Answer:
Step-by-step explanation:
Volume = 198 ft
length * width * height = 198
(x - 1) * (x + 4) * 3 = 198
(x - 1) * (x + 4) = 198/3
(x - 1) * (x + 4) = 66
x*x + x*4 -1*x - 1*4 = 66 {Use FOIL method to multiply}
x² + 4x - x - 4 = 66
x² + 3x - 4 =66
x² + 3x - 4 - 66 = 0
x² + 3x - 70 = 0
Now factorize.
x² + 10x - 7x - 7*10 = 0
x(x +10) - 7(x + 10 ) = 0
(x + 10)(x - 7) = 0
x - 7 = 0 {x + 10 is ignored because measurement cannot be in negative}
x = 7
length = x - 1 = 7 - 1 = 6ft
Width = x + 4 = 7 + 4 = 11 ft
Given:
f(x) = 70n - 400 : equation for monthly profit.
n = number of students enrolled in the guitar class.
70 refers to the amount charged per student.
400 is the fixed expense made by the instructor.
For the instructor to have a profit, the product of 70n must be more than 400.
400/70 = 5.7 or 6
There must be at least 6 students enrolled in class for the instructor to generate profit.
f(x) = 70(6) - 400 = 420 - 400 = 20
1000 = 70n - 400
1000 + 400 = 70n
1400 = 70n
1400/70 = n
20 = n
There must be 20 students enrolled in class for the instructor to earn 1000 in profit.
1000 = 70(20) - 400
1000 = 1400 - 400
1000 = 1000
-6×-6=36
f-34=36
34+36=70
f=70
You can solve this problem by applying the proccedure below:
You have:
a) 18/21=2/3
18x3/21x2
36≠42 (2/3 is not proportinal to 18/21).
b)18/21=30/35
18x35/21x30
630=630 (30/35 is proportional to 18/21)
c)18/21=36/48
18x48/21x36
864≠756 (36/48<span> is</span><span> not proportinal to 18/21)
</span>
d)18/21=1/3
18x3/21x1
54≠21 (<span> 1/3 is</span><span> not proportinal to 18/21)
</span>
Therefore, you can conclude that the correct option is: B.30/35
Use calculating software for the quickest answer. The answer would be yes with a rate of increase of 1.75
