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mafiozo [28]
2 years ago
12

Elizabeth is a high school basketball player. In a particular game, she made some free

Mathematics
2 answers:
k0ka [10]2 years ago
8 0
2x / y = 16
2x because she made twice the shots with free throws then two point shots
Serga [27]2 years ago
3 0

Answer:

Elizabeth made 8 free throws and 4 two-point shots.

Explaination:

Variable Definitions:

x=   the number of free throws made

y=   the number of two point shots made

Each free throw scores 1 point, so x free throws would score 1x points. Each two point shot scores 2 points, so yy two point shots would score 2y points. Therefore, the total number of points scored 1x+2y equals 16:

1x+2y=16

Since Elizabeth scored twice as many free throws as two point shots, she made more free throws, so if we multiply 2 by the number of two point shots made, we will get the number of free throws made, meaning x equals 2y.

x=2y

Write System of Equations:

​1x+2y=    16

x=  2y

Solve for y in each equation:

1x+2y=16         x=2y

2y=-1x+16         2y=x

2y/2=-1x+16/2     y=1/2x

y=-1/2x-8

The x variable represents the number of free throws made and the y variable represents the number of two point shots made. Since the lines intersect at the point (8,4) we can say:

Elizabeth made 8 free throws and 4 two-point shots.

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Step-by-step explanation:

So I'm going to use vieta's formula.

Let u and v the zeros of the given quadratic in ax^2+bx+c form.

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Let's see if uv=u+v holds.

uv=\frac{2+2i\sqrt{2}}{3} \cdot \frac{2-2i\sqrt{2}}{3}

Keep in mind you are multiplying conjugates:

uv=\frac{1}{9}(4-4i^2(2))

uv=\frac{1}{9}(4+4(2))

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Let's see what u+v is now:

u+v=\frac{2+2i\sqrt{2}}{3}+\frac{2-2i\sqrt{2}}{3}

u+v=\frac{2}{3}+\frac{2}{3}=\frac{4}{3}

We have confirmed uv=u+v for k=2.

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