Solve Diophantusâs Problem Bâ8: To find two numbers
such that their difference and the difference of their cubes
are equal to two given numbers. (Write the equations as
x â y = a, x3 â y3 = b. Diophantus takes a = 10, b =
2120.) Derive necessary conditions on a and b that ensure
a rational solution.

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Elin HesselLv2

30 Apr 2019

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peachpug329

Write a system of two equations using x and y in each for the following. The sum of two numbers is 170 and their difference is 26. Choose one answer. x + y = 170 and x-y = 26 x-y = 170 and x + y = 26 2x + 170-26 = 2y x + y = 170 and 2x = 26 The sum of two numbers is 170 and their difference is 26. Find the two numbers. Choose one answer. 72 and 98 72 and 89 27 and 98 97 and 28 Write the solution as an ordered pair, (x, y) Choose one answer. Not possible (72,89) (27,89) (72,98) To skate at Roller Heaven, each person must pay a membership fee (m) and a fee for each session (f). Art attended five sessions and paid $25 in all. Later, when he had attended 10 sessions, he paid $40 in all. How much is the membership fee and how much are the sessions. Write a system of two equations with the variables m and f in each to represent this problem. Choose one answer. m + f = 25 and m + f = 40 m + 5f = 25 and m + 10f = 40 5m + f = 25 and m + 10f = 40 m +5 f = 25 and 10m + f = 40 To skate at Roller Heaven, each person must pay a membership fee (m) and a fee for each session (f). Art attended 5 sessions and paid $25 in all. Later, when he had attended 10 sessions, he paid $40 in all. How much is the membership fee and how much are the sessions. Choose one answer. m = 3 and f = 10 m = 10 and f = 3 m = 10 and f = 10 m = 3 and f = 3 To celebrate a win for the academic team, the coach treated them to a late lunch. If five students have burgers and three have sub sandwiches, the bill will be $35. If three students have burgers and five have sub sandwiches, the bill will be $37. What is the cost of each type of student? Choose one answer. burger = $5 and sub sandwich = $4 burger = $4 and sub sandwich = $4 burger = $5 and sub sandwich = $5 burger = $4 and sub sandwich = $5 The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46 centimeters. The measure y is 4 centimeters longer than the measure x. Write two equations which represent the two sentences. 2x + x = 46 and y + x = 4 x +2 y = 46 and y + x = 4 2x + y = 46 and y = x + 4 2x + y = 46 and y = 2x + 4 The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46. The measure y is 4 centimeters longer than the measure x. Write two equations which represent the two sentences. x = 18 and y = 14 x = 18 and y = 18 x = 14 and y = 14 x = 14 and y = 18 The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46. The measure y is 4 centimeters longer than the measure x. Write the solution for this as an ordered pair. Choose one answer. (18.14) (14,18) (14,14) (18,18) Write a system of two equations using x and y to represent the following problem. A chemist is mixing two solutions together. The chemist wants 100 gallons when complete. He is mixing a 24% solution with a 50% solution to get a 36% solution. How many gallons of each will he use? x + y = 100 and x + y = .36 x + y = 100 and .24x + .50y = 100 x + y = 100 and .24x + .50y = .36(100) x + y = 100 and .24 + .50 = .36

