Compare the numbers below using , or = -2+-4_-3+-9

Mathematics

1 answer:

weqwewe [10]3 years ago

5 0

-3+-9 is greater than -2+-4

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Fred and Frank play a game. Fred picks an even number X and asks Frank to add all even numbers between 0 and X (inclusive) as fa

TiliK225 [7]

Answer:

The even numbers between 0 and X represents an arithmetic sequence with a common difference of 2

The rule of arithmetic sequence = a + d(n - 1)

Where a is the first term and n is the number of terms

So, for the even numbers between 0 and X

The first term = a = 0

d = 2

So, we need to find n at the last term which is X

∴ X = 0 + 2 ( n -1 )

∴ n - 1 = X/2

∴ n = X/2 + 1

The sum of the arithmetic sequence = (n/2) × (2a + (n−1)d)

Substitute with a and d and X

So, the sum = (n/2) * (2*0 + (n−1)*2)

= (n/2) * ((n−1)*2)

= n(n-1)

= (X/2 + 1) * (X/2)

= X/2 by (X/2 + 1)

So, The quick way to add all even numbers between 0 and X always works.

8 0

4 years ago

Joe bikes at the speed of 30 km/h from his home toward his work. If Joe's wife leaves home 5 mins later by car, how fast should

GuDViN [60]

Answer:

Joe's wife must drive at a rate of 45km/hour.

Step-by-step explanation:

We are given that Joe leaves home and bikes at a speed of 30km/hour. Joe's wife leaves home five minutes later by car, and we want to determine her speed in order for her to catch up to Joe in 10 minutes.

Since Joe bikes at a speed of 30km/hour, he bikes at the equivalent rate of 0.5km/min.

Then after five minutes, when his wife leaves, Joe is 5(0.5) or 2.5 km from the house. He will still be traveling at a rate of 0.5km/min, so his distance from the house can be given by:

$2.5+0.5t$