Graph the linear equation: - x + 3y = 5

1 answer:

7 0

its easiest if you put it in y = mx + b form, where b is the number you plot on the y axis and m is your slope.
rearranging...
x + 3y = -5 3y = -x - 5 y = -1/3 x - 5/3
so your b value is -5/3, which is where you'll plot a point on the y axis. the slope is -1/3
since slope is rise over run, [and this case its negative] you'll go down 1 and to the right three.
edit: then draw a point there, connect the points, and you'll have a line =]

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A contractor builds homes of 12 different models and presently has 5 lots to build on. In how many different ways can he arrange

Alecsey [184]

Considering the definition of permutation, in 95,040 different ways he can arrange homes on the lots.

<h3>Definition of Permutation</h3>

Permutation is placing elements in different positions. So, permutations of m elements in n positions are called the different ways in which the m elements can be arranged occupying only the n positions.

In other words, permutations are ways of grouping elements of a set in which:

take all the elements of a set.
the elements of the set are not repeated.
order matters.

To obtain the total of ways in which m elements can be placed in n positions, the following expression is used:

$m Pn=\frac{m!}{(m-n)!}$

where "!" indicates the factorial of a positive integer, which is defined as the product of all natural numbers before or equal to it.

In this case, you know:

A contractor builds homes of 12 different models.
Presently the constractor has 5 lots to build on.

To obtain the total of ways in which he can arrange homes on these lots, you use the permutation. This is, 12 elements o models can be arranged occupying only the 5 positions:

$12P5=\frac{12!}{(12-5)!}$