The figure shows the location of three points around a lake. The length of the lake, BC, is also shown. (The figure is not drawn to scale.)

A picture of a right triangle ABC with a right angle at B is shown. The length of the side AC is labeled as 5 miles. The length BC of the triangle is labeled as 2 miles. This length BC is also the length of an irregular gray shaded shape.

Which of the following choices is closest to the distance (in miles) between points A and B?

1.73 miles
2.65 miles
3.16 miles
4.58 miles

In a 45-45-90 right triangle, what is the ratio of the length of one leg to the length of the other leg? а . 1: 2 в. 2: 1 с. 2: 1 d. 1: 1

Gabrielle's age is two times mikhail's age. the sum of their ages is 84. what is mikhail's age?

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).