Show transcribed image text Write a system of two equations using x and y in each for the following. The sum of two numbers is 170 and their difference is 26. Choose one answer. x + y = 170 and x-y = 26 x-y = 170 and x + y = 26 2x + 170-26 = 2y x + y = 170 and 2x = 26 The sum of two numbers is 170 and their difference is 26. Find the two numbers. Choose one answer. 72 and 98 72 and 89 27 and 98 97 and 28 Write the solution as an ordered pair, (x, y) Choose one answer. Not possible (72,89) (27,89) (72,98) To skate at Roller Heaven, each person must pay a membership fee (m) and a fee for each session (f). Art attended five sessions and paid $25 in all. Later, when he had attended 10 sessions, he paid $40 in all. How much is the membership fee and how much are the sessions. Write a system of two equations with the variables m and f in each to represent this problem. Choose one answer. m + f = 25 and m + f = 40 m + 5f = 25 and m + 10f = 40 5m + f = 25 and m + 10f = 40 m +5 f = 25 and 10m + f = 40 To skate at Roller Heaven, each person must pay a membership fee (m) and a fee for each session (f). Art attended 5 sessions and paid $25 in all. Later, when he had attended 10 sessions, he paid $40 in all. How much is the membership fee and how much are the sessions. Choose one answer. m = 3 and f = 10 m = 10 and f = 3 m = 10 and f = 10 m = 3 and f = 3 To celebrate a win for the academic team, the coach treated them to a late lunch. If five students have burgers and three have sub sandwiches, the bill will be $35. If three students have burgers and five have sub sandwiches, the bill will be $37. What is the cost of each type of student? Choose one answer. burger = $5 and sub sandwich = $4 burger = $4 and sub sandwich = $4 burger = $5 and sub sandwich = $5 burger = $4 and sub sandwich = $5 The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46 centimeters. The measure y is 4 centimeters longer than the measure x. Write two equations which represent the two sentences. 2x + x = 46 and y + x = 4 x +2 y = 46 and y + x = 4 2x + y = 46 and y = x + 4 2x + y = 46 and y = 2x + 4 The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46. The measure y is 4 centimeters longer than the measure x. Write two equations which represent the two sentences. x = 18 and y = 14 x = 18 and y = 18 x = 14 and y = 14 x = 14 and y = 18 The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46. The measure y is 4 centimeters longer than the measure x. Write the solution for this as an ordered pair. Choose one answer. (18.14) (14,18) (14,14) (18,18) Write a system of two equations using x and y to represent the following problem. A chemist is mixing two solutions together. The chemist wants 100 gallons when complete. He is mixing a 24% solution with a 50% solution to get a 36% solution. How many gallons of each will he use? x + y = 100 and x + y = .36 x + y = 100 and .24x + .50y = 100 x + y = 100 and .24x + .50y = .36(100) x + y = 100 and .24 + .50 = .36

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Write a system of two equations using x and y in each for the following. The sum of two numbers is 170 and their difference is 26. Choose one answer. x + y = 170 and x - y = 26 x - y = 170 and x + y = 26 2x + 170 - 26 = 2y x + y = 170 and 2x = 26 The sum of two numbers is 170 and their difference is 26. Find the two numbers. Choose one answer. 72 and 98 72 and 69 27 and 96 97 and 26 Write the solution as an ordered pair, (x, y) Choose one answer. Not possible (72, 69) (27, 69) (72, 98) To skate at Roller Heaven, each person must pay a membership fee (m) and a fee for each session (f). Art attended five sessions and paid $25 in all. Later, when he had attended 10 sessions, he paid $40 in all. How much is the membership fee and how much are the sessions. Write a system of two equations with the variables m and f in each to represent this problem. Choose one answer. m + f = 25 and m + f = 40 m + 5f = 25 and m + 10f = 40 5m + f = 25 and m + 10f = 40 m +5 f = 25 and 10m + f = 40 To skate at Roller Heaven, each person must pay a membership fee (m) and a fee for each session (f). Art attended 5 sessions and paid $25 in all. Later, when he had attended 10 sessions, he paid $40 in all. How much is the membership fee and how much are the sessions. Choose one answer. m = 3 and f = 10 m = 10 and f = 3 m = 10 and f = 10 m = 3 and f = 3 To celebrate a win for the academic team, the coach treated them to a late lunch. If five students have burgers and three have sub sandwiches, the bill will be $35. If three students have burgers and five have sub sandwiches, the bill will be $37. What is the cost of each type of student? Choose one answer. burger = $5 and sub sandwich = $4 burger = $4 and sub sandwich = $4 burger = $5 and sub sandwich = $5 burger = $4 and sub sandwich = $5 The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46 centimeters. The measure y is 4 centimeters longer than the measure x. Write two equations which represent the two sentences. Choose one answer. 2x + x = 46 and y + x = 4 x +2 y = 46 and y + x = 4 2x + y = 46 and y = x + 4 2x + y = 46 and y = 2x + 4 The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46. The measure y is 4 centimeters longer than the measure x. Write two equations which represent the two sentences. Choose one answer. x = 18 and y = 14 x = 18 and y = 18 x = 14 and y = 14 x = 14 and y = 18 The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46. The measure y is 4 centimeters longer than the measure x. Write the solution for this as an ordered pair. Choose one answer. (18,14) (14,18) (14,14) (18,18) Write a system of two equations using x and y to represent the following problem. A chemist is mixing two solutions together. The chemist wants 100 gallons when complete. He is mixing a 24% solution with a 50% solution to get a 36% solution. How many gallons of each will he use? Choose one answer. x + y = 100 and x + y = 36 x + y = 100 and 24x + 50y = 100 x + y = 100 and 24x + 50y = 36(100) x + y = 100 and 24 + 50 = 36

