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Solve the system by elimination . 2x-y=10 , -3x+y=-12

IceJOKER [234]

Answer:

x would equal 2 and y would equal -6 so, (2,-6)

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Santa's elves are selling

Andreas93 [3]

cost of one peppermint cookies = $ 0.6

cost of one cinnamon sugar cookies = $ 0.3

<h3><u>Solution:</u></h3>

Let "p" be the cost of one peppermint cookies

Let "c" be the cost of one cinnamon sugar cookies

<u><em>To find: cost of each cookie</em></u>

<h3><u><em>On the first day, they sold 120 peppermint cookies and 30 cinnamon sugar cookies for a total of $81</em></u></h3>

We can frame a equation as:

120 peppermint cookies x cost of one peppermint cookies + 30 cinnamon sugar cookies x cost of one cinnamon sugar cookies = $ 81

$120 \times p + 30 \times c = 81$

120p + 30c = 81 --------- eqn 1

<h3><u><em>The next day they made $60 by selling 70 peppermint cookies and 60 cinnamon sugar cookies</em></u></h3>

70 peppermint cookies x cost of one peppermint cookies + 60 cinnamon sugar cookies x cost of one cinnamon sugar cookies = $ 60

$70 \times p + 60 \times c = 60$

70p + 60c = 60 --------- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "p" and "c"

Multiply eqn 1 by 2

240p + 60c = 162 --- eqn 3

Subtract eqn 2 from eqn 3

240p + 60c = 162

70p + 60c = 60

(-) -------------------------

170p = 102

Substitute p = 0.6 in eqn 1

120p + 30c = 81

120(0.6) + 30c = 81

72 + 30c = 81

30c = 9

<u><em>Summarizing the results:</em></u>

<em>cost of one peppermint cookies = $ 0.6</em>

<em>cost of one cinnamon sugar cookies = $ 0.3</em>

6 0

3 years ago

The distance from the earth to the moon is 3.84 x 105 km

Anarel [89]

Part (a)

<h3>Answer: $3.84 \times 10^8 \text{ meters}$ </h3>

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Explanation:

Multiply by 1000 to go from km to meters.

This is because 1000 m = 1 km.

Multiplying by 1000 in scientific notation means we add 3 to the exponent 5. The 3 is because 1000 = 10^3.

So the $3.84 \times 10^5 \text{ km}$ becomes $3.84 \times 10^8 \text{ meters}$

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Part (b)

Answer in standard form: 960,000 seconds

Answer in scientific notation: $9.6\times10^{5} \text{ seconds}$

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Work Shown:

$\text{distance} = \text{rate}*\text{time}\\\\\text{time} = \frac{\text{distance}}{\text{time}}\\\\\text{time} = \frac{3.84 \times 10^8 \text{ meters}}{400 \ \text{ m}/\text{s}}\\\\\text{time} = \frac{3.84 \times 10^8}{4 \times 10^2} \text{ seconds}\\\\\text{time} = \frac{3.84}{4}*\frac{10^{8}}{10^2} \text{ seconds}\\\\\text{time} = 0.96 \times 10^{8-2} \text{ seconds}\\\\\text{time} = 0.96\times 10^{6} \text{ seconds}\\\\$

$\text{time} = (9.6\times10^{-1})\times10^{6} \text{ seconds}\\\\\text{time} = 9.6\times(10^{-1}*10^{6}) \text{ seconds}\\\\\text{time} = 9.6\times10^{-1+6} \text{ seconds}\\\\\text{time} = 9.6\times10^{5} \text{ seconds}\\\\\text{time} = 960,000 \text{ seconds}\\\\$