If \( x + \frac{1}{x} = 5 \), find the value of \( x^2 + \frac{1}{x^2} \).


Total distance = 150 + 200 = <<150+200=350>>350 km.
Total time = 2 + 2 = <<2+2=4>>4 hours.
A sequence starts with 3 and increases by multiplying the previous term by 2. What is the 8th term?
This is a geometric sequence: a = 3, r = 2.
The ratio of boys to girls in a class is 5:7. If there are 48 students total, how many more girls than boys?
Difference = 28 - 20 = <<28-20=8>>8.
First, divide every term by 144 to rewrite the equation in standard form:
= (ac + adi + bci + bd) + (ac - adi + bci - bd)
Solution: The average speed over $ t = 1 $ to $ t = 3 $ is
Given $ b = 4a $, this becomes $ 4a + 4a = 8a $.