A businessman is reducing the size of a rectangular shape house whose dimensions are 50 by 80 yards. He decided that he will use 180 yards of fencing to enclose the house. He will reduce the length and width by 4x yards all around. Find the new dimensions of the house.

The lines shown below are parallel. if the green line has a slope of -1, what is the slope of the red line?

Evaluate 8x2 + 9x − 1 2x3 + 3x2 − 2x dx. solution since the degree of the numerator is less than the degree of the denominator, we don't need to divide. we factor the denominator as 2x3 + 3x2 − 2x = x(2x2 + 3x − 2) = x(2x − 1)(x + 2). since the denominator has three distinct linear factors, the partial fraction decomposition of the integrand has the form† 8x2 + 9x − 1 x(2x − 1)(x + 2) = correct: your answer is correct. to determine the values of a, b, and c, we multiply both sides of this equation by the product of the denominators, x(2x − 1)(x + 2), obtaining 8x2 + 9x − 1 = a correct: your answer is correct. (x + 2) + bx(x + 2) + cx(2x − 1).

Amath club has 40 members. the number of girls y is 6 less than the number of boys. how many members are boys x? how many members are girls y?