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2 years ago

What is the value of x in the equation 5(2x-7)=15x-10?

Mathematics

1 answer:

Ymorist [56]2 years ago

6 0

Answer:

x = -5

Step-by-step explanation:

First distribute the 5 on the right side of the equation.

10x - 35 = 15x - 10

Then subtract 10x on each side

-35 = 5x - 10

Then add 10 on each side

-25 = 5x

Divide 5 on each side to get x

-25 / 5 = -5

I hope this helps! :)

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F() = x2 + 1<br> g(x) = 5 - x<br> (f+g)(x) =

frutty [35]

Answer:

(f+g)(x) = x² - x + 6

Step-by-step explanation:

We can find (f+g)(x) by adding f(x) and g(x).

f(x) = x² + 1

g(x) = 5 - x

(f+g)(x) = f(x) + g(x)

(f+g)(x) = (x² + 1) + (5 - x)

(f+g)(x) = x² + 1 + 5 - x

(f+g)(x) = x² - x + 6

4 0

3 years ago

Solve the following differential equation: (2x+5y)dx+(5x−4y)dy=0 *Hint: they are exact<br><br> C=.

Tpy6a [65]

Answer with Step-by-step explanation:

The given differential equation is

$(2x+5y)dx+(5x-4y)dy=0$

Now the above differential equation can be re-written as

$P(x,y)dx+Q(x,y)dy=0$

Checking for exactness we should have

$\frac{\partial P}{\partial y}=\frac{\partial Q}{\partial x}$

$\frac{\partial P}{\partial y}=\frac{\partial (2x+5y)}{\partial y}=5$

$\frac{\partial Q}{\partial x}=\frac{\partial (5x-4y)}{\partial x}=5$

As we see that the 2 values are equal thus we conclude that the given differential equation is exact

The solution of exact differential equation is given by

$u(x,y)=\int P(x,y)dx+\phi(y)\\\\u(x,y)=\int (2x+5y)dx+\phi (y)\\\\u(x,y)=x^2+5xy+\phi (y)$

The value of $\phi (y)$ can be obtained by differentiating u(x,y) partially with respect to 'y' and equating the result with P(x,y)

$\frac{\partial u}{\partial y}=\frac{\partial (x^2+5xy+\phi (y)))}{\partial y}=Q(x,y))\\\\5y+\phi '(y)=(5x-4y)\\\\\phi '(y)=5x-9y\\\\\int\phi '(y)\partial y=\int (5x-9y)\partial y\\\\\phi (y)=5xy-\frac{9y^2}{2}\\\\\therefore u(x,y)=x^2+10xy-\frac{9y^2}{2}+c$