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Neporo4naja [7]
2 years ago
13

Please help me with number #3 and check if the others are correct please I really need help

Mathematics
1 answer:
Sveta_85 [38]2 years ago
6 0
All I can say is 1 and 2 are correct.
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Using the Extended Euclidean Algorithm, find integers x and y such that 26x + 9y = 1.
Xelga [282]

Answer:

The solution is: x=-1 and y=3.

Step-by-step explanation:

Let's find the solution, but first let's remember the following:

A / B = C + R where:

A=dividend, B=divisor, C=quotient, and R=remainder. This can be express as follows:

A = (C * B) + R, which is the structure we are going to use next.

Using the Euclidian Algorithm we need to find the highst common factor (HCF) between the coefficients from your equation, this means:

The original equation: 26x+9y=1 is in the form Ax+By=C, so A=26, B=9 and C=1.

We need to find the HCF of 'A' and 'B'. Using the Euclidan Algorithm (EA), so we have:

A = (C * B) + R, using our values:

26 = (2 * 9) + 8, look that the divisor (B) is 9 and the remainder (R) is 8.

Now using the (EA) we divide the divisor (B=9) by the obtained remainder (R=8). And we do the same for each obtained result until the las remainder (R) is equal to 0, like this:

A = (C * B) + R

9 = (8 * 1) + 1

using the divisor (B=8) and the remainder (R=1) we obtain:

A = (C * B) + R

8 = (1 * 8) + 0, look that the remainder is now 0, so in summary we can use the method as follows:

26 = (2 * 9) + 8

9 = (8 * 1) + 1

8 = (1 * 8) + 0; and this equations are the ones we are going to use in order to find a solution.

Next step is to use the equation before R=0, so:

9 = (8 * 1) + 1, which is:

9 - (8 * 1) = 1; but if you consider the first obtained equation: 26 = (2 * 9) + 8, we can write:

26 - (2 * 9) = 8, and we can use this expression in the previous one, so:

9 - (8 * 1) = 1, is:

9 - ((26 - (2 * 9)) * 1) = 1, simplifying:

9 - 26 + (2*9) = 1

9 - 26 + (9 + 9) = 1

-26 + (9 + 9 + 9) = 1

-26 + (3 * 9) = 1

26*(-1) + 9*(3) = 1; if you compare the last expression with the original equation, which is: 26x+9y=1, you can see the similarity, where x=-1 and y=3.

So, the solution is: x=-1 and y=3.

8 0
3 years ago
What is 15,000 in percentage
Kay [80]

Add more details to answer

Helpful source:

https://percent-calc.com/what-is-9-of-15000

5 0
3 years ago
Read 2 more answers
A large cheese pizza costs $7.50. Diego has $40 to spend on pizzas. How many large cheese pizzas can he afford? Explain or show
ololo11 [35]

Answer:

5 pizzas

Step-by-step explanation:

He will have $2.50 left over after he buys the 5 pizzas. Hope this helps! Brainliest is appriciated.

3 0
3 years ago
Which word should replace the question mark (?) in the
artcher [175]

Answer:

speed I'm pretty sure sorry if its wrong

7 0
3 years ago
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Find the slope of the line that contains the following points. R(-3, 5), S(3, -2) 7/6 7/6 undefined
Musya8 [376]

Answer:

-\frac{7}{6}

Step-by-step explanation:

We can use the slope formula for the segment that joins any two points (x_1, y_1) and (x_2, y_2):

slope=\frac{y_2-y_1}{x_2-x_1}

which in our case gives:

slope=\frac{y_2-y_1}{x_2-x_1}  = \frac{-2-5}{3-(-3)}=\frac{-7}{6} =-\frac{7}{6}

5 0
3 years ago
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