If a@b = (a - b) + (b - a), find 5@6.
These funky formula problems are just about substitution! The 5 replaces the a and the 6 replaces the b in the formula. 5@6 = (5 - 6) + (6 - 5). 5@6 = (-1) + (1) = 0
Can a triangle be formed with side lengths 12 cm, 12 cm, and 24 cm?
According to the Triangle Inequality Theorem, two sides of a triangle must add to a sum greater than the 3rd side. In this case, 12 cm + 12 cm is equal to the third side, but not greater. Therefore, no triangle is possible!
The sum of the first and fourth consecutive even integer is equal to the third integer subtracted from 70. Find the integers.
Let the first integer = x. The other integers become: x + 2, x + 4, and x + 6 as even integers are always two units apart. The sum of the first and fourth integer means: x + x + 6 = 2x + 6 The equation is: 2x + 6 = 70 - (x + 4) (be careful - Subtract from is a backwards phrase!) now distribute the negative! 2x + 6 = 70 - x - 4 2x + 6 = 66 - x 3x = 60 x = 20 So the integers are 20, 22, 24, and 26.