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3 years ago

Help for brainliest

Mathematics

1 answer:

BigorU [14]3 years ago

7 0

Zeros: x = 2, x = 4

Turning point: (halfway between the zeros) x = 3, y = -1

y-intercept: where x=0, at f(0) = 8.

Axis of symmetry: the vertical line through the turning point: x = 3.

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Kyle works at a donut factory, where a 10-oz cup of coffee costs 95¢, a 14-oz cup costs $1.15, and a 20-oz cup costs $1.5

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Kyle filled 4 10-oz cups, 6 14-oz cups, and 4 20-oz cups.

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Let 10-oz, 14-oz, and 20-oz coffees be represented by the variables a, b, and c, respectively.

Since a total of 14 cups of coffee was served:

$a+b+c=14$

A total of 204 ounces of coffee was served. Therefore:

$10a+14b+20c=204$

A total of $16.70 was collected. Hence:

$0.95a+1.15b+1.5c=16.7$

This yields a triple system of equations. In order to solve a triple system, we should isolate the system to only two variables first.

From the first equation, let's subtract a and b from both sides:

$c=14-a-b$

Substitute this into both the second and third equations:

$10a+14b+20(14-a-b)=204$

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$0.95a+1.15b+1.5(14-a-b)=16.7$

In this way, we've successfully created a system of two equations, which can be more easily solved. Distribute:

For the Second Equation:

$\displaystyle \begin{aligned} 10a+14b+280-20a-20b&=204\\ -10a-6b&=-76\\5a+3b&=38\end{aligned}$

And for the Third:

$\displaystyle \begin{aligned} 0.95a+1.15b+21-1.5a-1.5b&=16.7\\ -0.55a-0.35b&=-4.3\end{aligned}$

We can solve this using substitution. From the second equation, isolate a:

$\displaystyle a=\frac{1}{5}(38-3b)=7.6-0.6b$

Substitute into the third:

$-0.55(7.6-0.6b)-0.35b=-4.3$

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$-4.18+0.33b-0.35b=-4.3$

Therefore:

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Using the equation for a:

$a=7.6-0.6(6)=4$

And using the equation for c:

$c=14-(4)-(6)=14-10=4$

Therefore, Kyle filled 4 10-oz cups, 6 14-oz cups, and 4 20-oz cups.

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