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3 years ago

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Suppose that gcd(a,b)=1. Prove that for every integer c, the equation ax+by=c has a solution in integers x and y. [Hint: Find a

solution to au+bv=1 and multiply by c] Find a solution to 37x + 47y = 103. Try to make x and y as small as possible

1 answer:

frosja888 [35]3 years ago

4 0

Answer:

okie

Step-by-step explanation:

You might be interested in

Find the value of x and please show how

Rzqust [24]

Answer:

?=91 degrees.

Step-by-step explanation:

There is no x- I'll find ? though.

So, angles in a triangle must equal 180.

180-29-62=89. The last angle in the triangle is 89 degrees.

A straight angle is equal to 180 degrees. ? + 89=180.

180-89=91.

?=91 degrees.

Hope this helped!

5 0

3 years ago

Patrick has just finished building a pen for his new dog. The pen is 3 feet wider than it is long. He also built a doghouse to p

zalisa [80]

General Idea:

(i) Assign variable for the unknown that we need to find

(ii) Sketch a diagram to help us visualize the problem

(iii) Write the mathematical equation representing the description given.

(iv) Solve the equation by substitution method. Solving means finding the values of the variables which will make both the equation TRUE

Applying the concept:

Given: x represents the length of the pen and y represents the area of the doghouse

<u>Statement 1: </u>"The pen is 3 feet wider than it is long"

$Length \; of\; the \; pen = x\\ Width \; of\; the\; pen=x+3$

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<u>Statement 2: "He also built a doghouse to put in the pen which has a perimeter that is equal to the area of its base"</u>

$Area \; of\; the\; Dog \; house=y\\ Perimeter \; of\; Dog\; house=y$

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<u>Statement 3: "After putting the doghouse in the pen, he calculates that the dog will have 178 square feet of space to run around inside the pen."</u>

$Area \; of \; the\; Pen - Area \;of \;the\;Dog \;House=\;Space\;inside\;Pen\\ \\ x \cdot (x+3)-y=178\\ Distributing \;x\;in\;the\;left\;side\;of\;the\;equation\\ \\ x^2+3x-y=178\Rightarrow\; 1^{st}\; Equation\\$

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<u>Statement 4: "The perimeter of the pen is 3 times greater than the perimeter of the doghouse."</u>

$Perimeter\; of\; the\; Pen=3\; \cdot \; Perimeter\; of\; the\; Dog\; House\\ \\ 2(x \; + \; x+3)=3 \cdot y\\ Combine\; like\; terms\; inside\; the\; parenthesis\\ \\ 2(2x+3)=3y\\ Distribute\; 2\; in\; the\; left\; side\; of\; the\; equation\\ \\ 4x+6=3y\\ Subtract \; 6\; and \; 3y\; on\; both\; sides\; of\; the\; equation\\ \\ 4x+6-3y-6=3y-3y-6\\ Combine\; like\; terms\\ \\ 4x-3y=-6 \Rightarrow \; \; 2^{nd}\; Equation\\$

Conclusion:

The systems of equations that can be used to determine the length and width of the pen and the area of the doghouse is given in Option B.

$178=x^2+3x-y\\ \\ -6=4x-3y$

8 0

4 years ago

Read 2 more answers

If you knew that two angles were comlementary and were given the measure of one of those angles, would you be able to find the m

Mnenie [13.5K]

Answer:

Yes, any pair of complementary angles add up to 90 degrees. By simply using 90-x you can find the other angle.

3 0

3 years ago

Read 2 more answers

Wyatt received a paycheck of $650. This amount reflects his weekly earnings minus 10% of his earnings for deductions. Write an e

muminat

That would be 650 = x - 0.1x

5 0

3 years ago

Find (f/g) (x) for the functions provided: ƒ(x) = x3 − 27, g(x) = 3x − 9

AnnZ [28]

Answer:

$(\frac{f}{g})(x)=\frac{1}{3}(x^2+3x+9)$

Step-by-step explanation:

We have been given that

$f(x)=x^3-27,g(x)=3x-9$

We can use the formula for difference of cubes to simplify the function f(x)

difference of cubes - $a^3-b^3=(a-b)(a^2+ab+b^2)$

$f(x)=x^3-27\\\\=x^3-3^3\\\\=(x-3)(x^2+3x+9)$

And g(x) can be written as

$g(x)=3x-9\\=3(x-3)$

Thus, we have

$(\frac{f}{g})(x)=\frac{(x-3)(x^2+3x+9)}{3(x-3}$

On cancelling the common factors, we get

$(\frac{f}{g})(x)=\frac{1}{3}(x^2+3x+9)$

5 0

3 years ago