The three lines shown in the diagram below intersect at the same point. The measure of some of the angels in degrees are given as 3(x-2) degrees, (3/5y) degrees,12 degrees, 42 degrees. Write and solve an equation that can be used to find the value of x.

Evaluate the discriminant of each equation. tell how many solutions each equation has and whether the solutions are real or imaginary. 4x^2 + 20x + 25 = 0

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).

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