The number of entertainment websites in 1995 was 54. By 2004, there were 793 entertainment websites.

Approximately what was the rate of change for the number of websites for this period of time?

1: [tex]3n^{2}+9n+6[/tex]

notice that each part is divisible by 3

[tex]3n^{2}[/tex] ÷ 3 = [tex]n^{2}[/tex]

9n ÷ 3 = 3n

6 ÷ 3 = 2

so it becomes [tex]3(n^{2} +3n+2)[/tex]

3n can be rewritten as 2n+n

-you want to rewrite it into two numbers that multiply to the number that's alone (in this case 2)

which would get you

[tex]3(n^{2} +2n+n+2)[/tex]

Now that it's rewritten, you can factor out n + 2 from the equation.

the answer is

3(n+2)(n+1)

And you can check that by multiplying (n+2)(n+1) which is [tex]n^{2} +2n+n+2[/tex] and then each of those by 3, which is [tex]3n^{2} +6n+3n+6[/tex] or [tex]3n^{2}+9n+6[/tex], our origional equation

2: [tex]28+x^{2} -11x[/tex]

So I rewrote this as [tex]x^{2} -11x+28[/tex] (it's the same thing, just reordered using the commutative property)

now -11x can be rewritten as -4x-7x

(remember, the two numbers should multiply to equal 28, which is our constant.)

[tex]x^{2} -4x-7x+28[/tex]

now we can factor out x from the first expression and -7 from the second

[tex]x(x-4)-7(x-4)[/tex]

and lastly you factor out x-4,

which would give you

(x-4)(x-7)

Make sure to check your work and make sure it multiplies to [tex]x^{2} -11x+28[/tex]

3: [tex]9x^{2} -12x+4[/tex]

The first thing I notice when looking at this problem is that both 9 and 4 are perfect squares. Not only that, but they are the squares of 2 and 3, which are products of -12

So if you rewrite 9 as [tex]3^{2}[/tex] and 4 as [tex]2^{2}[/tex], the equation becomes

[tex]3^{2} x^{2} -12x+2^{2}[/tex]

now that [tex]3^{2} x^{2}[/tex] is ugly so it can be turned into [tex](3x)^{2}[/tex]

and -12x can be rewritten as [tex]-2*3x*2[/tex]

so our equation now looks like [tex](3x)^2-2*3x*2+2^{2}[/tex]

There's a rule that says [tex]a^{2} -2ab+b^{2} = (a-b)^{2}[/tex]

In our case, a=3x and b=2

so the final answer is

[tex](3x-2)^2[/tex]

Answer:

64000

Step-by-step explanation:

Step-by-step explanation:

[tex]40 \times 40 \times 40[/tex]

[tex]160 \times 40[/tex]

[tex]6400[/tex]

Answer:

B. 15/4 z + 12

Step-by-step explanation:

Apply the distributive property and multiply 3/4 by 5z and by 16.

3/4 (5z + 16) = 3/4 × 5z + 3/4 × 16 = 15/4 z + 12

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Question reads....}[/tex]

[tex]\large\text{Write an expression that is equivalent to }\rm{\dfrac{3}{4}(5z + 16).}[/tex]

[tex]\huge\textbf{In order to answer this question, you}\\\huge\textbf{have to distribute. If you're unsure what}\\\huge\textbf{the distributive property formula is, it is:}[/tex]

[tex]\large\textsf{a(b + c)}[/tex]

[tex]\rightarrow\large\textsf{a}\times\large\textsf{{b + a}}\times\large\textsf{c}[/tex]

[tex]\rightarrow\large\textsf{ab + ac}[/tex]

[tex]\huge\textbf{Now, that we have that much}\\\huge\textbf{information out of the way, we can}\\\huge\textbf{now begin to answer the given question.}[/tex]

[tex]\huge\textbf{Here's what your equation looks like:}[/tex]

[tex]\mathsf{\dfrac{3}{4}(5z + 16)}[/tex]

[tex]\huge\textbf{Solving it:}[/tex]

[tex]\mathsf{\dfrac{3}{4}(5z + 16)}[/tex]

[tex]\rightarrow\mathsf{\dfrac{3}{4} \times 5z + \dfrac{3}{4} \times 16}[/tex]

[tex]\rightarrow\mathsf{\dfrac{15}{4}z + 12}[/tex]

[tex]\huge\textbf{Therefore, your answer is most likely:\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] }[/tex][tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{Option\ B. \dfrac{15}{4}\mathsf{z} + 12}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]