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Elodia [21]
3 years ago
9

Solve the system of equations by graphing: 2x + 3y = 2 6x + 18y = 9

Mathematics
1 answer:
cluponka [151]3 years ago
7 0
The answer is  A: x=1/2 , y= 1/3

Solve the following system:
{2 x + 3 y = 2 | (equation 1)
{6 x + 18 y = 9 | (equation 2)

Swap equation 1 with equation 2:
{6 x + 18 y = 9 | (equation 1)
{2 x + 3 y = 2 | (equation 2)

Subtract 1/3 × (equation 1) from equation 2:
{6 x + 18 y = 9 | (equation 1)
{0 x - 3 y = -1 | (equation 2)

Divide equation 1 by 3:
{2 x + 6 y = 3 | (equation 1)
{0 x - 3 y = -1 | (equation 2)

Multiply equation 2 by -1:
{2 x + 6 y = 3 | (equation 1)
{0 x+3 y = 1 | (equation 2)

Divide equation 2 by 3:
{2 x + 6 y = 3 | (equation 1)
{0 x+y = 1/3 | (equation 2)

Subtract 6 × (equation 2) from equation 1:
{2 x+0 y = 1 | (equation 1)
v0 x+y = 1/3 | (equation 2)

Divide equation 1 by 2:
{x+0 y = 1/2 | (equation 1)
v0 x+y = 1/3 | (equation 2)

Collect results:
Answer:  {x = 1/2, y = 1/3

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Consider that a 1/2 cup serving of 1% cottage cheese is equivalent to 125 grams. If 1 ounce of cottage cheese is equivalent to 2
VikaD [51]

Answer:

4.42 ounces.

Step-by-step explanation:

We have been given that a 1/2 cup serving of 1% cottage cheese is equivalent to 125 grams. 1 ounce of cottage cheese is equivalent to 28.35 grams.  We are asked to find the ounces in 1/2 cup serving.

We will use proportions to solve our given problem.

\frac{\text{Ounce}}{\text{Grams}}=\frac{1}{28.25}

Upon substituting our given values, we will get:

\frac{\text{Ounce}}{125}=\frac{1}{28.25}

\frac{\text{Ounce}}{125}\times 125=\frac{1}{28.25}\times 125

\text{Ounce}=4.42477876

Upon rounding to nearest hundredth, we will get:

\text{Ounce}\approx 4.42

Therefore, 1/2 cup serving contains 4.42 ounces.

7 0
3 years ago
If the complement of an angle is equal to the supplement of four times the angle, then find the measure of the angle.
lisabon 2012 [21]

Answer:

Step-by-step explanation:

Note that:

Two angles are Complementary when they add up to 90 degrees

Two angles are supplementary when they add up to 180 degrees

Let the angle = x

If the complement of an angle is equal to the supplement of four times the angle, then find the measure of the angle.

90 - x = 180 - 4x

6 0
3 years ago
70/9 as a mixed number
Makovka662 [10]
70/9
Divide 
9*7 = 63
70-63 = 7

7  7/9
7 0
2 years ago
Read 2 more answers
Convert y = 8x^2-80x-32 to vertex form by completing the square. ​
lidiya [134]

Answer:

y = 8(x-5)^2 -232

Step-by-step explanation:

Factor out the 8 to get

y = 8(x^2-10x-4)

y = 8(x-5)^2 -232

8 0
2 years ago
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Tammy bought a nightstand that was marked down 60% from an original price of $50. If she paid 10% sales tax, what was the total
AURORKA [14]

Answer: the total cost of the nightstand is $22

Step-by-step explanation:

The original price of the night stand is $50. If the original price of the night stand was marked down by 60%, it means that the amount of money by which it was reduced would be

60/100 × 50 = 0.6 × 50 = 30

The new selling price would be

50 - 30 = $20

If she paid 10% sales tax,the amount of tax paid would be

10/100 × 20 = 0.1 × 20 = 2

Therefore, the total cost of the nightstand would be

20 + 2 = $22

7 0
3 years ago
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