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MA_775_DIABLO [31]
3 years ago
8

{QuEsTiOn}" alt=" \huge \mathfrak \red{QuEsTiOn}" align="absmiddle" class="latex-formula">
What is Euclid's Division Lemma?

What is Thales Theorem? Prove it by explaining.

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OR ELSE YOU'LL BE REPORTED! ​
Mathematics
2 answers:
vodka [1.7K]3 years ago
4 0

Heyaaaa....here's ur answer ⤵️

Step-by-step explanation:

So, according to Euclid's division lemma, If we have two positive integers a and b, then there would be whole numbers q and r that satisfy the equation: a = bq + r, where 0 < r < b . a is the dividend. b is the divisor. q is the quotient and r is the reminder.

If a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then other two sides are divided in the same ratio ...this is Thales theorem

HOPE IT HELPS U✌

trapecia [35]3 years ago
3 0

Answer:

1. In number theory, Euclid's lemma is a lemma that captures a fundamental property of prime numbers, namely: Euclid's lemma — If a prime p divides the product ab of two integers a and b, then p must divide at least one of those integers a and b.

2. The Thales theorem states that: If three points A, B, and C lie on the circumference of a circle, whereby the line AC is the diameter of the circle, then the angle ∠ABC is a right angle (90°).

Step-by-step explanation:

hope it helps

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2 years ago
I’m Really lost if I could get a answer it would be greatly appreciated
Nataly [62]
<h3>Answers:</h3>

f(g(x)) = \sqrt{x^2+5}+5\\\\g(f(x)) = x+30+10\sqrt{x-1}

================================================

Work Shown:

Part 1

f(x) = \sqrt{x-1}+5\\\\f(g(x)) = \sqrt{g(x)-1}+5\\\\f(g(x)) = \sqrt{x^2+6-1}+5\\\\f(g(x)) = \sqrt{x^2+5}+5\\\\

Notice how I replaced every x with g(x) in step 2. Then I plugged in g(x) = x^2+6 and simplified.

------------------

Part 2

g(x) = x^2+6\\\\g(f(x)) = \left(f(x)\right)^2+6\\\\g(f(x)) = \left(\sqrt{x-1}+5\right)^2+6\\\\g(f(x)) = \left(\sqrt{x-1}\right)^2+2*5*\sqrt{x-1}+\left(5\right)^2+6\\\\g(f(x)) = x-1+10\sqrt{x-1}+25+6\\\\g(f(x)) = x+30+10\sqrt{x-1}\\\\

In step 4, I used the rule (a+b)^2 = a^2+2ab+b^2

In this case, a = sqrt(x-1) and b = 5.

You could also use the box method as a visual way to expand out \left(\sqrt{x-1}+5\right)^2

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Quesuon 10 of 10
Bad White [126]

Answer:

(p, q) is (2, 5)

Step-by-step explanation:

Given the expression

x^2  + 3x - 10

Factorize;

x^2 + 5x - 2x - 10

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q=  5

Hence (p, q) is (2, 5)

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