Answer:
The third side is sqrt(77)
Step-by-step explanation:
Since this is a right triangle we can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
2^2 + b^2 = 9^2
4+ b^2 = 81
Subtract 4 from each side
b^2 = 81-4
b^2=77
Take the square root of each side
sqrt(b^2) = sqrt(77)
b = sqrt(77)
The third side is sqrt(77)
Answer:
See explanation below
Step-by-step explanation:
a. f(x) is increasing at (-∞, 1] and [7, ∞) because f'(x) is positive at those intervals.
b. f(x) is concave up at [4, ∞) because the slope of f'(x) or f''(x) is positive.
Explanation:
let's break down the expression to get the final result:
Answer:
profit will be maximized by making 20 doodles and 20 paintings = ($10 x 20) + ($20 x 20) = $600
Step-by-step explanation:
we have to maximize the following equation:
$10P + $20D
where:
P = number of portraits
D = number of doodles
the constraints are:
P + D ≤ 40
P ≤ 30
D ≤ 20
we do not need to use solver or any other type of linear programming tool to solve this, since profit will be maximized by making 20 doodles and 20 paintings = ($10 x 20) + ($20 x 20) = $600
