/4.
There are 2 outcomes in his tree that have all coins with the same side up: HHH and TTT. There are 8 total outcomes. This makes the probability 2/8 = 1/4.
Answer: C
Step-by-step explanation:
For this problem, we need to know the standard form of a sine function and the meaning of each part.
Standard form:
a=amplitude
b=period
h=phase shift
k=vertical replacement/shifting
Now that we know the standard form and the components, we know that we can forget about k and plug in 0 for h. This would leave us with . We know that the amplitude is 2, therefore, a=2. To find the period, you divide 2π by the given period. , therefore, b=1/2.
[plug in a=2]
[plug in b=1/2]
Therefore, C is the correct answer.