All categories

3 years ago

Simplify (5x−2+3x^2)+(4x+3)

Mathematics

1 answer:

Art [367]3 years ago

5 0

Answer:

3x^2 + 9x + 1

3x ( x + 3 ) + 1

Step-by-step explanation:

(5x - 2 +3x^2 ) + (4x + 3 )

To make this a little bit more easier to read, you can remove the parentheses:

5x - 2 + 3x^2 + 4x + 3

Now, write in a way so that the like terms are next to each other:

3x^2 + 5x + 4x - 2 + 3

Now simplify the 'x' terms to get:

3x^2 + 9x - 2 + 3

Now, simplify the integers (the ones with now variables with them) to get:

3x^2 + 9x + 1

If you want, you can factor out the 3x for two of the terms to get :

3x ( x + 3 ) + 1

Therefore, your simplest form can either be 3x^2 + 9x + 1 OR 3x (x + 3 ) + 1

You might be interested in

Strawberry chews cost 3 cents more than lollipops. Sarah pays 54 cents for two strawberry chews and four lollipops. What is the

djyliett [7]

Hcrjudgrrnekjdbrhsuehr

6 0

3 years ago

Look at the triangle. What is the value of sin x°?

Andre45 [30]

Sin(x) = 12/13
x = 67.38 degrees

6 0

3 years ago

Read 2 more answers

1. - 2(x + 11) = -18

77julia77 [94]

Answer:

x = - 2

Step-by-step explanation:

Step 1:

-2 ( x + 11 ) = - 18 Equation

Step 2:

- 2x - 22 = - 18 Multiply

Step 3:

- 2x = 4 Add 22 on both sides

Step 4:

x = 4 ÷ - 2

Answer:

x = - 2

Hope This Helps :)

8 0

3 years ago

An ancient Chinese candle clock tells the amount of time that has passed by the amount of wax that has been melted off the candl

maxonik [38]

Answer:

$Time = 560\ mins$

Step-by-step explanation:

Given

$Candles = 2$ --- candles melted

$Divisions = 12$

$Time = 4\ hrs$ --- time to melt

Required

The time since the first was lit

If 1 candle melts in 4 hours, 2 candles will melt in 8 hours.

i.e.

$x = Candles * Time$

$x = 2 * 4hrs$

$x = 8hrs$

For the 3rd candle that has melted, 4 inches

First, calculate the fraction that melt

$Fraction = \frac{Melt}{Division}$

$Fraction = \frac{4}{12}$

$Fraction = \frac{1}{3}$

The time to melt is:

$y = Fraction * Time$

$y= 4 * \frac{1}{3}$

$y= \frac{4}{3}hrs$

So, the required time is:

$Time = x + y$

$Time = 8hrs + \frac{4}{3}hrs$

Convert to minutes

$Time = 8*60mins + \frac{4}{3}*60mins$

$Time = 480mins + 80mins$

$Time = 560\ mins$

4 0

3 years ago

SEE ATTACHED

fenix001 [56]

To me personally, the first bit f(g(x)) is easy and the domain is tricky. Let's try explain this.

A function takes an input number and returns an output number depending on the function. Look at f(x) = x+3, if we let the input number be 2 then we say that f(2) = 5. We could do f(π) to give us π+3 or even f(x²) to give us x² +3. The trick is to substitute the input into the function equation.

You have been asked to find f(g(x)). You know f(x) = $\frac{1+x}{1-x}$ . Putting numbers in at this point would be easy (try work out f(2), you'll do it really quick) but you have to put in g(x).

f(g(x)) = $\frac{1+g(x)}{1-g(x)}$
we also know that g(x) = $\frac{x}{1-x}$ so we can say that
f(g(x)) = $\frac{1+ \frac{x}{1-x} }{1- \frac{x}{1-x} }$ and that is f(g(x)) but the question requires that we simplify it so
$\frac{1+ \frac{x}{1-x} }{1- \frac{x}{1-x} } = \frac{ \frac{1-x}{1-x} + \frac{x}{1-x} }{ \frac{1-x}{1-x} - \frac{x}{1-x} } = \frac{ \frac{1}{1-x} }{ \frac{1-2x}{1-x} } = \frac{1}{1-2x}$

f(g(x)) = $\frac{1}{1-2x}$

Now for the tricky bit (for me, at least). The domain is the full set of values that you can 'put in to' the function and still get a real value out. So how do we work out what numbers 'break' the function? I like to use the fact that DIVIDING BY ZERO IS IMPOSSIBLE. What value of x can we put into the function to make it so the function is being divided by 0? i.e. 1-2x = 0 solve that and you have a value of x that isn't part of the domain.

This means the domain is all real numbers EXCEPT the solution to that equation. (Because if we put that value into f(g(x)) it's impossible to get a value out.)

[I know this was a lot to read, if you have any questions or don't get anything feel free to message me or leave a comment.]

5 0

3 years ago