The answers 1, 2, 4, and 5 are right
Hope this helps
Answer:
f(x) = (x -6)² +14
Step-by-step explanation:
Completing the square involves writing part of the function as a perfect square trinomial.
<h3>Perfect square trinomial</h3>
The square of a binomial results in a perfect square trinomial:
(x -h)² = x² -2hx +h²
The constant term (h²) in this trinomial is the square of half the coefficient of the linear term: h² = ((-2h)/2)².
<h3>Completing the square</h3>
One way to "complete the square" is to add and subtract the constant necessary to make a perfect square trinomial from the variable terms.
Here, we recognize the coefficient of the linear term is -12, so the necessary constant is (-12/2)² = 36. Adding and subtracting this, we have ...
f(x) = x² -12x +36 +50 -36
Rearranging into the desired form, this is ...
f(x) = (x -6)² +14
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<em>Additional comment</em>
Another way to achieve the same effect is to split the given constant into two parts, one of which is the constant necessary to complete the square.
f(x) = x² -12x +(36 +14)
f(x) = (x² -12x +36) +14
f(x) = (x -6)² +14
Downstream DATA:
distance = 12 miles
time = 2 hours
rate = 12/2 = 6 mph
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Upstream DATA:
distance = 12 miles
time = 4 hrs
rate = 12/4 = 3 mph
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Equations:
Downstream: b + c = 6
Upstream::: b - c = 3
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Add to get:
2b = 9
b = 4.5 mph (speed of the boat in still water.)
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Solve for "c":
b + c = 6
4.5 + c = 6
c = 1.5 mph (speed of the current)
The answer is 1.5 mph
Step-by-step explanation:
f(x) = 3x + 2
g(x) = 4x
= f(x) + g(x)
= 3x + 2 + 4x
= (3 + 4)x + 2
= 7x + 2
(f+g)(x) = 7x + 2
The calculations are incorrect because the angles in a parallelogram are either:
The same
or complimentary (add up to 180)
Neither case is true here so the calculations are incorrect.
