Work out the bearings

Step-by-step explanation:

Use Pythagorean Theorem: a^2+b^2=c^2  (a squared plus b squared equals c squared), where a and b are legs from the 90 degree angle and c is the opposite side of the triangle.

So for part a: a=AB=30  b=AC=30 and c=BC

    a^2 +b^2  =  c^2  Plug in the knowns

  30^2 +30^2=c^2  Use Pemdas, Exponents first.

30^2=900  Simplify the equation

900+900=c^2      Simplify again

1800=c^2  Now to get rid of the ^2 we need to know the square root of 1800.

It is 42.426406871(There are more numbers in the decimal.  Choose your stopping point and round)  I'm going to round to the hundredths.

So, the answer to part a is 42.43 kilometers.  

Now for part b.   a=AD=45   b=AB=30  c=DB

Same equation

a^2     +  b^2    =c^2     Plug in the knowns

45^2   +  30^2  =c^2       Simplify

2025  +  900    =c^2       Simplify

2925     =c^2                      Find the square root

54.3083269  Round to the decimal place needed.  I'm going with Hundredths.

Part b answer is 54.31 kilometers.

Choice A

7(10+9) = 70 + 63

Explanation:

when we multiply 7 by 19, we start off multiplying just 7*9 = 63 so just focus on the units or ones digit of 19 to have it multiply with 7. We have 63 as the result so we write down "3" as part of the answer, and carry the 6.

Then you move onto the tens digit. The tens digit of 19 is 1. Multiply 1 by 7 and we get 7, which adds on to the carry digit 6 to get 7+6 = 13. Therefore we'll stick a 13 in front of the 3 we got earlier to end up with the final answer 133

Using the distribution rule is much easier in my opinion

19 = 10+9

7*19 = 7*(10+9)

7*19 = 70+63

7*19 = 133

The idea is to multiply the outer 7 by each term inside the parenthesis

7*(10+9) = 7*10 + 7*9 = 70 + 63

So we multiplied the 7 by the 10 first to get 7*10 = 70

Then did the same for the 9 term as well 7*9 = 63

After those two multiplications, we add the results up: 70+63 = 133