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inn [45]
3 years ago
8

If the mean of x and 4x is 10, the x = ?

Mathematics
2 answers:
goblinko [34]3 years ago
7 0
\dfrac{x+4x}{2}=10\\\\\dfrac{5x}{2}=10\ \ \ \ |multiply\ both\ sides\ by\ 2\\\\5x=20\ \ \ |divide\ both\ sides\ by\ 5\\\\\boxed{x=4}
Tom [10]3 years ago
4 0
Divide the 10 by 4, which makes the x be 2.5. You can check it by multiplying 4 by 2.5, which will give you 10.
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What is the solution to the equation?<br> 2/3x=10<br> A. 15<br> B. 30<br> C. 6 2/3<br> D. 6 1/2
Andreyy89
It is A 
<span><span><span>23</span>x</span>=10</span>Step 1: Multiply both sides by 3/2.<span><span><span>(<span>32</span>)</span>*<span>(<span><span>23</span>x</span>)</span></span>=<span><span>(<span>32</span>)</span>*<span>(10)</span></span></span><span>x=<span>15
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Arturiano [62]
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4 0
2 years ago
Write three functions. In the first function, y should vary directly with x. In the second function, y should vary inversely wit
skelet666 [1.2K]
<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.
</span>
3 0
3 years ago
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