Answer For A: 1:2 probability
Answer For B: 3:4 probability
Step-by-step explanation: Since there is 3 odds and 3 evens in a 6 sided dice, there is 1:2 probability for you to land on a even or a odd. But if you were to roll the dice twice, your probability rate increases by half. So your probability rate for winning if rolled twice is 3:4.
The horizontal axis in the coordinate plane is called the x-axis. The vertical axis is called the y-axis. The point at which the two axes intersect is called the origin. The origin is at 0 on the x-axis and 0 on the y-axis.
Answer:
B
Step-by-step explanation:
We are given that:
Are consecutive terms of an arithmetic sequence.
And we want to determine the common difference <em>d</em>.
Recall that for an arithmetic sequence, each subsequent term is <em>d</em> more than the previous term.
In other words, the second term is one <em>d</em> more than the first term. So:
And the third term is two <em>d</em> more than the first term. So:
We can isolate the <em>d</em> in the first equation:
As well as the second:
Then by substitution:
Solve for <em>x:</em>
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The isolated first equation tells us that:
Therefore:
Our final answer is B.
Answer:
2(x - 3)(3x + 2)
Step-by-step explanation:
Given
6x² - 14x - 12 ← factor out 2 from each term
= 2(3x² - 7x - 6) ← factor the quadratic
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 3 × - 6 = - 18 and sum = - 7
The factors are - 9 and + 2
Use these factors to split the x- term
3x² - 9x + 2x - 6 ( factor the first/second and third/fourth terms )
= 3x(x - 3) + 2(x - 3) ← factor out (x - 3) from each term
= (x - 3)(3x + 2)
Thus
3x² - 7x - 6 = (x - 3)(3x + 2) and
6x² - 14x - 12 = 2(x - 3)(3x + 2) ← in factored form
