Answer:
![\dfrac{7}{12}](https://tex.z-dn.net/?f=%5Cdfrac%7B7%7D%7B12%7D)
Step-by-step explanation:
<u>Method 1</u>
convert the fractions so that their denominators are 12:
![\dfrac12=\dfrac{1 \times 6}{2 \times 6}=\dfrac{6}{12}](https://tex.z-dn.net/?f=%5Cdfrac12%3D%5Cdfrac%7B1%20%5Ctimes%206%7D%7B2%20%5Ctimes%206%7D%3D%5Cdfrac%7B6%7D%7B12%7D)
![\dfrac23=\dfrac{2\times4}{3\times4}=\dfrac{8}{12}](https://tex.z-dn.net/?f=%5Cdfrac23%3D%5Cdfrac%7B2%5Ctimes4%7D%7B3%5Ctimes4%7D%3D%5Cdfrac%7B8%7D%7B12%7D)
From inspection, we can determine that the fraction that lies exactly halfway between
and
is ![\dfrac{7}{12}](https://tex.z-dn.net/?f=%5Cdfrac%7B7%7D%7B12%7D)
<u>Method 2</u>
Find the difference between the fractions and divide by 2:
![\dfrac{\dfrac23-\dfrac12}{2}=\dfrac{1}{12}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cdfrac23-%5Cdfrac12%7D%7B2%7D%3D%5Cdfrac%7B1%7D%7B12%7D)
Add this to the smallest fraction (1/2):
![\dfrac12+\dfrac{1}{12}=\dfrac{7}{12}](https://tex.z-dn.net/?f=%5Cdfrac12%2B%5Cdfrac%7B1%7D%7B12%7D%3D%5Cdfrac%7B7%7D%7B12%7D)
Answer:
64 square cm
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Thank you!
He can put 5 of each fruit into each box without exceeding 5 kilograms.
The type of limacon graphed is a convex.
Here we're presented with a quadratic equation which needs to be expanded and then rewritten in descending powers of x:
1x^2 + m^2x^2 + 6mx + 9 - 3 = 0.
Let's group like terms: 1x^2 + m^2x^2 + 6mx + 6 = 0.
The first 2 terms can be rewritten as a single term: (1+m^2)x^2, and so we now have:
(1+m^2)x^2 + 6mx + 6 = 0.
We must now calculate the discriminant and set the resulting expression = to 0, as a preliminary to finding the value of m for which the given quadratic has equal roots:
discriminant: (6m)^2 - 4(1+m^2)(6) = 0
Then 36m^2 - 24(1+m^2) = 0, which simplifies to 12m^2 - 24 = 0.
Then 12 m^2 = 24; m^2 = 2, and m = √2.
When the discriminant is zero, as it is here when m = √2, then the given quadratic has two equal roots.