Answer:
Step-by-step explanation:
first one is-0
second-1
$28.75 an hour.
If she worked $25 an hour, then got a raise of 15%...It turns into $28.75.
To get the days income, you simply multiply the rate by the time. $28.75 times 8 to get $230.
Hope this helps!
Not all expressions of this form can be simplified; but if one can, we
would like the square root to have the form
sqrt(a) + sqrt(b) or sqrt(a) - sqrt(b)
where a and b are positive rational numbers, and a > b to give the
positive square root.
If we assume that sqrt(2-sqrt(3)) has this form, then this must be
true:
(sqrt(a) +- sqrt(b))^2 = 2 - sqrt(3)
Expanding, we get
a + b +- 2 sqrt(ab) = 2 - sqrt(3)
Equating the rational and irrational parts of this equation,
a + b = 2
+-2 sqrt(ab) = -sqrt(3)
The second equation here tells us that we will have to choose the
negative sign in order to have a solution, since square roots have to
be positive. If we now square this equation, we have
a + b = 2
4ab = 3
Solving these equations by substituting in the second, we get
4a(2 - a) = 3
4a^2 - 8a - 3 = 0
8 +- sqrt(64 + 48)
a = ------------------ = 1/2 or 3/2
8
and
b = 2 - a = 3/2 or 1/2.
One choice here will give the positive root, the other the negative
root. We take a > b, so that a = 3/2 and b = 1/2. Consequently, our
solution is
sqrt(2 - sqrt(3)) = sqrt(3/2) - sqrt(1/2) = (sqrt(6) - sqrt(2))/2
Looking for information on this technique, which I didn't recall being
taught, I found this page, which together with some rather advanced
techniques includes a quote from an old algebra text about the method:
Cot=cos/son
Cot(a)=cos(a) / sin(a)
Cos(a)=5
Sin(a)=12
2sina-3cosa / 4sina-9cosa
2(12)-3(5) / 4(12)-9(5)
24-15 / 48-45
9/3
3
12/16, 7/16, 10/16 (not simplified, just with LCD);The LCD of the 3 fractions is 16 (from denominators) so all we have to do is multiply both the numerator by the same number that multiplies with the denominators to get 16. We leave 7/16 alone since it already has denominator of 16.
3/4 * 4 = 12/16
5/8 * 2 = 10/16