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Zina [86]
3 years ago
14

What is the relationship between a conjecture, a theorem, and a two-column proof?

Mathematics
1 answer:
Bad White [126]3 years ago
5 0
<span>mathematics, a proof is a deductive argument for a mathematical statement. In the argument, other previously established statements, such as theorems, can be used. In principle, a proof can be traced back to self-evident or assumed statements, known as axioms.(2)(3)(4) Proofs are examples of deductive reasoning and are distinguished from inductive or empirical arguments; a proof must demonstrate that a statement is always true (occasionally by listing all possible cases and showing that it holds in each), rather than enumerate many confirmatory cases. An unproven statement that is believed true is known as a conjecture.
 
Proofs employ logic but usually include some amount of natural language which usually admits some ambiguity. In fact, the vast majority of proofs in written mathematics can be considered as applications of rigorous informal logic. Purely formal proofs, written in symbolic language instead of natural language, are considered in proof theory. The distinction between formal and informal proofs has led to much examination of current and historical mathematical practice, quasi-empiricism in mathematics, and so-called folk mathematics (in both senses of that term). The philosophy of mathematics is concerned with the role of language and logic in proofs, and mathematics as a language</span>
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Which expression equals 6x − 5y + 2 − 8x + 3( y + 5)? A) 3x − 2y + 17 B) −3x + 2y + 17 C) −2x − 2y + 17 D) −2x − 2y − 17
inysia [295]

Answer:

<u>C) −2x − 2y + 17</u>

Step-by-step explanation (PEMDAS):

First, we do <u>3 (y + 5)</u> because of the parenthesis:

6x − 5y + 2 − 8x + 3y + 15

Since there are no exponents, multiplication ,or division, we will add and subtract. But we have to make sure we <u>combine like terms</u>. X with X's, Y with Y's and constants with constants. And ALWAYS go from left to right

6x − 5y + 2 − 8x + 3y + 15

<u>−2x</u> − 5y + 2 + 3y + 15

−2x <u>− 2y</u> + 2 + 15

<em>−2x − 2y</em><em> </em><em>+ </em><em><u>17</u></em><em>.</em>

8 0
3 years ago
Simplify the expression.<br><br> [(11 - 4)^3]^2 ÷ (4 + 3)^5
MAXImum [283]

Answer:

<h2>7</h2>

Step-by-step explanation:

\left[\left(11\:-\:4\right)^3\right]^2\:\div \left(4\:+\:3\right)^5\\\\\frac{\left(\left(11-4\right)^3\right)^2}{\left(4+3\right)^5}\\\\\mathrm{Subtract\:the\:numbers:}\:11-4=7\\\\=\frac{\left(7^3\right)^2}{\left(4+3\right)^5}\\\\\mathrm{Add\:the\:numbers:}\:4+3=7\\\\=\frac{\left(7^3\right)^2}{7^5}\\\\\left(7^3\right)^2=7^6\\\\=\frac{7^6}{7^5}\\\\\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}\\\\\frac{7^6}{7^5}=7^{6-5}\\\\\mathrm{Subtract\:the\:numbers:}\:6-5=1\\\\=7

5 0
3 years ago
Is 1/4 of 8 equal to 2
Svet_ta [14]
Yes, 1/4 of 8 is equal to two.
1/4x8=2
Hope this helps! :)
5 0
3 years ago
Read 2 more answers
Help me with acellus
dybincka [34]
For the first one it is x=1 the second one X=8
3 0
2 years ago
Read 2 more answers
After the tour, Tyler’s mom bought a pretzel and a bottle of water for each family member. The bottles of water cost $1.50 each.
Delicious77 [7]
Each pretzel is 4.5 $

1.50 • 5 = 7.5
7.5 - 30 = 22.5
22.5 / 5 = 4.5

so in conclusion, those are some expensive a** pretzels.
5 0
2 years ago
Read 2 more answers
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