Answer:
35
Step-by-step explanation:
We know the factors of Lena's age are 2 and 5. The least common multiple must have these factors and the factors of 14, so will at least have factors of 2, 5, and 7.
Apparently, the dad's age is 5·7 = 35.
___
The GCF is 5; the LCM is 70 = 5×14.
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Sometimes, I use a little 3-part diagram to think about LCM and GCF. Here, it would look like ...
(2 [5) 7]
where the numbers in curved brackets (2·5) and the numbers in square brackets [5·7] are factors of the two numbers of concern (Lena's age, her dad's age). The middle number in both brackets [5) is the greatest common factor, and the product of all three numbers is their least common multiple.
Here, the product of outside numbers, 2·7 = 14, represents the ratio of the LCM to the GCF. We know that Lena's age has factors of only 2 and 5, so the numbers in the diagram have to be (2[5)7], where 2 and 7 are on the ends and 5 is in the middle.
A. You can factor it to those terms
Answer:
Step-by-step explanation:
Answer:
We would have

where " l " is length, " w" is width and "h" is height.
Step-by-step explanation:
Step 1
Remember that
Surface area for a box with no top = 
where " l " is length, " w" is width and "h" is height.
Step 2.
Remember as well that
Volume of the box = 
Step 3
We can now use lagrange multipliers. Lets say,

and

By the lagrange multipliers method we know that

Step 4
Remember that

and

So basically you will have the system of equations

Now, remember that you can multiply the first eqation, by "l" the second equation by "w" and the third one by "h" and you would get

Then you would get

You can get rid of
from these equations and you would get

And from those equations you would get

Now remember the original equation

If we plug in what we just got, we would have

Answer:
m = -1/6.
b = 5.
Step-by-step explanation:
Slope m = (3 - 6) / (12 - -6)
= -3 / 18
= -1/6.
y = -1/6 x + b
when x = 12 y = 3 so
3 = -1/6 * 12 + b
b = 3 + 2 = 5.