Determine whether the set, together with the standard operations. is a vector space. If it is not. Identity at least one of the ten vector space axioms that fails. The set of all quadratic functions whose graphs pass through the origin. 1) The set {(x, 1/2 x): x is a real number} 2) The set of all 2 x 2 matrices of the form [a c b 0] 3) The set of all 2 X 2 matrices of the form [a c b 1] 4) The set of all 4 x 4 matrices of the form [0 a a a a 0 b b b b 0 c c c c 0] 5) The set of all 3 X 3 upper triangular matrices. C[-1, 1]. 6) The set of all continuous functions defined on the interval [-1, 1]. Let V be the set of all positive real numbers.

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

you forgot an image

step-by-step explanation:

a = 3.14

b = 18

c = 18/5 or 3.6 or 3 3/5

step-by-step explanation: