Using the completing the square method, which of the following is the solution to x2 + 8x

Janet buys 12 pens for $5.88. What is the cost per pencil?

Vikki [24]

.49 cents per pencil

8 0

3 years ago

PLEASE ANSWER I WILL GIVE 50 POINTS AND BRAINLIEST TO WHOEVER ANSWERS FIRST!! PLZZZ ANSWEERRR!!

Serhud [2]

Answer:

3375 $\pi \\$ cubic centimeters

Step-by-step explanation:

Trick question: The largest piece is the entire cone.

First lets identify the equation for volume.

V= 1/3 h pi r^2

h=45

r=15

V= 1/3 45 * pi 15^2

v= 15* pi 225

3375 pi

You keep pi because the answer has pi.

8 0

3 years ago

In six months, 33.6 gallons were used. Find the unit rate.

Nana76 [90]

I believe the answer is 5.6

Just divide 33.6 by 6

6 0

4 years ago

A. Use composition to prove whether or not the functions are inverses of each other.

kogti [31]

A. In a composition of two functions the first function is evaluated, and then the second function is evaluated on the result of the first function. In other word, you are going to evaluate the second function in the first function.

Remember that you can evaluate function at any number just replacing the variable in the function with the number. For example, let's evaluate our function $f(x)$ at $x=1$ :

$f(x)=\frac{1}{x-3}$

$f(1)=\frac{1}{1-3}$

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

Similarly, to find the composition of $f(x)$ and $g(x)$ , we are going to evaluate $f(x)$ at $g(x)$ . In other words, we are going to replace $x$ in $f(x)$ with $\frac{3x+1}{x}$ :

$f(x)=\frac{1}{x-3}$

$f(g(x) = f(\frac{3x+1}{x} ) = \frac{1}{\frac{3x+1}{x} -3}$

Remember that two functions are inverse if after simplifying their composition, we end up with just $x$ . Let's simplify and see what happens.

$f(g(x)=\frac{1}{\frac{3x+1}{x} -3}$

$f(g(x)=\frac{1}{\frac{3x+1-3x}{x} }$

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

$f(g(x)=x$

Now let's do the same for $g(f(x))$ :

$g(\frac{1}{x-3} )=\frac{3(\frac{1}{x-3})+1}{x}$

$g(\frac{1}{x-3} )=\frac{\frac{3}{x-3}+1}{x}$

$g(\frac{1}{x-3} )=\frac{\frac{3+x-3}{x-3}}{x}$

$g(\frac{1}{x-3} )=\frac{\frac{x}{x-3}}{x}$

$g(\frac{1}{x-3} )=\frac{x}{x(x-3)}$

$g(f(x))=\frac{x}{x(x-3)}$

We can conclude that $g(x)$ is the inverse function of $f(x)$ , but $f(x)$ is not the inverse function of $g(x)$ .

B. The domain of a function is the set of all the possible values the independent variable can have. In other words, the domain are all the possible x-values of function.

Now, interval notation is a way to represent and interval using an ordered pair of numbers called the end points; we use brackets [ ] to indicate that the end points are included in the interval and parenthesis ( ) to indicate that they are excluded.

Notice that when $x=0$ , $g(x)=\frac{3(0)+1}{0} =\frac{0}{0}$ , so when $x=0$ , $g(x)$ is not defined; therefore we have to exclude zero from the domain of $f(g(x))$ .

We can conclude that the domain of the composite function $f(g(x))$ in interval notation is (-∞,0)U(0,∞)

Now let's do the same for $g(f(x))$ .

Notice that the composition is not defined when its denominator equals zero, so we are going to set its denominator equal to zero to find the values we should exclude from its domain:

$x(x-3)=0$