Your Turn #1: Elphaba has a sapling that she planted in her yard. After 1 year, the tree was 40 inches tall. It grows 10 inches each year. Fill in the table and graph the relationship. Is the
relationship a proportional relationship? Explain why or why not. Show work to support your
answer
80
Age (years)
1
4
60
Height (inches)
40
80
Tree height (in)
40
20
0
2
4
6
8
Age (years)

Danny draws a transversal, t, on two parallel lines ab and cd, as shown below: he makes the following table to prove that the alternate interior angles are equal: which is the missing justification? (6 points) corresponding angles formed by a transversal on parallel lines are supplementary. corresponding angles formed by a transversal on parallel lines are congruent. co-interior angles formed by a transversal on parallel lines are congruent. co-exterior angles formed by a transversal on parallel lines are congruent.

How many quarts of a 50% solution of acid must be added to 20 quarts of a 20% solution of acid in order to get a 40% solution of acid?

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).