Answer:
Ground seats = 450 people
Balcony seats= 132 people
Step-by-step explanation:
Hi, to answer this question we have to write a system of equations:
The money raised (6480) must be equal to the product of the charge per balcony seats (15) and the number of balcony seats sold (b) ;plus the product of the charge per ground seats (10) and the number of ground seats sold (g)
15 b +10 g =6480
The total number of people (582) must be equal to the sum of balcony seats sold (b) and ground seats sold (g).
b+g = 582
Multiplying the second equation by 10, and subtracting it to the first equation:
15 b +10 g =6480
-
10b+10g = 5820
__________
5b =660
Solving for b
b = 660/5 = 132
Substituting b=132 in the second equation:
132+g = 582
g= 582-132
g= 450
You were doing everything correctly! Keep in mind that a straight line is 180 degrees and a triangle has 180 degrees, because I see that some of your questions involve lines.
also remember vertical angles! If you have any specific question, I would be happy to help!
-9(6m-3)+6(1+4m)
=54m+27+6(1+4m)
=54m+27+6+24m
= -30m+33
1st,since this GP is convergent that means the common ratio r <1
2nd, sum of a GP = a₁(1-rⁿ)/(1-r), where a₁ = 1st term and n=number of terms
3rd, for any convergent GP, r<1 and the sum of all terms =a₁/(1-r): Why?
[since r<1 → lim rⁿ when n→∞, =0 in the formula of the 2nd)]
Now let's solve :
a) Sum = a₁(1-r³)/(1-r) = 19 (sum of the first 3 terms)
b) Σ(Sum) = a₁/(1-r) = 27 (sum of all terms of this CONVERGENT GP)
Divide a) by b):
[a₁(1-r³)/(1-r)] / [a₁/(1-r)] = 19 /27 ↔ [a₁(1-r³)/(1-r)] x [(1-r)/a₁]=19/27.
Simplify:
(1-r³) = 19/27
-r³ = 19/27 - 1
r³ = 8/27
r = ∛(8/27)
r = 2/3 and a₁ = 9 (Plug r in the Σ sum)
Hence first term a₁ = 9
and common ration r =2/3
Answer:
Step-by-step explanation:
For this case we have 2 secant lines and an exterior angle x.
Then by definition the measure of the outer angle is equal to half the difference of the arcs formed by the sides.
This means that the angle x is equal to:
the answer is:
