Answer:
The final temperature for the day was -16 degrees.
Step-by-step explanation:
6-12= -6
-6-10= -16
The difference of 32 · x² / (x² + 8 · x + 15) - 14 · x² / (x² - 9) is equal to [18 · x³ - 166 · x²] / [(x + 3) · (x + 5) · (x - 3)]. (Correct choice: B)
<h3>What is the result of the subtraction between two algebraic rational functions?</h3>
In this question we have a subtraction between two <em>rational</em> functions, which have to be simplified by <em>algebra</em> properties. The complete procedure is presented below:
32 · x² / (x² + 8 · x + 15) - 14 · x² / (x² - 9) Given
32 · x² / [(x + 3) · (x + 5)] - 14 · x² / [(x + 3) · (x - 3)] Factorization
[x² / (x + 3)] · [32 / (x + 5) - 14 / (x - 3)] Distributive and associative properties
[x² / (x + 3)] · [32 · (x - 3) - 14 · (x + 5)] / [(x + 5) · (x - 3)] Subtraction of rational numbers with distinct denominators
[x² / (x + 3)] · [32 · x - 96 - 14 · x - 70] / [(x + 5) · (x - 3)] Distributive property / (- 1) · a = - a
[x² / (x + 3)] · (18 · x - 166) / [(x + 5) · (x - 3)] Distributive property / Definitions of addition and subtraction
[18 · x³ - 166 · x²] / [(x + 3) · (x + 5) · (x - 3)] Mutiplication between rational numbers / Multiplication between powers / Distributive property
The difference of 32 · x² / (x² + 8 · x + 15) - 14 · x² / (x² - 9) is equal to [18 · x³ - 166 · x²] / [(x + 3) · (x + 5) · (x - 3)]. (Correct choice: B)
To learn more on rational functions: brainly.com/question/27914791
#SPJ1
Answer:
There are typically 12 decision variables and 7 constraints. ( option A )
Step-by-step explanation:
Given that there are 4 sources and 3 destinations The true statement is :
There are typically 12 decision variables and 7 constraints.
Because : In general linear programming optimization
number of decision variables in transportation = destination * source
= 3 * 4 = 12 variables
number of constraints = destination + sources = 3 + 4 = 7 constraints
Answer:
x^2 + y^2 -2x -8y -47 =0
Step-by-step explanation:
The center is at (1,4) and the radius is 8 units
We can write the equation as
(x-h)^2 + (y-k)^2 = r^2
where (h,k) is the center and r is the radius
(x-1)^2 + (y-4)^2 = 8^2
Foil
x^2 -2x+1 + y^2 -8y +16 = 64
x^2 + y^2 -2x -8y +17 =64
Subtract 64 from each side
x^2 + y^2 -2x -8y +17-64 =64-64
x^2 + y^2 -2x -8y -47 =0
Answer:
58 passengers
Step-by-step explanation:
Capacity of the cruise ship = 68 people
Minimum number for an excursion = 46 people
Maximum cost per person = $ 70
Let the additional passenger = y
y minimum =1
y maximum = 68- 46
= 22
y can be represented in the inequality below:
1 ≤ y ≤ 22
New ticket cost of excursion for every added passenger = (70-y)
Total passengers = (46+y)
Income (I) = (70-y) (46+y)
= 3220 + 70y -46y - y²
= 3220 +24y -y²------------------------------- (1)
To maximize the income function I (y) in equation (1), dI/dy =0 , and (1) becomes :
24-2y = 0
2y = 24
y =12
So the total number of passengers that maximizes income is :
= (46+y)
= (46+12
= 58 passengers