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enot [183]
3 years ago
14

The number of pizzas is in a proportional relationship to the weight of the shredded cheese toppings. When​ shredded, a 30​-lb b

lock of cheese is enough to make 127.5 large pizzas. Find the constant of proportionality. Explain how you can use a constant of proportionality to find how much cheese is on one slice of pizza if there are 8 slices per pizza.
Mathematics
1 answer:
Snowcat [4.5K]3 years ago
4 0
30......................127,5
1.........................x

30x = 127,5
x = 127,5/30
x = 4,25 

1 libra = 4,25 pizzas
4,25 pizzas.............1 libra
1 pizza.....................y

4,25y = 1
y = 1/4,25
y = 0,2353 libra (1 pizza)
1/8 de pizza = 0,2353/8 = 0,0294
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Answer:

20. x = 5, y = -2

21. x = 11, y = 12

22. x = 22, y = 11

23. x = 11, y = 10

Step-by-step explanation:

20. Opposite sides in the parallelogram are congruent, so

2y+18=3x-1\\ \\6x-3=17-5y

Solve this system of two equations:

\left\{\begin{array}{l}2y-3x=-19\\ \\6x+5y=20\end{array}\right.

Multiply the first equation by 2 and add two equations:

2(2y-3x)+6x+5y=2\cdot (-19)+20\\ \\4y-6x+6x+5y=-38+20\\ \\9y=-18\\ \\y=-2

Substitute it into the first equation:

2\cdot (-2)-3x=-19\\ \\-3x=-19+4\\ \\-3x=-15\\ \\x=5

21. Opposite angles in the parallelogram are congruent, so

11x+5=10y+6

Consecutive angles are supplementary, so

6x-y+11x+5=180^{\circ}

Solve this system of two equations:

\left\{\begin{array}{l}11x-10y=1\\ \\17x-y=175\end{array}\right.

From the second equation

y=17x-175

Substitute it into the first equation:

11x-10(17x-175)=1\\ \\11x-170x+1750=1\\ \\-159x=-1749\\ \\x=11\\ \\y=17\cdot 11-175=187-175=12

22. Opposite angles in the parallelogram are congruent, so

2x-5=3y-12

Consecutive angles are supplementary, so

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Solve this system of two equations:

\left\{\begin{array}{l}2x-3y=-7\\ \\3x+7y=185\end{array}\right.

From the first equation

x=-3.5+1.5y

Substitute it into the second equation:

3(-3.5+1.5y)+7y=185\\ \\-10.5+4.5y+7y=185\\ \\-105+45y+70y=1,850\\ \\115y=1,850+105\\ \\115y=1,955\\ \\y=17\\ \\x=-3.5+1.5\cdot 17=22

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Multiply the second equation by 2 and subtract it from the first equation:

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Substitute it into the first equation:

2\cdot 11-4y=-18\\ \\-4y=-18-22\\ \\-4y=-40\\ \\y=10

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