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3 years ago

Help anyone pic is provided!!

Mathematics

2 answers:

AfilCa [17]3 years ago

7 0

Answer:

True, because they are under 180 degrees

"Supplementary angles are two angles with a sum of 18 0 ∘ 180 ^\circ 180∘ . A common case is when they lie on the same side of a straight line."

-Dominant- [34]3 years ago

7 0

Answer:

Step-by-step explanation:

They are supplementary because 60 +120 is 180, which is what supplementary means.

They are not adjacent, they do not touch and share no common vertex or side.

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If anyone knows how to obtain the answer, please notify me.

Tems11 [23]

Answer:

Area =

b1 + b2

×h

2 + 6

× 5

20 centimeters2

Step-by-step explanation:

6 0

3 years ago

Help please. what does x equal.

Tresset [83]

The answer would be 53

4 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

3 years ago

Explain how bacteria are both helpful and harmful to out bodies

Pavel [41]

Answer:

Step-by-step explanation:

Bacteria is helpful because it helps protect the cells in your intestines. Its, harmful because itI can cause a disease in your lungs.

Hope this helps!

8 0

3 years ago

Is the sum the sum of the arithmetic 1635?

horsena [70]

Answer:

1199

Step-by-step explanation:

There are 22 terms in the sum:

23 + 26 + 29 + ... + 80 + 83 + 86 =

= (23 + 86) + (26 + 83) + ... + (53 + 56)

= 109 + 109 + ... + 109

= 11(109)

= 1199

7 0

3 years ago

Read 2 more answers