Write systems of equations from context Lincoln is preparing many gifts for a family holiday party each gift must either be wrap
ped with wrapping paper or prepared in a gift bag. Lincoln can wrap a single gift in 6.5 minutes and he can do a gift bag in 2 minutes Lincoln prepared a total 13 gifts in 57.5 minutes. Write a system of equations that could be used to determine the number of gifts Lincoln wrapped and the number of gift bags he prepared define the variables that you use to write the system.
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We know that the points at which the parabola intersects the x axis are
(-5,0) and (1,0)
So the extent between these two points would be the base of the triangle
lets find the length of the base using the distance formula
the base b=6
We will get the height of the triangle when we put x=0 in the equation
y=a(0+5)(0-1)
y=-5a
so height = -5a (we take +5a since it is the height)
We know that the area of the triangle =
× 6 × (5a) = 12
15a=12
a=