Answer:
x₁ = -4
x₂ = 3
Step-by-step explanation:
x²+ x + 12 = 0
x = {-1±√((1²)-(4*1*-12))} / (2*1)
x = {-1±√(1+48)} / 2
x = {-1±√49} / 2
x = {-1±7} / 2
x₁ = {-1-7} / 2 = -8/2 = -4
x₂ = {-1+7} / 2 = 6/2 = 3
Check:
x₁
-4² + (-4) - 12 = 0
16 - 4 - 12 = 0
x₂
3² + 3 - 12 = 0
9 + 3 - 12 = 0
Answer:
√(cd)*∛d
Step-by-step explanation:
This problem becomes a bit easier if we group the variables c and d together.
(cd)^(1/2)*d*(1/3) = c^(1/2)*d^(1/2+1/3)
Continuing, we get c^(1/2)*d^(5/6) (by adding the exponents 1/2 and 1/3)
Now c^(1/2) is equivalent to the radical form √c, and
d^(5/6) is equivalent to d^(5/3)^(1/2), which, as a radical, is √d(5/3).
Summarizing this:
(cd)^(1/2)*d*(1/3) = c^(1/2)*d^(1/2+1/3) = (cd)^(1/2)*d^(1/3),
which, in radical form, is √(cd)*∛d
The answer to h) is 12k squared (to the second power) and the answer to i) is 24p cubed (to the third power)
Answer:
Answer is the second bullet
Step-by-step explanation:
The first step to find how many 1/4 inch segments are in 1 and 1/2 inches is to convert 1 and 1/2 into an improper fraction.
To do this, convert 1 into a fraction with the same denominator as 1/2, which is 2.
1 = 1/1
1/1 = 2/2
Now add 2/2, which is the same as 1, to 1/2.
2/2 + 1/2 = 3/2
So 1 and 1/2 = 3/2
Now multiply both the numerator and denominator by 2 so you can see how many times 1/4 goes into the fraction equivalent to 1 and 1/2.
3/2 = 6/4
1/4 goes into 6/4 6 times, since the numerator of 1 goes into the numerator of 6 6 times.
So the answer is that 6 1/4 inch segments are in 1 and 1/2 inches.