A
This is like a base form of a prime polynomial
X^2+x+1
I'm not sure what this means. If you have choices you should list them.
(1/2)*(1/4 + 1/6) is an example of what should be given. There are two ways to solve this.
1. Use the distributive property.
1/2*1/4 + 1/2* 1/6
1/8 + 1/12 Which can be added using the LCD of 24
3/24 + 2/24 = 5/24
Method 2
Add what is inside the brackets first.
1/2 ( 1/4 + 1/6)
1/2(3/12 + 2/12 = 5/12
Now multiply by 1/2
1/2(5/12) = 5*1/(12 * 2) = 5 / 24 Same answer.
Answer: the amount of interest after 3 years is $60
Step-by-step explanation:
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the amount of money deposited.
P represents the principal or amount of money deposited.
R represents interest rate on the deposit.
T represents the duration of the deposit in years.
From the information given,
P = $500
R = 4%
T = 3 years
Therefore,
I = (500 × 4 × 3)/100
I = $60
<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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