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4 years ago

Understanding this proof for the proposition "For all integers a, gcd(9a+4, 2a+1) = 1.

Mathematics

1 answer:

olganol [36]4 years ago

3 0

First line because 4(2a+1)=8a+4 and 9a+4-(8a+4)= a

Second line because a times 2 =2a and 2a+1-2a=1

<span>Although the second equality is more or less obvious since 2a+1 leaves a remainder of 1 when divided by a.</span>

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What is the value of x in the equation 4 . 10 X+52 3 +35x+1 5 ?<br><br>:)

pashok25 [27]

Answer:

$x=-3$

Step-by-step explanation:

Given:

$4\frac{3}{10}-(2\frac{2}{5}x+5\frac{1}{2})=\frac{1}{2}(-3\frac{3}{5}x+1\frac{1}{5})$

Distribute to remove parentheses:

$4\frac{3}{10}-2\frac{2}{5}x-5\frac{1}{2}=-\frac{18}{10}x+\frac{6}{10}$

For simplification and clarity, reduce all mixed numbers to simplified common fractions:

$\frac{43}{10}-\frac{12}{5}x-\frac{11}{2}=-\frac{9}{5}x+\frac{3}{5}$

Combine like terms:

$-\frac{12}{5}x-\frac{6}{5}=-\frac{9}{5}x+\frac{3}{5}$

Add 6/5 to both sides, then add 9/5x to both sides:

$-\frac{3}{5}x=\frac{9}{5}$

Divide both sides by -3/5 to isolate x (recall dividing by a number is equal to multiplying by its reciprocal):

$x=\frac{9}{5}\cdot -\frac{5}{3}, \\x=\frac{-9}{3},\\x=\boxed{-3}$

3 0

3 years ago

Line P has a slope of -3/2 line Q is perpendicular to p what is the slope of line Q?

Slav-nsk [51]

Answer: positive 2/3

Slope of perpendicular is the opposite sign and reciprocal

Step-by-step explanation:

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4 years ago

Find the area of the red shaded region round to the nearest tenth.

sattari [20]

Answer:

28.5 in²

Step-by-step explanation:

find the area of the quarter circle:

(pi x r²)/4

100pi/4 =

25pi

To get the shaded region minus the triangle from the quarter circle:

Formula for triangle is bh/2

25 pi - Area of triangle

25 pi - (10x10)/2

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Which is approximately 28.5 square inches.

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2 years ago

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3 years ago

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Arada [10]

Answer:

Step-by-step explanation:

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