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There is a 2 digit number such that the sum of its digits is 6 while the product of the digits is one-third the original number Find the number?
if the digits are A and B, then we are given:A + B = 6A * B = (10A + B) / 3∴ B = 6 - A∴ A * (6 - A) = (10A + [6 - A]) / 3∴ 6A - A2 = (9A + 6) / 3∴ 6A - A2 = 3A + 2∴ 6A - A2 - 3A - 2 = 0∴ A2 - 3A + 2 = 0∴(A - 2)(A - 1) = 0∴A ∈ {1, 2}A + B = 6∴ B ∈ {5, 4}∴ The numbers 15 or 24 both meet these conditions.
What are the dimensions of a garden with an area of 72 square feet and a perimeter of 36 feet?
If the length and width are L and B feet, then 2(L + B) = 36 => L + B = 18 => L = 18 - B L*B = 72 => (18 - B)B = 72 B2 - 18B + 72 = 0 => (B - 6)(B -12) = 0 => B = 6 or B = 12 B = 6 => L = 12 and B = 12 => L = 6 So the dimensions are 6 ft x 12 ft. The dimensions are: length 12 feet and width 6 feet. --- Area = length x width a x b = 72 Perimeter = 2 x length + 2 x width 2a+2b=36 The two equations can be solved by substituting a for b (a2-18a+72=0), with the results a = 6 or 12 and b is the other
Can you help me with this in a 2 by 2 matrix -1 2 -1 -4 times a 2 by 1 matrix 1 2 equals a b what is a and what is b?
-1 2 2 0 x = -1 -4 1 -6 Answer: a = 0 and b = -6
What square of a number minus five times the number is 6 Find all such numbers?
x^2-5x-6+0 (X-6)(x+1) = 0 X = 6 X = -1 or you can use quadratic formula x = (-b+/-sqrt(b^2-4ac))/2 where a = 1 b = -5 c = -6 X = 6,-1
3x2squared plus bx-5 equals 0?
3x2 + bx - 5 = 0 ∴ 3x2 + bx = 5 ∴ x2 + bx/3 = 5/3 ∴ x2 + bx/3 + (b/6)2 = 5/3 + (b/6)2 ∴ (x + b/6)2 = (45 + b2) / 36 ∴ x + b/6 = ±[(45 + b2) / 36]1/2 ∴ x = [-b ± (45 + b2)1/2] / 6
