Functions whose graphs resemble sets of stairsteps are known as step functions.
The most famous of the step functions is the greatest integer function, which is
denoted by:
![f(x)=[x]](https://tex.z-dn.net/?f=f%28x%29%3D%5Bx%5D)
which graph is shown in the Figure below. As you can see from the graph:
![if \ x=-1.8 \ then \ f(-1.8)=[-1.8]=-2](https://tex.z-dn.net/?f=if%20%5C%20x%3D-1.8%20%5C%20then%20%5C%20f%28-1.8%29%3D%5B-1.8%5D%3D-2)
Therefore:
![f(-1.8)=-2[-1.8]+8=-2(-2)+8=\boxed{12}](https://tex.z-dn.net/?f=f%28-1.8%29%3D-2%5B-1.8%5D%2B8%3D-2%28-2%29%2B8%3D%5Cboxed%7B12%7D)
So the right answer is 12
Answer:
The standard form of the quadratic equation is 
Step-by-step explanation:
we know that
The standard form of a quadratic equation is
we have
convert to standard form
Answer: the two numbers are 6 and 11.
Set up the individual equation according to the verbal statements:
<em>A positive number is 5 less than another positive number:</em>
a = b - 5 (this also implies that a<b)
<em>Six times the lesser number minus 3 times the greater number is 3. </em>
<em>Find the two positive numbers.</em>
This is a system of linear equations - solve for a and b:
<em>
</em>
Answer:
B. Ethan is correct because all proportional relationships form a straight line and go through the origin and linear functions are linear, but they don’t all go through the origin so they are not always proportional.
Step-by-step explanation:
So a proportional relationship is just a special kind of linear relationship, i.e., all proportional relationships are linear relationships (although not all linear relationships are proportional).
Answer:
Length= 30 in
Width= 10 in
Step-by-step explanation:
Let the width of the rectangle be x in.
Length of rectangle
= 3 (width)
= 3x
Perimeter of rectangle= 2(length) +2(width)
80= 2(3x) +2(x)
80= 6x +2x
8x= 80 <em>(</em><em>simplify</em><em>)</em>
x= 80 ÷8 <em>(</em><em>÷</em><em>8</em><em> </em><em>on</em><em> </em><em>both</em><em> </em><em>sides</em><em>)</em>
x= 10
Thus width of rectangle= 10 in
Length of rectangle
= 3(10)
= 30 in
