Answer:
Her sister ate more cookies.
Step-by-step explanation:
If you convert 3/6 into a simplified fraction, it turns into half. Half of 12 is 6. Natalie ate 3 cookies. Therefore, her sister ate more.
Answers:
Functions
- y = -x+11
- y = 2x^2-6x+4
- y = -7
Not functions
- x = 3
- x^2+y^2 = 81
- y^2 = -5x-12
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Explanation:
A function is possible if and only if any given x input leads to exactly one y output.
For something like x^2+y^2 = 81, we can see that x = 0 leads to either y = 9 or y = -9. So this would <u>not</u> be a function. We would need x to pair with only y value to have it be a function.
We have the same thing going on with y^2 = -5x-12 as well.
For anything of the form x = k, where k is any real number, this is also not a function. We have one single input only and it leads to infinitely many outputs. So in a sense, this is even worse compared to the other examples.
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In summary, we have these three non-functions:
- x = 3
- x^2+y^2 = 81
- y^2 = -5x-12
Everything else is a function. You can use the vertical line test as a visual way to check.
Answer:
Option A:
y = 3*(x - 5)^2 - 4
Step-by-step explanation:
For a quadratic equation:
y = a*x^2 + b*x + c
with the vertex (h, k), we can rewrite the function as:
such that:
h = -b/2*a
y = a*(x - h)^2 + k
Here we have the function:
y = 3*x^2 - 30*x + 71
the x-value of the vertex will be:
h = -(-30)/(2*3) = 30/6 = 5
And k is given by:
k = y(5) = 3*(5)^2 - 30*5 + 71 = -4
Then the vertex is:
(5, - 4)
And we can rewrite the equation in the vertex form as:
y = 3*(x - 5)^2 + (-4)
y = 3*(x - 5)^2 - 4
Then the correct option is A.
Cost of 1 plant = $ p
Cost of 4 plants = $(4p)
Cost of a 10-gallon tank = $10
Cost of a water dish = $3
Total cost = 4p + 10 + 3 = 4p + 13