Step-by-step explanation:
area of the base is the area of the rectangle 5×12.
B = 5×12 = 60 in²
the height h is then the side going up from that base rectangle : 4 in.
the perimeter of the base (rectangle) is 2×length + 2×width
P = 2×12 + 2×5 = 24 + 10 = 34 in.
Problema Solution
You have 800 feet of fencing and you want to make two fenced in enclosures by splitting one enclosure in half. What are the largest dimensions of this enclosure that you could build?
Answer provided by our tutors
Make a drawing and denote:
x = half of the length of the enclosure
2x = the length of the enclosure
y = the width of the enclosure
P = 800 ft the perimeter
The perimeter of the two enclosures can be expressed P = 4x + 2y thus
4x + 3y = 800
Solving for y:
........
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........
y = 800/3 - 4x/3
The area of the two enclosure is A = 2xy.
Substituting y = 800/3 - 4x/3 in A = 2xy we get
A = 2x(800/3 - 4x/3)
A =1600x/3 - 8x^2/3
We need to find the x for which the parabolic function A = (- 8/3)x^2 + (1600/3)x has maximum:
x max = -b/2a, a = (-8/3), b = 1600/3
x max = (-1600/3)/(2*(-8/3))
x max = 100 ft
y = 800/3 - 4*100/3
y = 133.33 ft
2x = 2*100
2x = 200 ft
Answer:
amount of nuts = 2 pounds
amount of dried fruit = 4 pounds
Explanation:
We are given that x is the amount of nuts and y is the amount of dried fruit.
We are also given that:
1- Hunter needs to make 6 pounds of trail mix. This means that:
x + y = 6
This can be rewritten as:
x = 6 - y .........> equation I
2- x costs $4 per pound, y costs $3.5 and Hunter can spend a total of $22. This means that:
4x + 3.5y = 22 ..........> equation II
Substitute with equation I in equation II and solve for y as follows:
4x + 3.5y = 22
4(6-y) + 3.5y = 22
24 - 4y + 3.5y = 22
24-22 = 4y-3.5y
2 = 0.5y
y = 4 pounds
Substitute with y in equation I to get the value of x as follows:
x = 6-y
x = 6-4
x = 2 pounds
Hope this helps :)
-6 x -7 because they multiply and add
The total number of combinations available to just pick 1 t-shirt is 20
<u>Explanation:</u>
Given:
4 different sizes of t-shirts are available
5 different colors of t-shirt are available
Different outcomes if the t-shirts have to be picked one by one:
Different outcomes = 4! + 5!
= 24 + 120
= 144
Number of combinations available to just pick 1 t-shirt is:
Number of combinations = 4 X 5
= 20
Therefore, the total number of combinations available to just pick 1 t-shirt is 20