Question

(х+18):10+15= НОД (54, 90) (х+11):3+16= НОД (78, 104) Найти: А) 7х+7у, если х+у=17 Б) 27х-27у, если х-у= 29

Answer 1

Ответ:(х+18)/10+15=18

х+18=(18-15)*10

х+18=30

х=30-18

х=12. НОД(54,90)=18

(х+11)/3+16=26

х+11=(26-16)*3

х+11=30

х=30-11

х=19. НОД(78,104)=26

Пошаговое объяснение:

Answer 2

To find the values of A) 7x + 7y and B) 27x - 27y, we need to first solve the systems of equations given by the two statements. Let's start with each one:

A) (x + 18) / 10 + 15 = GCD(54, 90)

To find the GCD of 54 and 90, we can use the Euclidean algorithm: GCD(54, 90) = GCD(90, 54) = GCD(54, 36) = GCD(36, 18) = GCD(18, 18) = 18

So, we have: (x + 18) / 10 + 15 = 18

Now, let's solve for x: (x + 18) / 10 = 18 - 15 (x + 18) / 10 = 3

Multiply both sides by 10 to isolate x: x + 18 = 30

Subtract 18 from both sides to find the value of x: x = 30 - 18 x = 12

Now that we have the value of x, we can find y using the equation x + y = 17:

x + y = 17 12 + y = 17

Subtract 12 from both sides to find y: y = 17 - 12 y = 5

Now, we can find A) 7x + 7y:

A = 7x + 7y A = 7 * 12 + 7 * 5 A = 84 + 35 A = 119

Therefore, A) 7x + 7y = 119.

B) (x + 11) / 3 + 16 = GCD(78, 104)

To find the GCD of 78 and 104, we can use the Euclidean algorithm: GCD(78, 104) = GCD(104, 78) = GCD(78, 26) = GCD(52, 26) = GCD(26, 26) = 26

So, we have: (x + 11) / 3 + 16 = 26

Now, let's solve for x: (x + 11) / 3 = 26 - 16 (x + 11) / 3 = 10

Multiply both sides by 3 to isolate x: x + 11 = 30

Subtract 11 from both sides to find the value of x: x = 30 - 11 x = 19

Now that we have the value of x, we can find y using the equation x - y = 29:

x - y = 29 19 - y = 29

Subtract 19 from both sides to find y: y = 19 - 29 y = -10

Now, we can find B) 27x - 27y:

B = 27x - 27y B = 27 * 19 - 27 * (-10) B = 513 + 270 B = 783

Therefore, B) 27x - 27y = 783.