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3 years ago

How do you graph a linear equation?For example, -18x+9y=72

Mathematics

2 answers:

nikdorinn [45]3 years ago

4 0

Basically with the example you have you need to have the x and y variables on different sides.
Equation:
-18x+9y=72 (now you want to add 18x on both sides)
+18x +18x
9y=72+18x (next you divide 9 to both sides to get x and y alone)
9
y=8+2x (now that you have the x and y alone this is the final equation)

On the graph you want to put a dot on 8 since it's the y-intercept or the starting point of the equation. After that you want to add 2 every time you go by 1 on the x-axis. I have a picture of a graph...

I hope this help you out :D

EleoNora [17]3 years ago

3 0

Answer:

The graph of given equation is shown below.

Step-by-step explanation:

We need to draw the graph of linear equation.

Let as consider a linear equation.

$-18x+9y=72$

First we need to find any two points on the line. So, will find x and y-intercept of the line.

Substitute x=0 in the given equation to find the y-intercept.

$-18(0)+9y=72$

$9y=72$

Divide both sides by 9.

$y=8$

⇒ y-intercept of the line is 8.

Substitute y=0 in the given equation to find the x-intercept.

$-18x+9(0)=72$

$-18=72$

Divide both sides by -18.

$y=-4$

⇒ x-intercept of the line is -4.

Now, plot these two points (0,8) and (-4,0) on a coordinate plane and connect them by a straight line.

Therefore, the graph of given equation is shown below.

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The equations that must be solved for maximum or minimum values of a differentiable function w=f(x,y,z) subject to two constrai

sammy [17]

The Lagrangian is

$L(x,y,z,\lambda,\mu)=x^2+y^2+z^2+\lambda(4x^2+4y^2-z^2)+\mu(2x+4z-2)$

with partial derivatives (set equal to 0)

$L_x=2x+8\lambda x+2\mu=0\implies x(1+4\lambda)+\mu=0$

$L_y=2y+8\lambda y=0\implies y(1+4\lambda)=0$

$L_z=2z-2\lambda z+4\mu=0\implies z(1-\lambda)+2\mu=0$

$L_\lambda=4x^2+4y^2-z^2=0$

$L_\mu=2x+4z-2=0\implies x+2z=1$

Case 1: If $y=0$ , then

$4x^2-z^2=0\implies4x^2=z^2\implies2|x|=|z|$

Then

$x+2z=1\implies x=1-2z\implies2|1-2z|=|z|\implies z=\dfrac25\text{ or }z=\dfrac23$

$\implies x=\dfrac15\text{ or }x=-\dfrac13$

So we have two critical points, $\left(\dfrac15,0,\dfrac25\right)$ and $\left(-\dfrac13,0,\dfrac23\right)$

Case 2: If $\lambda=-\dfrac14$ , then in the first equation we get

$x(1+4\lambda)+\mu=\mu=0$

and from the third equation,

$z(1-\lambda)+2\mu=\dfrac54z=0\implies z=0$

Then

$x+2z=1\implies x=1$

$4x^2+4y^2-z^2=0\implies1+y^2=0$

but there are no real solutions for $y$ , so this case yields no additional critical points.

So at the two critical points we've found, we get extreme values of

$f\left(\dfrac15,0,\dfrac25\right)=\dfrac15$ (min)

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3 years ago

Find 0. Trigonometry problems.

aivan3 [116]

In the triangle with legs 7 and 9 cm, you can find the length of the hypotenuse by using the Pythagorean theorem. If the hypotenuse is $x$ , then

$7^2+9^2=x^2\implies x=\sqrt{130}$

The other right triangle with leg 6 cm and containing the angle $\theta$ satisfies

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3 years ago

. Kerry bought a bag of dog food for $37.99. If sales tax is 7.6%, how much did she pay in tax?

Charra [1.4K]

Answer

Find out the how much did kerry pay in tax .

To proof

As given

Kerry bought a bag of dog food for $37.99.

If sales tax is 7.6%

7.6 % is written in the decimal form

$= \frac{7.6}{100}$

= 0.076

7.6 % of the $37.99 = 0.076 ×37.99

= 2.88724

= $2.89 ( approx)

Kerry pay in the sales tax be $2.89

Hence proved

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tester [92]

Answer: $\sqrt{41}$

===========================================

Work Shown:

Use the distance formula.

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Or you could use the pythagorean theorem, which is how the distance formula is set up.

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S_A_V [24]

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