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
• So we know that.....
x represent bags of snack and y is bottles of water.
This equations shows the total amount and the cost of each water bottle and snack:
20.00 = 2.50x + 1.00y
Total: $20.00
Snack: $2.50
Water Bottle: $1.00
And this question shows the total items:
11 = x + y
Which there will be some snack + some water bottle = 11 items
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• Now I’m going to first solve for x, which is the amount of bags of snack.
I will use the equation, 11 = x + y.
(First, we’ll subtract y from both side, since we’re solving for x [UNDO])
11 = x + y
-y = - y
_______
11 - y = x —> so x is equal to 11 minus y.
—————————————————————
• Now we’re going to plug the 11 - y as x in the equation: 20.00 = 2.50x + 1.00y to solve for y.
20.00 = 2.50 (11 - y) + 1.00y
20.00 = 27.5 - 2.50y + 1.00y (Distributed)
20.00 = 27.5 - 1.50y (Combine like terms)
20.00 = 27.5 - 1.50y
-27.5 = -27.5 (Subtract -27.5 both side)
——————————
-7.5 = - 1.50y
-7.5 = -1.50y
—— ——— (Divide both side by -1.50)
- 1.50 = -1.50
5 = y
y is equals to 5, which means that there are 5 water bottles.
Now we know there are 11 items total and because there are 5 water bottles, there will be 6 bags of snacks. 11-5=6
—————————————————————
ANSWER:
They bought 6 bags of snacks! :)
The circle graph is usually used to show proportions of a whole.
The Venn Diagram is used to represent the relationship between two or more collection of objects.
The double bar graph is used to compare two variables over a period of time.
The line graph is used to compare the trends of a variable over a period of time.
Therefore, the <span>graphical representation that would best display the number of points a home team and a visitor’s team scored in each game this season is the double bar graph.</span>
Answer:
S’ (-5,-3)
T’ (4,-6)
U’ (-3,-7)
Step-by-step explanation:
Basically, we want to apply the given transformation rule of the axes to get the coordinates of the images
The rule is that we subtract 1 from the x-coordinates and also subtract 5 from the y-coordinates
Thus, we proceed as follows;
S’ = (-4-1, 2-5) = (-5,-3)
T’ = (5-1, -1-5) = (4,-6)
U’ = (-2-1,-2-5) = (-3,-7)
For the -5+5y=40 the answers is y=9
And for 4x+3y=24 is x=-3/4y +6
