Solve for y in the first equation.
y = 4x + 6
Substitute <span>4x + 6 into the second equation.
-5x - (</span><span>4x + 6) = 21
Distribute
-5x - 4x - 6 = 21
Combine like terms
-9x = 27
Divide both sides by -9
x = -3
Substitute back into first equation
-4(-3) + y = 6
Solve for y
y = -6</span>
Answer:
175.929188601
Step-by-step explanation:
Answer:
P(X = x, Y = y) = f(x, y)
Step-by-step explanation:
Let X be a discrete random variable, and suppose that the possible values that it can assume are given by x1, x2, x3, . . . , arranged in some order. Suppose also that these values are assumed with probabilities given by
P(X = xk) = f(xk) k = 1, 2, . . . (1)
It is convenient to introduce the probability function, also referred to as probability distribution, given by
P(X = x) = f(x)
If X and Y are two discrete random variables, we define the joint probability function
of X and Y by
P(X = x, Y = y) = f(x, y)
where f(x, y) ≥ 0
Answer:
a = 3
Step-by-step explanation:
Factor both expressions
x² - x - 6
Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (- 1)
The factors are - 3 and + 2 , since
- 3 × 2 = - 6 and - 3 + 2 = - 1 , thus
x² - x - 6 = (x - 3)(x + 2)
-----------------------------------
x² + 3x - 18
consider factors of constant term (- 18) which sum to give the coefficient of the x- term (+ 3)
The factors are + 6 and - 3 , since
6 × - 3 = - 18 and 6 - 3 = + 3 , thus
x² + 3x - 18 = (x + 6)(x - 3)
Both expressions have a common factor of (x - 3)
Compare with (x - a ), then a = 3
