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Lines, Angles, and Mathematical Proofs: Mastery Test
In the figure, Pl|9 and "||5. Match each pair of congruent angles with the reason for their congruency.
corresponding angles for
parallel lines p and q cut by
the transversal
210 214
25 213
Linear Pair Theorem
corresponding angles for
parallel lines p and q cut by
the transversal s
corresponding angles for
parallel lines rand s cut by
the transversalg
Vertical Angles Theorem
213 = 216
2125

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).