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Softa [21]
3 years ago
5

6 plates and 5 cups cost 23.80 dollars. 7 plates and 6 cups cost 28.00. Each plate costs the same as the other plates, each cup

costs the same as the other cups. What is the cost of 1 plate? What is the cost of 1 cup?
Mathematics
1 answer:
andrey2020 [161]3 years ago
7 0
Cups = c
Plates = p

6p + 5c = 23.80 ==> multiply by 6 ==> 36p + 30c = 142.80
7p + 6c = 28.00 ==> multiply by 5 ==> 35p + 30c = 140.00


Now use algebra to have the 30c be on one side and the rest on the other:

36p + 30c = 142.80 | -36p

30c = 142.80 - 36p


35p + 30c = 140.00 | -35p

30c = 140.00 - 35p


Now set them equal to each other about the 30c:

142.80 - 36p = 140.00 - 35p


Use algebra to solve for p:

142.80 - 36p = 140.00 - 35p | +36p

142.80 = 140.00 + p | - 140

2.80 = p


Go back to one of the "30c" equations and plug in the value for p:

30c = 140 - 35p

30c = 140 - 35(2.80)

30c = 140 - 98

30c = 42 | /30

c = 42/30

c = 1.4


Plates are $2.80
Cups are $1.40
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Given the triangle

PQR

with points

P(8,0)

Q(6,2)

R(-2,-4)

And the triangle

P'Q'R'

with points

P'(4,0)

Q'(3,1)

R'(-1,-2)

Part A. Scale factor

Using the vertex

P( 8, 0)

P'(4,0)

the dilatation factor is given by

\frac{4}{8}=\frac{1}{2}

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Part B:

P''Q''R'' after using P'Q'R' reflected about the y axis

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P^{\prime}(4,0)\rightarrow P^{\prime\prime}(-4,0)Q^{\prime}(3,1)\rightarrow Q^{\prime\prime}(-3,1)R^{\prime}(-1,-2)\rightarrow R^{\prime\prime}(1,-2)

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P''(-4,0)

Q''(-3,1)

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Part C:

PQR is congruent to P''Q''R''?

Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.

Then the triangles are not congruent

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1 year ago
What two number that are the same have the product of 0.2 and the quotient of 0.8
Pie
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Step-by-step explanation:

there are 5 fifths in 1 hinting the name fifths

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Zeke deposited $300 into a savings account. The interest rate on the account is 3%, compounded continuously. To determine how lo
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