The "standard" parabola with roots 0 and 2 is
All multiples of this parabola, i.e.
have the same roots. We can choose the factor such that the parabola passes through the desided point: if we plug 1, 5 for x, y we have
So, our claim is that the parabola
has roots 0 and 2 and vertex at (1, 5).
You can easily verify this: the roots are guaranteed by the fact that we can write the equation as
The vertex must be at x=1, because it's the midpoint of the roots. Moreover, if we evaluate the function at x=1 we have
as required.
Answer:
24
Step-by-step explanation:
It take 4 to make one yard and you need six yards soo..
6 x 4 = 24
20 + 40x = 260
40x = 260 - 20
40x = 240
x = 240/40
x = 6 fulltime employees needed
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Step-by-step explanation:
Question 5
y = - 3x
Question 6
Lets name the number of guppies in the tank as x
number of goldfish in the tank is 6 times the amount of guppies.
since the amount of guppies is x, then number of goldfish is 6 * x = 6x
therefore total amount of guppies and goldfish is x + 6x
there are total of 21 fish
therefore x + 6x = 21
7x = 21
x = 21/7
x = 3
therefore number of guppies = 3
number of goldfish -6x and x = 3 therefore 3 x 6 = 18 goldfish
we are asked to find how many more goldfish than guppies
we have to find the difference
18 - 3 = 15
there are 15 more goldfish than guppies