Represent these consecutive numbers (assuming that they are all integers):

x
x+1
x+2
x+3
x+4
x+5
and so on
x+8
x+9 is the tenth number. x+9 = 10, so x = 9.

Think of it this way: there are 10 consecutive numbers, and the last one is 10.

Working backwards, we get the sequence 10, 9, ... 3, 2, 1.

The sum of such an arith sequence is equal to the count of the numbers times the average of the first and last terms:

sum here = 10(1+10)/2 = 5(11) = 55 (answer)

7 0

2 years ago

Consider vectors u and v, where u = (1, -1) and v = (1, 1). What is the measure of the angle between the vectors?

7nadin3 [17]

Answer:

I believe the answer is C. 90 degrees

Step-by-step explanation:

First you find the lengths of the two vectors, which are both $\sqrt{2}$ . Then you find the angle given the cos using: cos(∅)= $\frac{u*v}{|u|*|v|}$ = $\frac{0}{\sqrt{2}*\sqrt{2} }$ = 0. Then using ∅=acos(0)= $\frac{\pi }{2}$ = 90°

6 0

3 years ago

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