<span>let x = the original no. of students
then
(x+10) = the actual no. that went on the trip
:
= the original cost per student
and
= the actual cost
:
Original cost - actual cost = $12.50
- = 12.50
multiply equation by x(x+10)
x(x+10)* - x(x+10)* = 12.50x(x+10)
Cancel the denominators
1500(x+10) - 1500x = 12.5x(x+10)
1500x + 15000 - 1500x = 12.5x^2 + 125x
Combine on the right to form a quadratic equation
0 = 12.5x^2 + 125x - 15000
Simplify, divide equation by 12.5
x^2 + 10x - 1200 = 0
You can use the quadratic formula; a=1; b=10; c=-1200, but this will factor to
(x + 40(x - 30) = 0
The positive solution is what we want here
x = 30 students in the original group
Check this by finding the cost per student for each scenario
1500/30 = $50.00; original cost
1500/40 = $37.50; actual cost
---------------------
saving: $12.50</span>
Answer:
Step-by-step explanation:
<span>The answer is x=<span>−<span><span>1<span> and </span></span>y</span></span></span>=<span>6. You can solve it using a graph, substitution, or elimination. </span>
(9)^4 × (27)^3 × (81)^2 / (3)^24 = 3.
Explanation:
- All the numbers in the numerator i.e. 9, 27, 81 are multiples of 3.
- 9 = 3 × 3 = 3², 27 = 3 × 3 × 3 = 3³, 81 = 3 × 3 × 3 × 3 =
. 
= (3^2)^4, 27³ = (3^3)^3, 81^2 = (3^4)^2.- According to the power rule, (a^x)^y = a^xy.
- So the given numbers can be written as follows = 3^8, 27³ = 3^9 and 81² = 3^8.
- According to the product rule, (a^x) × (a^y) = a^xy.
- So the numerator can be written as × 27³ × 81² = (3^8) × (3^9) × (3^8) = 3^(8+9+8) = 3^25.
- So the fraction becomes 3^25 / 3^24 = 3 × 3^24 / 3^24 = 3.
Answer:
Step-by-step explanation:
volume of a sphere 4/3 pi r^3
vol=4/3 pi 20^3
= 4/3 x 3.1415x 8000
= 33510km^3
