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larisa86 [58]
3 years ago
7

How many 6 ounce cups can you completely fill using a package of Kool-aid that makes two quarts Remember that there are 32fl oz

in a quart
Mathematics
1 answer:
aliya0001 [1]3 years ago
4 0
You can completely fill 10 cups
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Step-by-step explanation:

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3 years ago
Find all solutions to the following system of equations -y²+6y+x-9=0 ; 6y=x+27.Illustrate with a graph.
Dimas [21]

Answer:

The solution to the system is the pair (9, 6)

Step-by-step explanation:

Hi!

First, let´s write the system of equations:

-y² + 6y + x -9 = 0

6y = x +27

The solutions of the system are the pairs (x, y) that satisfy both equations.

Let´s take the second equation and solve it for x:

6y = x +27

Subtract 27 from both sides of the equation

6y - 27 = x

Now, we can replace x in the first equation and solve it for y:

-y² + 6y + x -9 = 0

-y² + 6y + 6y - 27 -9 = 0

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Notice that -y² + 12y - 36 = -(y - 6)², then:

-(y - 6)² = 0

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(alternatively you can solve the quadratic equation using the quadratic formula).

Now let´s find the value of x:

x = 6y -27

x = 6·6 -27

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The solution to the system is the pair (9, 6)

Please see the attached figure. The point where the curves intersect is the solution to the system.

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