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oksano4ka [1.4K]
2 years ago
10

Please help. Is algebra.

Mathematics
2 answers:
tatyana61 [14]2 years ago
5 0

Answer:

a

Step-by-step explanation:

hope this helps :)

Anit [1.1K]2 years ago
3 0

Answer:

A

Step-by-step explanation:

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Can you use the SSS Postulate or the SAS Postulate to prove triangle FEZ is congruent to triangle FGZ?
love history [14]
SAS only. The 3rd side cannot be proven. 
8 0
3 years ago
Describe the term linear pair, and give an example from the diagram.
Burka [1]

Answer/Step-by-step explanation:

A linear pair is formed when two straight lines intersect to form two angles that are adjacent to each other and are on a straight line. The sum of both adjacent angles equals 180°.

From the diagram given, examples of linear pair are:

<FEG and <GEN

<CDE and <ADC

These are some of the few examples we can see in the given diagram that are linear pairs.

6 0
2 years ago
Prove or disprove (from i=0 to n) sum([2i]^4) &lt;= (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
Factorise<br> 24p2 + pq - 23q²​
Novosadov [1.4K]

<em>24p² + pq - 23q² = </em>

<em>= 24p² + 24pq - 23pq - 23q²</em>

<em>= 24p(p + q) - 23q(p + q)</em>

<em>= (p + q)(24p - 23q)</em>

<em />

<em />

3 0
3 years ago
An angle is 74∘ more than its complement. Find the angle.<br><br> degrees
agasfer [191]
The answer is 16 degrees to your problem.
7 0
3 years ago
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