f(x) = (x - 4)^2 - 1
g(x) = -(1/4) ( x - 4)^2 + 4
both the x and y values have to be the same. Start with the y values
f(x) = g(x)
(x - 4)^2 - 1 = -(1/4) (x - 4)^2 + 4 Add 1 to both sides.
(x - 4)^2 = -(1/4) (x - 4)^2 + 5 Add 1/4(x - 4)^2 to both sides.
(5/4) (x - 4)^2 = 5 Divide by 5/4 on both sides.
(x - 4)^2 = 5//(5/4)
(x - 4)^2 = (5/1)//5/4 Invert the second fraction and multiply
(x - 4)^2 = 5/1 * 4/5
(x - 4)^2 = 4 The 5s cancel
(x - 4)^2 = 4 Take the square root of both sides.
(x - 4) = +/- 2 Add 4 to each answer. Start with +2 on the right.
x - 4 + 4 = 2 + 4
x = 4 + 2 = 6
The x value that makes f(x)- g(x) = 0 is x = 6 The point is (6,3) answer.
Answer C.
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You do not need this next part. It is just for completeness.
x - 4 = - 2
x = 4 -2
x = 2
What are the y values for these 2 x values?
y = (x - 4)^2 - 1
y = (6 - 4)^2 - 1
y = 4 - 1
y = 3
The point where f(x) - g(x) = 0 is (6,3) <<<<<< Answer 1
The second point is
y = (x - 4)^2 - 1
y = (2 - 4)^2 - 1
y = (-2)^2 - 1
y = 4 - 1
y = 3
The second point is (2,3). Answer 2
Note the y values are the same. You might expect that.
Answer:
The answer is (D) the starting temperature was 82 degrees F and dropped at a rate of 8 degrees per hour.
Step-by-step explanation:
For every 2 hours the temperature drops 8 degrees.
hope it helps
The formula for arc length is:
s= r∅
Given that ∅= 7π/4
and r= 5
Therefore, arc length s= 7π/4 *5 = 35π/4
Show the picture to answer this
Simplifying
h(t) = -1t2 + -2t + 30
Multiply h * t
ht = -1t2 + -2t + 30
Reorder the terms:
ht = 30 + -2t + -1t2
Solving
ht = 30 + -2t + -1t2
Solving for variable 'h'.
Move all terms containing h to the left, all other terms to the right.
Divide each side by 't'.
h = 30t-1 + -2 + -1t
Simplifying
h = 30t-1 + -2 + -1t
Reorder the terms:
h = -2 + 30t-1 + -1t
