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2 years ago

Solve the system of equations. -12x-5y=40 and 12x-11y=88 x= y=

Mathematics

2 answers:

SpyIntel [72]2 years ago

3 0

Answer:

(0,-8)

x=0

y=-8

Step-by-step explanation:

There are a couple of ways you can solve this I used what I think is called the elimination method

We first start by writing the equations in linear form (y=mx+b)

For the first one we have -12x-5y=40

we add 5y to both sides and subtract 40 to get

-12x-40=5y

divide by 5 to get

-12/5x-8=y

Then the second one we have

12x-11y=88

same deal here, add 11y and subtract 88 to get

12x-88=11y

divide by 11 and get

12/11x-8=y

We then set the two equations equal to each other and get

-12/5x-8=12/11x-8

We can add 8 to both sides and get

-12/5x=12/11x

Just by looking at it you can see that the only solution for x is 0

Plug in 0 to the first equation and get -12*0-5y=40

This means that -5y=40

Solve for y and get -8

Aleksandr-060686 [28]2 years ago

3 0

Answer:

x=0 , y= -8

Step-by-step explanation:

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3 years ago

Let L be a tangent line to the hyperbola x y = 2 at x = 9 . Find the area of the triangle bounded by L and the coordinate axes.

mafiozo [28]

Answer:

$A = 4$

Step-by-step explanation:

The equation of the slope of the tangent line L is obtained by deriving the equation of the hyperbola:

$y = \frac{2}{x}$

$y'=-2\cdot x^{-2}$

The numerical value of the slope is:

$y' = -2 \cdot (9)^{-2}\\y' = -\frac{2}{81}$

The component of the y-axis is:

$y = \frac{2}{9}$

Now, the tangent line has the following mathematical model:

$y = m \cdot x + b$

The value of the intercept is found by isolating it within the equation and replacing all known variables:

$b = y - m \cdot x$

$b = \frac{2}{9}-(-\frac{2}{81} )\cdot (9)\\b = \frac{4}{9}$

Thus, the tangent line is:

$y = -\frac{2}{81}\cdot x + \frac{4}{9}$

The vertical distance between a point of the tangent line and the origin is given by the intercept.

$d_{y} = \frac{4}{9}$

In order to find horizontal distance between a point of the tangent line and the origin, let equalize y to zero and clear x:

$-\frac{2}{81}\cdot x + \frac{4}{9}=0$

$-\frac{2}{9}\cdot x + 4 = 0$

$x = 18$

$d_{x} = 18$

The area of the triangle is computed by this formula:

$A = \frac{1}{2}\cdot d_{x}\cdot d_{y}$

$A = \frac{1}{2}\cdot (18)\cdot (\frac{4}{9} )$

$A = 4$

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3 years ago

Evaluate f(x) =3x+8 for x=1

SpyIntel [72]

X= 11
If you plug in 1 for X in the equation, you will get:
f(x) =3+8
3+8=11
Hope this helps.

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