Answer:
I believe its 33.60 because if you add up 33.+5% that would give you 33.6 so its 33.60
Step-by-step explanation:
Hope its right
Answer:
Step-by-step explanation:
As the statement is ‘‘if and only if’’ we need to prove two implications
is surjective implies there exists a function
such that
.- If there exists a function
such that
, then
is surjective
Let us start by the first implication.
Our hypothesis is that the function
is surjective. From this we know that for every
there exist, at least, one
such that
.
Now, define the sets
. Notice that the set
is the pre-image of the element
. Also, from the fact that
is a function we deduce that
, and because
the sets
are no empty.
From each set
choose only one element
, and notice that
.
So, we can define the function
as
. It is no difficult to conclude that
. With this we have that
, and the prove is complete.
Now, let us prove the second implication.
We have that there exists a function
such that
.
Take an element
, then
. Now, write
and notice that
. Also, with this we have that
.
So, for every element
we have found that an element
(recall that
) such that
, which is equivalent to the fact that
is surjective. Therefore, the prove is complete.
Step-by-step explanation:
the area of a triangle is
baseline × height / 2
so, in our case we know this is 10 :
(x+3)(x-1)/2 = 10
(x+3)(x-1) = 20
x² - x + 3x - 3 = 20
x² + 2x - 23 = 0
that is exactly the provided equation. so, yes, x satisfies it.
the general solution to a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = 2
c = -23
x = (-2 ± sqrt(2² - 4×1×-23))/(2×1) =
= (-2 ± sqrt(4 + 92))/2 = (-2 ± sqrt(96))/2 =
= (-2 ± sqrt(16×6))/2 = (-2 ± 4×sqrt(6))/2 =
= -1 ± 2×sqrt(6)
x1 = -1 + 2×sqrt(6) = 3.898979486... ≈ 4
or using sqrt(6) ≈ 2.45
= -1 + 2×2.45 = -1 + 4.9 = 3.9 ≈ 4
x2 = -1 - 2×sqrt(6) = -5.898979486... ≈ -6
or using sqrt(6) ≈ 2.45
= -1 - 2×2.45 = -1 - 4.9 = -5.9 ≈ -6
x2 would give us negative lengths for the triangle, which does not make sense.
so, x = 4 is our solution.
and that makes the height x-1 = 4-1 = 3 units.
Step-by-step explanation:
you should only make one equation:
75 + 45x = 30 + 55x
subtract the 30 frim both sides, then subtract 45x from both sides. you are left with:
45 = 10x
Divide by 10 and get:
4.5 = x
After 4.5 hours, the cost is equal for either worker.