<u>answers to 1 - 4:</u>
1.<em> </em><em>GCF: </em>2
2. <em>GCF:</em> 3
3. <em>GCF : </em>7
4.<em> GCF:</em> 3
Let x represent the number of students in Janelle’s group.
If Janelle brings 3 markers for each person in her group, then she brings 3x markers for x students. You also know that she brings <span>5 extra markers for everyone to share. Thus, the total amount of markers she brings is 3x+5.
</span>
If Janelle brings in 23 markers in all, then the equation <span><span>3x+5=23 </span> represaents the mathematical model. </span>
3x=23-5,3x=18,x=6
Answer: there are 6 students in Janelle's group.
We know that
see the picture to better understand the problem
in the right triangle ABC
Applying the Pythagoras Theorem
AB²=BC²+AC²-------> BC²=AB²-AC²
AB=8 ft
AC=4 ft
BC²=8²-4²-----> BC²=48--------> BC=√48-------> BC=6.93 ft
the answer is6.93 ft
Answer:
1. 9 to the power of 7
2. 7 to the power of 8
3. 10 to the power of 8.
4. 3 to the power of 9.
5. 2 to the power of 12.
Step-by-step explanation:
Answer:
a is the _amplitude_(Length of the blades)_
The vertical shift, k, is the _Mill shaft height_


Step-by-step explanation:
In this problem the amplitude of the sinusoidal function is given by the length of the blades.

The mill is 40 feet above the ground, therefore the function must be displaced 40 units up on the y axis. So:

We know that the blades have an angular velocity w = 3 rotations per minute.
One rotation = 
1 minute = 60 sec.
So:


Finally:
a is the _amplitude_(Length of the blades)_
The vertical shift, k, is the _Mill shaft height_