Show transcribed image text Write a system of two equations using x and y in each for the following. The sum of two numbers is 170 and their difference is 26. Choose one answer. x + y = 170 and x - y = 26 x - y = 170 and x + y = 26 2x + 170 - 26 = 2y x + y = 170 and 2x = 26 The sum of two numbers is 170 and their difference is 26. Find the two numbers. Choose one answer. 72 and 98 72 and 69 27 and 96 97 and 26 Write the solution as an ordered pair, (x, y) Choose one answer. Not possible (72, 69) (27, 69) (72, 98) To skate at Roller Heaven, each person must pay a membership fee (m) and a fee for each session (f). Art attended five sessions and paid $25 in all. Later, when he had attended 10 sessions, he paid $40 in all. How much is the membership fee and how much are the sessions. Write a system of two equations with the variables m and f in each to represent this problem. Choose one answer. m + f = 25 and m + f = 40 m + 5f = 25 and m + 10f = 40 5m + f = 25 and m + 10f = 40 m +5 f = 25 and 10m + f = 40 To skate at Roller Heaven, each person must pay a membership fee (m) and a fee for each session (f). Art attended 5 sessions and paid $25 in all. Later, when he had attended 10 sessions, he paid $40 in all. How much is the membership fee and how much are the sessions. Choose one answer. m = 3 and f = 10 m = 10 and f = 3 m = 10 and f = 10 m = 3 and f = 3 To celebrate a win for the academic team, the coach treated them to a late lunch. If five students have burgers and three have sub sandwiches, the bill will be $35. If three students have burgers and five have sub sandwiches, the bill will be $37. What is the cost of each type of student? Choose one answer. burger = $5 and sub sandwich = $4 burger = $4 and sub sandwich = $4 burger = $5 and sub sandwich = $5 burger = $4 and sub sandwich = $5 The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46 centimeters. The measure y is 4 centimeters longer than the measure x. Write two equations which represent the two sentences. Choose one answer. 2x + x = 46 and y + x = 4 x +2 y = 46 and y + x = 4 2x + y = 46 and y = x + 4 2x + y = 46 and y = 2x + 4 The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46. The measure y is 4 centimeters longer than the measure x. Write two equations which represent the two sentences. Choose one answer. x = 18 and y = 14 x = 18 and y = 18 x = 14 and y = 14 x = 14 and y = 18 The sides of a triangle have measures of x, x, and y, and the perimeter of the triangle is 46. The measure y is 4 centimeters longer than the measure x. Write the solution for this as an ordered pair. Choose one answer. (18,14) (14,18) (14,14) (18,18) Write a system of two equations using x and y to represent the following problem. A chemist is mixing two solutions together. The chemist wants 100 gallons when complete. He is mixing a 24% solution with a 50% solution to get a 36% solution. How many gallons of each will he use? Choose one answer. x + y = 100 and x + y = 36 x + y = 100 and 24x + 50y = 100 x + y = 100 and 24x + 50y = 36(100) x + y = 100 and 24 + 50 = 36

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