Answer: Choice B
{(0,0), (1,2), (2,4), (3,4)}
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Explanation:
A function is only possible if each x input leads to exactly one y output. For choice A, we have x = 1 lead to y = 3 and y = 5 at the same time, which is what the points (1,3) and (1,5) are saying. Therefore, choice A is not a function.
Choice C is also ruled out because x = 2 repeats itself as well. In this case, (2,3) and (2,4) means that the input x = 2 leads to the two outputs y = 3 and y = 4.
Choice D can be eliminated also for two reasons: x = 0 shows up twice, so does x = 2.
Only choice B has each x value listed one time only. So that means each input leads to exactly one output.
If you graph choice A, C or D, you'll find they fail the vertical line test. The vertical line test is where you test if you can draw a vertical line through more than one point on the graph. If you can draw a vertical line through more than one point on the graph, then the relation fails to be a function.
The surface area of a cone is equal to the base plus the lateral area.
The base is a circle, and has a diameter of 16 meters.
The radius is always half the diameter, so it is 8 meters.
The area of a circle = πr², where r is the radius. π(8)² = 64π ≈ 201.06193
The area of the base is ≈ 201.06193.
To find the lateral area of the cone, we need to find the slant height.
Since the height, radius, and slant height of the cone form a right triangle, we can use the Pythagorean Theorem to find the slant height with what we are given.
radius² + height² = slant height²
8² + 37² = slant height²
64 + 1369 = slant height²
1433 = slant height²
slant height = √1433
The lateral area of a cone is equal to πrl, where r = radius and l = slant height.
πrl = π(8)(√1433) ≈ 951.39958
(there are other formulas which do the same thing, but it doesn't matter.)
Now we add the lateral area and base together to find our surface area.
201.06193 + 951.39958 = 1152.46151 which rounds to C. 1,152 m².
Answer:
Step-by-step explanation:
2 $4 bags = $8
$10 - $8 = $2 change
f(x) = 0.5x - money per ticket
g(x) = 8x - tickets per hour
We replace g(x) with its value (8x).
f(g(x)) = f(8x)
We replace the x in f(x) with 8x.
f(8x) = 0,5 × 8x
f(8x) = 4x
<u>⇒ f(g(x)) = 4x</u>
<u></u>
Correct answer:
a.<em> f(g(x)) = 4x, which represents the money Aurora made in dollars per hour</em>
