We have that
<span>p(t)=-3t^2+18t-4
using a graphing tool, we can see the maximum of the graph
(see the attached figure)
A) </span><span>In what year of operation does Mr. Cash’s business show maximum profit?
</span>
Mr. Cash’s business show maximum profit at year 3 (maximum in the parabole)
<span>B) What is the maximum profit?
23 (hundred of thousand of dollars) = 2.300.000 dollars
</span>c) What time will it be two late?
(This is the time when the graph crosses zero and the profits turn into losses )
5.77 years, or an estimate of about 69 months.
1.50c + 2.50a = 1100
c + a = 500
multiply the second equation by -1.50
1.50c + 2.50a = 1100
-1.50c - 1.50a = -7.50
I draw the two triangles, see the picture attached.
As you can see, angle 1 and 2 are vertically opposite angles because they are formed by the same two crossing lines and they face each other.
Angles <span>ABQ and QPR, as well as angles BAQ and QRP, are alternate interior angles because they are formed by </span><span>two parallel lines crossed by a transversal, and they are inside the two lines on opposite sides of the transversal.</span>
Hence, Allison's correct claims are:
1 = 2 because they are vertically opposite angles. BAQ = QRP because they are alternate interior angles. Therefore Allison, in order to prove her claim, can use the AA similarity theorem: if two angles of a triangle are congruent to two angles of the other triangle, then the two triangles are similar.
A really easy way to do this would be converting them all to decimals by dividing the top number by the bottom number.
7/5 = 1.4
15/4 = 3.75
3/2 = 1.5
11/4 = 2.75
13/3 = 4.33
Start with the whole numbers. 3/2 and 7/5 must go first since they both have a 1. 7/5 goes before 3/2 since it has a 4 in the tenths place, while 3/2 has a 5.
Next would be 11/4 since it has a 2, then 15/4 with a 3, and lastly 13/3 with a 4 as a whole number
Answer is 7/5 , 3/2 , 11/4, 15/4 , 13/3