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4 years ago

Solve the following system of equations: x - 2y = 14 x + 3y = 9

1 answer:

3 0

Solve your system of equations step by step.

x−2y=14;x+3y=9

Solve x−2y=14 for x:

x−2y+2y=14+2y (Add 2y to both sides)

x=2y+14

Substitute (2y+14) for x in x+3y=9:

x+3y=9

2y+14+3y=9

5y+14=9(Simplify both sides of the equation)

5y+14+−14=9+−14 (Add -14 to both sides)

5y=−5

5y5=−55 (Divide both sides by 5)

y=−1

Substitute (−1) for y in x=2y+14:

x=2y+14

x=(2)(−1)+14

x=12(Simplify both sides of the equation)

So,

y=-1
x=12

Answer is C)

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3 0

3 years ago

The rate at which the temperature is dropping is 6t 5t2 degrees Celsius per hour t hours after sundown. How much had the tempera

Whitepunk [10]

Using a differential equation, it is found that the temperature dropped 72 degrees Celsius between sundown and 3 hours after sundown.

<h3>What is the differential equation that describes the temperature in t hours after sundown?</h3>

The rate at which the temperature is dropping is $6t + 5t^2$ degrees Celsius per hour t hours after sundown, hence the <em>differential equation</em> is:

$\frac{dT}{dt} = 6t + 5t^2$

Applying <em>separation of variables</em>, we find the solution as follows:

$\frac{dT}{dt} = 6t + 5t^2$

$dT = (6t + 5t^2) dt$

$\int dT = \int (6t + 5t^2) dt$

$T(t) = \frac{5t^3}{3} + 3t^2 + T(0)$

In which T(0) is the temperature at sundown.

In 3 hours, the change will be of:

$C = T(3) - T(0) = \frac{5t^3}{3} + 3t^2|_{t = 3}$

Hence:

$\frac{5(3)^3}{3} + 3(3)^2 = 45 + 27 = 72$

The temperature dropped 72 degrees Celsius between sundown and 3 hours after sundown.

You can learn more about differential equations at brainly.com/question/24348029

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2 years ago

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Answer:

1/9

Step-by-step explanation:

3+4+2=9

9*2=18

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2/18=1/9

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3 years ago

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3 years ago

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3 years ago