As shown in the graph, δghi ≅ δg'h'i', since this is a vertical shift, and δg'h'i' ≅ δg''h''i'', since this is a horizontal shift. we can also show that triangles ghi and g''h''i'' are congruent directly, by using the translation a) (x, y) → (x + 3, y - 4). b) (x, y) → (x - 3, y + 1). c) (x, y) → (x + 2, y + 2). d) (x, y) → (x + 4, y - 5).

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).