Answer:
Trent has 6 quarters and 5 dimes.
Step-by-step explanation:
Consider the provided information.
Let q = Number of quarters
d = Number of dimes.
Trent has 11 quarters and dimes.
The worth of a quarter is 25 cents.
The worth of a dimes is 10 cents
Substitute the value of q in above equation.
Substitute the value of d in
Hence, Trent has 6 quarters and 5 dimes.
Answer:
50 Notebooks
Step-By-Step:
First write an equation
3/5x
The x represent the number of notebooks that can fit within the shelf.
So 3/5(50)=30
Answer:
20 gallons
Step-by-step explanation:
The living room is made up of white trim and blue surface area between the walls. Since the ratio of the blue surface area between the walls to the white trim is given by 1 : 10.
Also 2 gallons of blue paints are used for the walls, let x represent the number of white paint used in gallons. Hence:
number of white paint in gallons = [1 / (1 + 10)] * total number of paints = 1 / 11 * total number of paints
2 = 1/11 * total number of paints used
total number of paints = 22 gallons
number of white paint (x) = [10 / (1 + 10)] * total number of paints = 1 / 11 * total number of paints
x = 10/11 * 22
x = 20 gallons
Therefore 20 gallons of white paint was used
<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:
Well X=8 in standard form is NaN or 8 * 10 to the power of 0
