Abungee jumper falls 97.2 feet before bouncing back up at the end of his bungee cord. then he falls 64.8 feet before bouncing up again. on his third descent, he falls 43.2 feet before going back up. what is the total distance the bungee jumper drops after five falls if the distances continue in this pattern? (do not include the distance traveled up.)

234.0 ft
253.2 ft
789.8 ft
1,281.8 ft

253.2 ft

Step-by-step explanation:

Given,

The distance bungee jumper drops in first fall = 97.2 feet,

In second fall = 64.8 feet,

In third fall = 43.2 feet,

......., so on, ....

Thus, the sequence that show the situation is,

97.2, 64.8, 43.2,........

Since,

⇒ The above sequence is a GP,

Having first term, a = 97.2 ft,

And, common ratio, r = 2/3,

Hence, the total distance the bungee jumper drops after five falls,

Second option is correct.

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.