Determine whether the set, together with the indicated operations, is a vector space. If it is not, then identify one of the vector space axioms that fails.
(a) The set of all quadratic functions whose graphs pass through the point (0, 5) with the standard operations.

It isn't a vector space

Step-by-step explanation:

If f and g were elements of the set, then the sum f+g should be an element of the set. However the sum of quadratic funcitons may not neccesarily be a quadratic function. Lets look at

f(x) = x²+ x + 5

g(x) = -x²+5

Both f and g are quadratic functions and the graphs of both functions contain the point (0,5), because f(0) = g(0) = 5. However f(x) + g(x) = (x²+x+5)+(-x²+5) = x+10, which is not a quadratic funciton. Furthermore, f+g(0) = 10, so its graph doesnt contain the point (0,5). This shows that f+g is not in the set, therefore, the set cant be a vector space.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

a

step-by-step explanation:

when a number is between two straight lines it means the absolute value.

to find absolute value you need to know how many numbers is that number away from 0.

when finding absolute value the number will always come out positive

so absolute value of -3 is 3

absolute value of 3/2 is 3/2

absolute value of -2 is 2

absolute value of 3.5 is 3.5

absolute value of -1 is 1

now put these numbers in order:

a)   |-1|, |3/2|, |-2|, |-3|, |3.5|