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2 years ago

Write 2x/3x in simplest form

Mathematics

2 answers:

STatiana [176]2 years ago

6 0

The answer is $\frac{2}{3}$

*Remember x= $x^1$

You are technically dividing in this, whenever you divide anything with exponents, you subtract them. $x^1-x^1=0$

Therefore, the x's would cancel out, leaving just $\frac{2}{3}$

sveticcg [70]2 years ago

4 0

$\dfrac{2X}{3x}=\dfrac{2}{3}\cdot\dfrac{x}{x}=\dfrac{2}{3}\cdot\dfrac{\not x^1}{\not x_1}=\dfrac{2}{3}\cdot1=\boxed{\dfrac{2}{3}}$

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Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:

ryzh [129]

First find the critical points of <em>f</em> :

$f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7$

$\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1$

$\dfrac{\partial f}{\partial y}=6y=0\implies y=0$

so the point (1, 0) is the only critical point, at which we have

$f(1,0)=-7$

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

$f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t$

Find the critical points of <em>g</em> :

$\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0$

$\implies\sin t=0\text{ OR }1+5\cos t=0$

$\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi$

where <em>n</em> is any integer. We get 4 critical points in the interval [0, 2π) at

$t=0\implies f(10,0)=155$

$t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299$

$t=\pi\implies f(-10,0)=235$

$t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299$

So <em>f</em> has a minimum of -7 and a maximum of 299.

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2 years ago

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natali 33 [55]

Answer:

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Step-by-step explanation:

y=2/3x-11

plug in plot and remove intercept

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y=-2/3x+10

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2 years ago

(1+y) (4y+6) =0 algebra 2

marta [7]

Here is your answer! Hope this helped

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2 years ago

Find the slope of the line that passes through (10, 5) and (7, 4).

dimulka [17.4K]

Answer: M (slope) = -1 / -3 = 0.3

Step-by-step explanation:

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On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, 1) and (0, 3). Everything to th

Rom4ik [11]

The linear equality represented by the graph as, $\rm y > \frac{2}{3} x+3$

<h3>What is the definition of inequality?</h3>

Inequality is a sort of equation in which the equal sign is missing. As we will see, inequality is defined as a statement regarding the relative magnitude of two claims.

The slope of the dashed line is found as;

$\rm m = \frac{y_2-y_1}{x_2-x_1} \\\\\ m = \frac{3-1}{0+3} \\\\ m= \frac{2}{3}$

The slope-intercept form is;

y=mx+c

Substitute the obtained value;

$\rm y = \frac{2}{3}x+3$

We are aware that the given line Is a dashed line, and everything to its left is shadowed.

Hence, the linear equality is represented by the graph as, $\rm y > \frac{2}{3} x+3$

To learn more about inequity, refer to brainly.com/question/20383699

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1 year ago