Answer: Choice B. The vertex is (6,-4)
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Work Shown:
Step 1 is to expand out (x-8)(x-4) using the FOIL rule or the box method or the distribution rule
(x-8)(x-4) = x(x-4)-8(x-4)
(x-8)(x-4) = x*x+x*(-4)-8*x-8*(-4)
(x-8)(x-4) = x^2-4x-8x+32
(x-8)(x-4) = x^2-12x+32
So (x-8)(x-4) turns into x^2-12x+32
x^2-12x+32 is the same as 1x^2+(-12x)+32 which is in the form ax^2+bx+c. We see that a = 1, b = -12, c = 32
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Use the values of a & b to find the value of h, which is the x coordinate of the vertex
h = -b/(2*a)
h = -(-12)/(2*1)
h = 12/2
h = 6
Then this is plugged back into the original function to find the y coordinate of the vertex. We can use either (x-8)(x-4) or x^2-12x+32 since they are equivalent expressions
k = y coordinate of vertex
k = f(h) = f(6) since h = 6
f(x) = (x-8)(x-4)
f(6) = (6-8)(6-4)
f(6) = (-2)(2)
f(6) = -4
note that
f(x) = x^2-12x+32
f(6) = (6)^2-12(6)+32
f(6) = 36-72+32
f(6) = -36+32
f(6) = -4
So we get the same result using either expression
So k = f(h) = f(6) = -4
Since h = 6 and k = -4, the vertex is (h,k) = (6,-4). So that's why the answer is choice B.
Answer:
1157 / 500
Step-by-step explanation:
Answer:
Step-by-step explanation:
To Test :-
H0 :- P = 0.12
H1 :- P ≠ 0.12
P = X / n = 156/800 = 0.195
Test Statistic :-
Z = ( P - P0 ) / ( √((P0 * q0)/n)
Z = ( 0.195 - 0.12 ) / ( √(( 0.12 * 0.88) /800))
Z = 6.5279
Test Criteria :-
Reject null hypothesis if Z > Z(α/2)
Z(α/2) = Z(0.05/2) = 1.96
Z > Z(α/2) = 6.5279 > 1.96, hence we reject the null hypothesis
Conclusion :- We Reject H0
There is sufficient evidence to support the claim that there is a difference.
The factors of each term in the expression 8x + 12xy are shown below. 8x: 1, 2, 4, 8, x 12xy: 1, 2, 3, 4, 6, 12, x, y What is th
mariarad [96]
Answer:
4x
Step-by-step explanation:
4 is the largest number on both lists of divisors. "x" is the only variable on both lists of variables. The GCF is their product:
4·x
Answer:
t(x) = 6x + 438
Step-by-step explanation:
I dont know question 4 but if you copy and paste question 2 it is already answered on this site, hope this helps!
