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:
i dont know
Step-by-step explanation:
You gave $30.
[$30 * 0.20] (tip % amount) = $6.
You left $6 in tips.
Answer:
1) a. False, adding a multiple of one column to another does not change the value of the determinant.
2) d. True, column-equivalent matrices are matrices that can be obtained from each other by performing elementary column operations on the other.
Step-by-step explanation:
1) If the multiple of one column of a matrix A is added to another to form matrix B then we get: |A| = |B|. Here, the value of the determinant does not change. The correct option is A
a. False, adding a multiple of one column to another does not change the value of the determinant.
2) Two matrices can be column-equivalent when one matrix is changed to the other using a sequence of elementary column operations. Correc option is d.
d. True, column-equivalent matrices are matrices that can be obtained from each other by performing elementary column operations on the other.
Thank you for posting your question here. I hope the answer below will help.
Vo=110 feet per second
<span>ho=2 feet </span>
<span>So, h(t) = -16t^2 +110t +2 </span>
<span>Take the derivative: h'(t) = 110 -32t </span>
<span>The maximum height will be at the inflection when the derivative crosses the x-axis aka when h'(t)=0. </span>
<span>So, set h'(t)=0 and solve for t: </span>
<span>0 = 110 -32t </span>
<span>-110 = -32t </span>
<span>t=3.4375 </span>
<span>t=3.44 seconds </span>
