The roots of $y^2 + 5y - 11 = 0$ are $a$ and $b$. Find $(a + 3)(b + 3).$

Since a and b are roots of y² + 5y - 11, we have

y² + 5y - 11 = (y - a) (y - b)

and expanding the right side gives

y² + 5y - 11 = y² - (a + b) y + ab

so that

a + b = -5

ab = -11

Now,

(a + 3) (b + 3) = ab + 3 (a + b) + 9

(a + 3) (b + 3) = -11 + 3 (-5) + 9

(a + 3) (b + 3) = -17

the answers are in the images, i received 100% on this assignment. hope this !

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.