I'm not quite sure what you mean by common core way but the way to get the answer the question is this:
1.) You must covert the whole numbers into fractions.

(multiply the denominator by the whole number, which in this case is 4, then add the answer to the numerator).

(same steps will apply as before except in this case there is a different denominator and numerator).
There is no need to make the denominators the same number since it is multiplication and not addition or subtraction (the same can be done with division expect there is one crucial difference which I can explain if you want, in the comments).
2.) Next set up the equation to multiply:

5 and simplify (also note that the only way you can't simplify is across)

3.) Now multiply across:
NUMERATOR
21 × 7 = 147
DENOMINATOR
5 × 8 = 40
It will come together to be 147/40 or 3 27/40
It is important so you can be more fluent or faster in knowing bigger problems
We use
trigonometry for this problem. You might have learned about SOH CAH TOA. In right triangles, when given an angle, you can name the three sides of the triangle a certain part:
Opposite,
Adjacent, and
Hypotenuse.
For this problem, we are given the angle and the ADJACENT length (73). We want to find the OPPOSITE side's length.
TOA
We must use the tangent function.
TOA helps us remember this relationship:
tan( theta ) = opposite / adjacent.
Plug in our values:
tan(29 degrees) = opposite / 73
Multiply by 73 to isolate "opposite" and solve for it.
73 * tan(29) = opposite.
Using a calculator, the answer is approximately 40.46 ft.
Answer: 
<u>Step-by-step explanation:</u>
The explicit rule for a geometric sequence is: 


Answer: 3cm
Explanation:
We can use Pythagorean’s theorem to find that other side:
a^2 + b^2 = c^2
a^2 + 4^2 = 5^2
a^2 = 25 - 16
a^2 = 9
a = 3
Therefore, the other side is 3cm