Answer:
<em>n</em> - <em>k</em> + 1
Step-by-step explanation:
This is assuming (because you did not say) that <em>n</em> and <em>k</em> are integers and <em>n</em> is greater than <em>k</em>.
Example: from 2 to 5 {2, 3, 4, 5} includes 5 - 2 + 1 = 4 numbers.
Example: from -6 to 4 includes 4 - (-6) + 1 = 11 numbers, namely {-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4}
Answer:
Using Geometry to answer the question would be the simplest:
Step-by-step explanation:
Remembering the formula for the area of a triangle which is
. One can then tackle the question by doing the following:
Step 1 Find the y-intercepts
The y-intercepts are found by substituting in
.
Which gives you this when you plug it into both equations:

So the y-intercepts for the graphs are
, and
respectively.
Now one has to use elimination to solve the problems by adding up the equations we get:

Now to solve for the y component substitute:

Therefore, the graphs intersect at the following:

Now we have our triangle which is accompanied by the graph.
now to solve it we must figure out how long the base is:

The height must also be accounted for which is the following:

Now the formula can be used:

Answer:
9/-24 or ~ -0.38
Step-by-step explanation:
x y
3 9
12 -15
from 9 to -15 it will be subtracting 24
From 3 to 12 it will be adding 9
y/x = 9/-24 or -0.375 ~ -0.38
<span>Divide by 3 get a remainder of 2
5, 8, 11, 14, 17, 20, ...
Divide by 5 get a remainder of 2
7 , 12, 17, 23, ...
Divide by 7 get a reminder of 5
12, 19, 26, 33, ...
And find a number in all three lists
</span>
<span>Not the most convenient way for sure, but since 47 works it will not take too long</span><span>
</span>
A quadratic function is a function of the form

. The
vertex,

of a quadratic function is determined by the formula:

and

; where

is the
x-coordinate of the vertex and

is the
y-coordinate of the vertex. The value of

determines if the <span>
parabola opens upward or downward; if</span>

is positive, the parabola<span> opens upward and the vertex is the
minimum value, but if </span>

is negative <span>the graph opens downward and the vertex is the
maximum value. Since the quadratic function only has one vertex, it </span><span>could not contain both a minimum vertex and a maximum vertex at the same time.</span>