Which is a line segment?
2 answers:
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Answer:
Step-by-step explanation:
Let's call (as suggested)
p = the cost of one pizza
c = the cost of one cheeseburger
The Anderson Family ordered 2 pizzas and 4 cheeseburgers and paid $31.50, thus:
2p + 4c = 31.50 [1]
Next weekend, they ate at the same restaurant and ordered 3 pizzas and 2 cheeseburgers for $33.25, thus:
3p + 2c = 33.25 [2]
To know the cost of one pizza and one cheeseburger, we need to solve the system of equations defined by [1] and [2]
<h3>Answer: 33.75 feet</h3>
In fraction form, this value is equal to 135/4
33.75 ft is equivalent to 33 ft, 9 inches.
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Explanation:
Refer to the diagram below.
The key point to start with is point H, which is the vertex of the parabola.
Recall that vertex form is
y = a(x-h)^2 + k
What we'll do is plug in the vertex (h,k) = (60,30) which is the location of point H. We'll also plug in (0,45) which is the y intercept, aka the location of point C.
So,
y = a(x-h)^2 + k
y = a(x-60)^2 + 30 .... plug in vertex
45 = a(0-60)^2 + 30 .... plug in y intercept coordinates
45 = a(-60)^2 + 30
45 = a(3600) + 30
45 = 3600a + 30
45-30 = 3600a
3600a = 15
a = 15/3600
a = 1/240
This then means:
y = a(x-h)^2 + k
y = (1/240)(x-60)^2 + 30
This is the equation of our parabola. Plug in x = 30 to determine the height of point K
y = (1/240)(x-60)^2 + 30
y = (1/240)(30-60)^2 + 30
y = (1/240)(-30)^2 + 30
y = (1/240)(900) + 30
y = 15/4 + 30
y = 15/4 + 120/4
y = 135/4
y = 33.75
Therefore, the height of the power line, when it is 30 feet away from one of the poles, is 33.75 feet. This is the y coordinate of point K.
Side note: 33.75 ft = 33 ft + 0.75 ft = 33 ft + 12*0.75 in = 33 ft + 9 inches