The number of quarts of orange juice did Rebecca use is 7
Given that 28 glasses with orange juice are filled for a camp breakfast
Each glass holds 1 cup of juice
We need to find the number of quarts of orange juice did Rebecca use
We know that a quarts has 4 cups
We need to calculate the quarts from 28 glasses
Let the number of the quarts be x
So the equation formed is
4x = 28
Where x is number of quarts and 28 are the number of glasses
x = 7
Hence the number of quarts is 7
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<span>A) First function, y varies directly with x.
1) function: y = (3/4)x
2) graph: it is a straight line that passes through the origin and has slope 3/4. The slope means that the rate of change of the function is 3 units per every 4 units the x-value incresase or, what is the same 0.75 units per incresase unit of x - value.
3) real world example
A recipe of a cake instructs to use 3 cups of sugar for every 4 cups of flour. So, how much flour you need if you have 12 cups of sugar?
y = (3/4)x , so if x = 3, y = (3/4)*12 = 3*12/4 = 9.
So, given that the variation is direct you multiply the number of cups of sugar times the constant rate, 3/4, to get the number of cups of flour in relation with the given amount of sugar.
B) The second function: y varies inversely with x.
Inverse variation => y*x = constant or y = constant / x.
Tnat means that if x increase y will decrease in the same factor that x increases.
1) function: y = 12 / x
2) graph: the form of this graph is called hyperbola, it is a decreasing line from left to right. It has two asymptotes, the y-axis (x =0) and the x-axis (y = 0). That means that x and y can never be zero.
As the x-value approaches 0, the y value approaches positive or negative infinity; as the y-values approaches 0 the x-values approaches to positive or negative infinity.
If you take the positive values, the graph is a decreasing curve in the first quadrant (x and y are positive).
If you take the negative values, the graphs is a decreasing curve in the third quadrant (x and y are negative)
3) real world example.
The relatioship between velocity and time in a uniform motion.
If the distance run by an object is constant, as the velocity increases the time decreases in the same factor.
Suppse a distant of 100 km between cities A and B.
How long will it take to travel from A to B at 50 km/ h and 25 km/h ?:
100 km = velocity * time
at 50 km/h: 100 km = 50 km/h * t => t = [100 km ] / [50 km/h] = 2 hours
at 25 km/h: 100 kg = 25 km/h * t => t = [ 100 km ] / [25 km/h] = 4 hours.
C) Third case, the relationship between
x and y should is neither inverse variation nor direct variation.
Of course, there are infinite type of functions that are neither inverse variation nor direct variation: linear (that do not passe through the origin), quadratic, exponential, logarithmical, trigonometric sine, ...
1) example of function: y = 30 + 2x
2) graph: it is a straigh line with y-intercept 30 and slope 2.
3) real world example:
The cost of producing chairs consists of 30 dollars of rent for the facility plus 2 dollar to produce each chair, so the total cost y is 30 + 2x.
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Answer:
224
Step-by-step explanation:
Number of trains in the roller coaster = 2
Number cars in each train = 7
Total number of cars = Number of trains 
Number of cars in each train = 
= 14
Number of people in each car = 16
Total number of people in 14 cars = Number of people in one car Number of cars = 16 14 = 224
i.e.
Total number of people in the roller coaster in one run = 224
Number of runs made by each train in one hour = 10
Therefore, Total number of people that can ride the roller coaster in one hour can be found by multiplying the number of runs with total number of people in the roller coaster in one run.
224 10 = <em>2240</em>
Answer: Answer :Isolate the variable by dividing each side by factors that don't contain the variable.
Exact Form:
x
=
3
√
9
45
x
=
9
3
45
Decimal Form:
x
=
0.04622408
…
x
=
0.04622408
I hope this helps friend
Step-by-step explanation:
