A sandwich store charges a delivery fee to bring lunch to an office.
Delivery cost - D
Meatball sandwich cost - M
One office pays $40.50 for 5 meatball sandwiches.
40.50 = 5M + D
Another office pays $66.50 for 9 meat ball sandwiches
66.50 = 9M + D
A. How much does each meatball sandwich add to the cost of delivery?
D = 40.50 - 5M = 66.50 - 9M
40.50 - 5M = 66.50 - 9M
9M - 5M = 66.50 - 40.50
4M = 26.00
M = 6.50
B. What is the delivery fee
D = 40.50 - 5M = 40.50 - 5(6.50) = 40.50 - 32.50 = 8.00
Check
66.50 = 9M + D = 9(6.50) + 8 = 58.50 + 8.00 = 66.50
Answer:
Dimensions :
x (the longer side, only one side with fence ) = 90 ft
y ( the shorter side two sides with fence ) = 45 ft
Total fence used 45 * 2 + 90 = 180 ft
A(max) =
Step-by-step explanation: If a farmer has 180 ft of fencing to encloses a rectangular area with fence in three sides and the river on one side, the farmer surely wants to have a maximum enclosed area.
Lets call "x" one the longer side ( only one of the longer side of the rectangle will have fence, the other will be along the river and won´t need fence. "y" will be the shorter side
Then we have:
P = perimeter = 180 = 2y + x ⇒ y = ( 180 - x ) / 2 (1)
And A (r) = x * y
A(x) = x * ( 180 - x ) /2 ⇒ A(x) = (180/2) *x - x² / 2
Taking derivatives on both sides of the equation :
A´(x) = 90 - x
Then if A´(x) = 0 ⇒ 90 - x = 0 ⇒ x = 90 ft
and from : y = ( 180 - x ) / 2 ⇒ y = 90/2
y = 45 ft
And
A(max) = 90 * 45 = 4050 ft²
The expression which represents the other factor, or factors, of the given polynomial is option (C) (2x-1)(x+1)
A cubic equation in algebra is a one-variable equation of the form ax3+bx2+cx+d=0 where an is nonzero. The roots of the cubic function defined by the left side of this equation are the solutions to this equation.
Given expression 2x³-3x²-3x+2 whose one of factor is (x-2)
We have to find second factor of given equation
First we will be rational root theorem to given expression so will get following expression:

So one factor is (x-1) and now simplifying
we get 2x² - 5x +2 and the factor of 2x² - 5x +2 will be (2x-1)(x-2)
Hence the expression which represents the other factor, or factors, of the given polynomial is option (C) (2x-1)(x+1)
Learn more about Polynomial here:
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Answer:
P(yellow or red) =8/15
Step-by-step explanation:
There are 15 marbles, 3 green, 4 blue, and 5 red marbles.
3+4+5 = 12
That means there are 15-12 = 3 3 yellow marbles.
3 green,
4 blue
5 red
3 yellow
To find the probability of yellow or red, we add the number of yellow and red marbles together over the total number of marbles
P(yellow or red) = (yellow +red)/ total
= (3+5)/ 15
=8/15