2(5y-2)+x<br><br> combine like terms to simplify the following expressions

If you can please solve these for me and give me the steps how you solved it:

larisa86 [58]

Answer:

question number 16 :11 is answer

8 0

3 years ago

Prove or disprove (from i=0 to n) sum([2i]^4) <= (4n)^4. If true use induction, else give the smallest value of n that it doe

ddd [48]

Answer:

The statement is true for every n between 0 and 77 and it is false for $n\geq 78$

Step-by-step explanation:

First, observe that, for n=0 and n=1 the statement is true:

For n=0: $\sum^{n}_{i=0} (2i)^4=0 \leq 0=(4n)^4$

For n=1: $\sum^{n}_{i=0} (2i)^4=16 \leq 256=(4n)^4$

From this point we will assume that $n\geq 2$

As we can see, $\sum^{n}_{i=0} (2i)^4=\sum^{n}_{i=0} 16i^4=16\sum^{n}_{i=0} i^4$ and $(4n)^4=256n^4$ . Then,

$\sum^{n}_{i=0} (2i)^4 \leq(4n)^4 \iff \sum^{n}_{i=0} i^4 \leq 16n^4$

Now, we will use the formula for the sum of the first 4th powers:

$\sum^{n}_{i=0} i^4=\frac{n^5}{5} +\frac{n^4}{2} +\frac{n^3}{3}-\frac{n}{30}=\frac{6n^5+15n^4+10n^3-n}{30}$

Therefore:

$\sum^{n}_{i=0} i^4 \leq 16n^4 \iff \frac{6n^5+15n^4+10n^3-n}{30} \leq 16n^4 \\\\ \iff 6n^5+10n^3-n \leq 465n^4 \iff 465n^4-6n^5-10n^3+n\geq 0$

and, because $n \geq 0$ ,

$465n^4-6n^5-10n^3+n\geq 0 \iff n(465n^3-6n^4-10n^2+1)\geq 0 \\\iff 465n^3-6n^4-10n^2+1\geq 0 \iff 465n^3-6n^4-10n^2\geq -1\\\iff n^2(465n-6n^2-10)\geq -1$

Observe that, because $n \geq 2$ and is an integer,

$n^2(465n-6n^2-10)\geq -1 \iff 465n-6n^2-10 \geq 0 \iff n(465-6n) \geq 10\\\iff 465-6n \geq 0 \iff n \leq \frac{465}{6}=\frac{155}{2}=77.5$

In concusion, the statement is true if and only if n is a non negative integer such that $n\leq 77$

So, 78 is the smallest value of n that does not satisfy the inequality.

Note: If you compute $(4n)^4- \sum^{n}_{i=0} (2i)^4$ for 77 and 78 you will obtain:

$(4n)^4- \sum^{n}_{i=0} (2i)^4=53810064$

$(4n)^4- \sum^{n}_{i=0} (2i)^4=-61754992$

7 0

4 years ago

Please help me with this question.

Rasek [7]

The answer is 4,000 ft squared because since the sides are 100 ft and 80ft then we need to multiply them which is 8,000 then divide that by 2 since it’s a triangle which is 4,000 ft squared.

6 0

3 years ago

Yo!!!NEED HELP!!!!WILL GIVE BRAIN!!!!!!!

yawa3891 [41]

First, we are going to find if the function is odd or even. Remember that we can determine if a function is odd of even from its graph by looking at its ends; if both ends go to the same the direction, the function is even. If both ends go to opposite directions, the function is odd. At both ends, the graph of our function go towards the same direction, minus infinity, so we can conclude that our function is even.

Next, we are going to find the possible degree of our function. Remember that the possible degree of a function is the number of x-intercepts.
We can infer from our graph that the function intercepts the x-axis at least 6 times.

We can conclude that the correct answer is: even degrees of 6 or greater.

5 0

4 years ago

Please help me I need it now

Arada [10]

Answer:

I'm pretty sure the answer is B

Step-by-step explanation:

sorry if I'm wrong

3 0

3 years ago

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2(5y-2)+x combine like terms to simplify the following expressions