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3 years ago

How do you solve this system of linear equation by substitution x-3y=-12y=2x+9

1 answer:

6 0

Finding x:
If y=2x+9, substitute y into the equation x-3y=-12.
You will get: x-3(2x+9)=-12
Now, distribute: x-6x-27=-12
Add like terms: -5x-27=-12
Add 27 to both sides: -5x=15
Divide both sides by -5: x=-3

Now, substitute this value of x into the equation to find y: y=2(-3)+9
Multiply: y=-6+9
Add: y=3

Here is the solution: (x,y)=(-3,3)

Hope this explanation helped!

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Answer:

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Step-by-step explanation:

y=-3(x-7)(x+3)

y=-3(x^2-4x-21)

y=-3x^2+12x+63

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3 years ago

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3 years ago

Find the general indefinite integral. (Use C for the constant of integration. Remember to use absolute values where appropriate.

Maru [420]

Answer:

$9\text{ln}|x|+2\sqrt{x}+x+C$

Step-by-step explanation:

We have been an integral $\int \frac{9+\sqrt{x}+x}{x}dx$ . We are asked to find the general solution for the given indefinite integral.

We can rewrite our given integral as:

$\int \frac{9}{x}+\frac{\sqrt{x}}{x}+\frac{x}{x}dx$

$\int \frac{9}{x}+\frac{1}{\sqrt{x}}+1dx$

Now, we will apply the sum rule of integrals as:

$\int \frac{9}{x}dx+\int \frac{1}{\sqrt{x}}dx+\int 1dx$

$9\int \frac{1}{x}dx+\int x^{-\frac{1}{2}}dx+\int 1dx$

Using common integral $\int \frac{1}{x}dx=\text{ln}|x|$ , we will get:

$9\text{ln}|x|+\int x^{-\frac{1}{2}}dx+\int 1dx$

Now, we will use power rule of integrals as:

$9\text{ln}|x|+\frac{x^{-\frac{1}{2}+1}}{-\frac{1}{2}+1}+\int 1dx$

$9\text{ln}|x|+\frac{x^{\frac{1}{2}}}{\frac{1}{2}}+\int 1dx$

$9\text{ln}|x|+2x^{\frac{1}{2}}+\int 1dx$

$9\text{ln}|x|+2\sqrt{x}+\int 1dx$

We know that integral of a constant is equal to constant times x, so integral of 1 would be x.

$9\text{ln}|x|+2\sqrt{x}+x+C$

Therefore, our required integral would be $9\text{ln}|x|+2\sqrt{x}+x+C$ .

4 0

3 years ago

A certain shade of pink is created by adding 3 cups of red paint to 7 cups of white paint.

vazorg [7]

Answer:

7/3 is constant of proportionality and, 3/7 of a cup of red paint should be added to 1 cup of white paint.

Step-by-step explanation:

Constant of proportionality is the constant value of the ratio of two proportional quantities x and y; usually written y = kx, where k is the factor of proportionality.

To make color pink,

for every 3 cups of red , we need 7 cups of white.

Let 'r' be the cups of red required

let 'w' be the cups of white required

so , as per the question

for 3 r we need = 7 w

r = 7/3 w

so, 7/3 is constant of proportionality and, 3/7 of a cup of red paint should be added to 1 cup of white paint.

You already have the answer! ;)

4 0

3 years ago

6.5÷41.6= awnser this someone

satela [25.4K]

the answer is 0.15625

8 0

3 years ago

Read 2 more answers