Call the two equations above A and B, in order to not confuse them.
A: -2x + 6y = -38
B: 3x - 4y = 32
For this system we have opposites in x and y, so Elimination (or Linear Combination) works best. Either variable works, so let's work with x first and multiply A by 3 and B by 2. This is done so we get opposites in A and B then when added together give zero.
-2x + 6y = -38 ------> multiply by 3 ----> -6x + 18y = -114
3x - 4y = 32 ------> multiply by 2 -----> 6x - 8y = 64
Now we add the new equations. The -6x and 6x are opposites and go away. We are left with
10y = -50. We divide both sides by 10 and get that y = -5.
Now we take y = -5 and put it into an original equation. Let's use A.
-2x + 6y = -38 the original equation A
-2x + 6(-5) = -38 we found y = -5
-2x + (-30) = -38 evaluating and multiplying
-2x - 30 = -38 apply the parentheses
-2x = -8 add 30 to both sides
x = 4 divide on both sides by -2
Thus x = 4 and y = -5, or (4, -5) is the solution.
X (a + 2) = 7
First let's multiply out the brackets on the left side of the equation.
x (a + 2) --> Multiply everything inside the brackets by x.
xa + 2x = 7
Now, both elements of the left-hand side of the equation contain x, so we can divide both sides of the equation by x.
xa + 2x = 7
a + 2 = 7/x
To find a now, just subtract 2 from both sides.
a = 7/x - 2
Regarding conditional probabilities, the keyword is always given, as a previous event is considered to have happened.
<h3>What is Conditional Probability?</h3>
Conditional probability is the probability of one event happening, considering a previous event. The formula is:
In which:
- P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
- P(A) is the probability of A happening.
The previous event having happened is represented by keyword given.
More can be learned about conditional probability at brainly.com/question/14398287
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Answer:
volume = 14 2/3 units³
Step-by-step explanation:
volume = 7 1/3(2) = 14 2/3 units³
