What is 4/12 simplest form

If f(x)= 3x-2 and g(x) =2x+1 find (f- (x)

Travka [436]

$f(x)=3x-2;\ g(x)=2x+1\\\\(f-g)(x)=f(x)-g(x)=(3x-2)-(2x+1)=3x-2-2x-1=x-3$

Answer: (f - g)(x) = x - 3.

8 0

4 years ago

A 275 inch pipe is cut into two pieces. One piece is four times the length of the other. Find the length of the shorter piece.

Darina [25.2K]

Since one piece is four time the length <em>x, </em>we can represent that as 4x.

Thus making the equation:

4x+x=275

5x=275

x=55

4(55)=220

220+55=275

So, the length of the longer piece is 220 inches, and the length of the shorter piece is 55 inches.

3 0

4 years ago

The relationship between Mexican pesos and American dollars is a directly proportional relationship. During Kevin’s vacation, Ke

Harrizon [31]

Answer:

50 in Mexican is 935.12500

7 0

3 years ago

A carpentry shop currently sells 66000 decoy ducks per year at a cost of 16 dollars each. In the previous year when they raised

Rus_ich [418]

Answer:

19 dollars

Step-by-step explanation:

<h2>Buckle up! This is a good one!</h2>

First we have to find the line that goes trough the two points. And it has the form :

$y=mx+b$

<em>m is often called the slope.</em>

Given the two points (66000, 16) and (51000, 21) we find m with this formula:

$m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\\m=\frac{21-16}{51000-66000} \\m=-\frac{5}{15000} \\m=-\frac{1}{3000}$

We pick the point (51000,21) and plug it into the equation of the line and we find b:

$y= mx + b\\21=(-\frac{1}{3000} )(51000)+b\\21=-17+b\\21+17=b=38$

<h3>And we have got our line equation</h3>

$y= -\frac{1}{3000}x + 38\\$

<u>Where x represents the quantity and y represents the price.</u>

<u />

<h2>The revenue</h2>

The revenue is price times quantity, since price is y and quantity is x, we get

$y=-\frac{1}{3000} x+38\\y*x=x*(-\frac{1}{3000} x+38)\\yx=-\frac{1}{3000} x^2+38x\\R(x)=-\frac{1}{3000} x^2+38x$

<h3>to maximize the revenue, we get the first derivative:</h3>

$R(x)=-\frac{1}{3000} x^2+38x\\R'(x)=-(2)\frac{1}{3000} x+38\\R'(x)=-\frac{2}{3000} x+38\\\\R'(x)=-\frac{1}{1500} x+38\\\\$

$R'(x)=-\frac{1}{1500} x+38=0\\38=\frac{1}{1500} x\\38*1500=x=57000$

So the quantity that maximizes revenue is 57000,

<h3>let's find out the price by plugging it into the equation:</h3>

$y= -\frac{1}{3000}x + 38\\y= -\frac{1}{3000}(57000) + 38\\y= -19 + 38\\y=19$

<h2>And there you go! 19 dollars is the price the carpentry shop should charge per decoy duck.</h2>

7 0

3 years ago

Identify the graph that correctly represents the inequality |x + 1| + 2 > 5.

NeTakaya

$|x+1|\ \textgreater \ 3$

The greater than 3 means that the graph will have a shaded region for when the absolute value of (x+1) is greater than 3.

The absolute value means that we are interested in the magnitude of x+1. That means that the the graph will be shaded where x+1 > 3, and where -x-1 > 3

If we solve both of these for x, we get:

x > 2 and x < -4

So the graph will look like the attached picture. Notice that the vertical lines are dotted rather than solid. This means that we are dealing with a greater than sign, not a greater than or equal to.

8 0

3 years ago

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