Answer:
4 parameters are necessary to specify all solutions and correspond to the number of free variables of the system.
Step-by-step explanation:
Remember that the number of free variables of a system is equal to m-rank(A) where m is the number of unknowns variables and A is the matrix of the system.
Since the system is consistent and the rank of the matrix is 3 then echelon form of the augmented matrix has two rows of zeros.
Then m-rank(A)=7-3=4.
Answer:
2w^2 -7w-2
Step-by-step explanation:
(4w^2 – 4w – 8) – (2w^2 + 3w – 6)
Distribute the minus sign
(4w^2 – 4w – 8) – 2w^2 - 3w + 6
I like to line them up vertically
4w^2 – 4w – 8
– 2w^2 - 3w + 6
-----------------------------
2w^2 -7w-2
Answer: C
g(x) = 1/2 f (x)
Step-by-step explanation:
The solution to the composite function f(g(x)) is 9x² - 78x + 165.
<h3>
What is composite function?</h3>
A composite function is generally a function that is written inside another function.
Function composition is an operation that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g.
From the given composite function, the solution is determined as follows;
to solve for f(g(x)), we use the following methods.
f(x) = x² + 2x - 3, g(x) = 3x - 14
f(g(x)) = (3x - 14)² + 2(3x - 14) - 3
= 9x² - 84x + 196 + 6x - 28 - 3
= 9x² - 78x + 165
Thus, the solution to the composite function f(g(x)) is 9x² - 78x + 165.
Learn more about composite function here: brainly.com/question/10687170
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The complete question is below:
F(x) =x2+2x-3 g(x)=3x-14, find f(g(x))
Answer:
Step-by-step explanation:
Given
See attachment
Required
Determine the slope of the line
From the attachment, we have the following points
and
The slope m is then calculated using:
Substitute values for the x's and y's
<em>Hence, the slope is 0</em>
