One of the roots of the equation 2x^2 - x + M = 0 is twice the other root. Find the value of M.
unknown values: m
equation: 2*a^2-a+m=0
equation: 2(2*a)^2-2*a+m=0
answer: 1/9 | 0.111
5/6 of a number is 3/4. What is the number?
unknown values: n
equation: 5/6 * n = 3/4
answer: 9/10 | 0.9
What is the value of x in the following equation?3x - 4(x + 1) + 10 = 0
unknown values: x
equation: 3*x - 4(x + 1) + 10 = 0
answer: 6
A whole number between 100 and 1000 is to be formed so that one of the digits is 6, and all the digits are different. How many numbers are possible.
unknown values: x
equation: x = 9*8 + 8*8 + 8*8
answer: 200
If 4x-2y= -10 and 3x-2y=10 what is the value for y?
unknown values: y
equation: 4*x-2*y= -10
equation: 3*x-2*y=10
answer: -35
The square of x is equal to 4 times the square of y. If x is 1 more than twice y, what is the value of x?
unknown values: x
equation: x^2 = 4*y^2
equation: x = 1 + 2*y
answer: 1/2 | 0.5
if 2/3 of 3/4 of a number is 24, what is 1/4 of the same number?
unknown values: x
equation: (2/3)*(3/4)*n = 24
equation: x = (1/4)*n
answer: 12
Three consecutive odd integers have a sum equal to 105. What is the product for these numbers?
unknown values: p
equation: (2*n+1) + (2*n+3) + (2*n+5) = 105
equation: p = (2*n+1)(2*n+3)(2*n+5)
answer: 42735
The average of three consecutive multiples of 3 is a.The average of four consecutive multiples of 4 is a+27The average of the smallest and largest of these seven integers is 42.Determine the value of a.
unknown values: a
equation: (3*m + 3(m+1) + 3(m+2))/3 = a
equation: (4*n + 4(n+1) + 4(n+2) + 4(n+3))/4 = a + 27
equation: (3*m + 4(n+3))/2 = 42
answer: 27
The sum of three numbers is 4. The first, minus the second, plus 4 times the third, is -9. The third, plus 5 times the first, plus the second, is 24. What are the numbers?
unknown values: x,y,z
equation: x + y + z = 4
equation: x - y + 4*z = -9
equation: z + 5*x + y = 24
answer: 5; 2; -3