1. △abc is a. reflected across the y-axis b. reflected across the line y=x c. rotated 90 degrees counterclockwise about the origin 2. then △a′b′c′ is a. reflected across the x-axis b. translated 4 units down c. rotated 180 degrees about the origin 3. because the transformations are a. both rigid b. not both rigid 4. the pre-image and image are a. congruent b. not congruent

Yvaries directly as x. y =90 when x=6. find y when x=13

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).

Atriangle has vertices of (0,3.5), (3,1.5), (0, -1.5). if it is dilated with center at the origin, and a scale factor of 2, what will be the coordinates of the image?