The number of cookies Natalie can bake varies directly with the time she

Mathematics

2 answers:

EastWind [94]2 years ago

4 0

The answer would be 10 dozen cookies

CaHeK987 [17]2 years ago

3 0

We already know that 0.5 of an hour, or half of an hour, is 30 minutes. We also know that 3 dozen equals 36. With this information, we can conclude that Natalie can make 72 cookies in one hour. 72 times 5 is 360. 360 divided by 12 is 30, so, Natalie can bake 30 dozen, or 360, cookies in five hours.

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What equation represents a parabola with a focus of (0,4) and a directrix of y=2

scZoUnD [109]

We know that

Any point (x,y) on the parabola is equidistant from the focus and the directrix

Therefore,

focus (0,4) and directrix of y=2

√[(x−0)²+(y−4)²]=y−(2)

√[x²+(y-4)²]=y-2

x²+(y-4)²=(y-2)²

x²+y²-8y+16=y²-4y+4

x²=4y-12-----> 4y=x²+12----->y= (x²/4)+3

the answer is

y= (x²/4)+3

7 0

3 years ago

Use the following graph of the function f(x) = x3 − 3x2 − x + 3 to answer this question: graph of x cubed minus 3 x squared minu

Marina CMI [18]

The average rate of change is also known as the slope. If we are looking to find the average rate of change between x = -1 and x = 2, in order to find the slope between those 2 x values, we need the y's that go along with them. Fill in -1 for x in the function and solve for y: $(-1)^3-3(-1)^2-(-1)+3=0$ . That means that the coordinate is (-1, 0). Fill in 2 for x in the function and solve for y: $(2)^3-3(2)^2-(2)+3=-3$ . The coordinate there is (2, -3). Now we can set up the slope formula to find the average rate of change between those 2 points: $\frac{-3-0}{2-(-1)}=\frac{-3}{3}=-1$ . Therefore, the average rate of change between x = -1 and x = 2 is -1