x = child tickets
y = adult tickets
x + y = 141
5.60x + 9.30y = 974.60
y = 141 - x
5.60x + 9.30 ( 141 - x ) = 974.60
5.60x + 1311.3 - 9.30x = 974.60
-3.70x + 1311.3 = 974.60
-3.70x = 974.60 - 1311.3
-3.70x = -336.7
x = 91
91 child tickets were sold that day
Answer:
The cafeteria provides three meals per day.
<u>Reason 1</u>
Yes, they vary directly
As number of days increases ,Total number of meals i.e
1st day ⇒ 3
2nd day⇒6
3 rd day⇒9
4th day⇒12
......................
.........................
increases.
Total number of Meals = k×Number of days
But there is another possibility also
<u>Reason 2</u>
1 st day ⇒ 3
2nd day ⇒3
3rd day⇒ 3
.....................
.....................
As you can see from the above expression On each day number of meals is
constant.
So we can say that ,
On each Day=Constant amount of meal=3
So, there is no Proportionality between Days and Meal.
<span>Part I: Determining Dimensions
Arnold
has been given a 6 foot by 6 foot sheet of cardboard to make an open
box by cutting an equal size square from each corner, folding up the
resulting flaps, and taping at the corners. Your task is to label
dimensions on a sketch with the same size variable cut from each corner.
*You don't have to draw one, just explain what it would look like*
Answer:
Base of the box:
it is a square
side of the base = 6 foot - x - x. = 6 - 2x
Height of the box: x
Part II: Analyze
How does each variable expression relate to the length, width, and height of the box when folded?
Answer:
length = width = 6 - 2x
height = x
Part III: Extend your Findings
a. Based upon the variables you used in Part II, write a product for the volume.
Answer:
Volume = area of the base × height
Volume = (6 - 2x)² x
b. Expand the product to write a volume function.
Answer:
Volume = (36 - 24x + 4x²)x
Volume = 36x - 24x² + 4x³
c. What domain makes sense for the volume?
Answer:
Since x is a physical dimension x is greater than 0
Since the lenght of the cardboarc sheet is 6 and two squares are cut off, x has to be less than 3
So, the domain is (0, 3)
d. Guess and check values to find the size cut that produces a maximum volume.
*Six guesses are required*
Answer:
x </span>Volume = 36x - 24x² + 4x³
0.1 36(0.1) - 24(0.1)² + 4(0.1)³ = 3.36
0.5 36(0.5) - 24(0.5)² + 4(0.5)³ = 12.5
1.0 36 - 24 + 4 = 16
1.5 36(1.5) - 24(1.5)² + 4(1.5)³ = 13.5
2.0 36(2) - 24(2)² + 4(2)³ = 8
1.7 36(1.7) - 24(1.7)² + 4 (1.7)³ = 11.49
1.2 36(1.2) - 24(1.2)² + 4(1.2)³ = 15.55
Then you can guess that the maximum volume is pretty close to 16 and it is whenx is close to 1.
2.9
The <em>correct answer</em> is:
An identity is an equation that is true for all real numbers.
Explanation:
An identity is a mathematical statement that is always true. It does not matter what numbers you substitute in for the variables, the result will be the same.
