Answer:
Option b is correct (8,13).
Step-by-step explanation:
7x - 4y = 4
10x - 6y =2
it can be represented in matrix form as
A=
X=
B=
i.e, AX=B
or X= A⁻¹ B
A⁻¹ = 1/|A| * Adj A
determinant of A = |A|= (7*-6) - (-4*10)
= (-42)-(-40)
= (-42) + 40 = -2
so, |A| = -2
Adj A=
A⁻¹ = / -2
A⁻¹ =
X= A⁻¹ B
X=
X=
X=
X=
x= 8, y= 13
solution set= (8,13).
Option b is correct.
Hello there! The solution of your question has been given below.
<h3>Solution:</h3>Option B.
Answer:
B) Both functions have the same domain.
C) Both functions have the same x-intercepts.
D) Both functions are decreasing on the interval (−∞, −2).
Step-by-step explanation:
step 1
Find the vertex of f(x)
we know that
The x-coordinate of the vertex is the midpoint of the roots
we have
x=-1 and x=-3
so
the midpoint is
(-1-3)/2=-2
The y-coordinate of the vertex is -4 (because the range is [−4, ∞))
therefore
The vertex of f(x) is the point (-2,-4)
Is a vertical parabola open upward
The vertex is a minimum
The domain is all real numbers
step 2
we have
Find the vertex
Factor the leading coefficient
Complete the square
Rewrite as perfect squares
Is a vertical parabola open upward
The vertex is the point (-2,-2)
The domain is all real numbers
The range is the interval [−2, ∞)
Find the x-intercepts
For g(x)=0
so
The roots or x-intercepts are
x=-1 and x=-3
<u><em>Verify each statement</em></u>
A) Both functions have the same vertex
The statement is false
The vertex of f(x) is (-2,-4) and the vertex of g(x) is (-2,-2)
B) Both functions have the same domain.
The statement is true
The domain is all real numbers
C) Both functions have the same x-intercepts
The statement is true (see the explanation)
D) Both functions are decreasing on the interval (−∞, −2)
The statement is true
Because the x-coordinate of the vertex is the same in both functions, and both functions open upward
Answer:
option B
Step-by-step explanation:
F(x)= 5 x-7