A plan traveled for a total of 2,773 miles over the course of 8 hours. Heading south, the plan traveled at an average speed of 344 miles per hour and heading west. It traveled at an average speed of 351 miles per hour. For how many hours was the plane heading south?

  5 hours

Step-by-step explanation:

Let s and w represent hours spent traveling south and west, respectively. The problem statement tells us ...

  s + w = 8 . . . . . . total trip time

  344s + 351w = 2773 . . . . total mileage (using d = s·t)

By Cramer's rule, we can find the value of s as ...

  s = (1(2773) -351(8))/(1(344) -351(1)) = -35/-7 = 5

The plane was heading south for 5 hours.

Comment on Cramer's rule

For the equations ...

  ax +by = c

  dx +ey = f

The solution for x can be found to be ...

  x = (bf-ec)/(bd-ea)

Similarly, the solution for y is ...

  y = (cd-fa)/(bd-ea)

c. 65°

step-by-step explanation:

we are given a triangle with two known angles, 62° and 53°, while the third angle x is unknown and we are to find its value.

we know that the sum of angles in a triangle is equal to a total of 180 degrees. so we can write it as:

x + 62° + 53° = 180°

solving to find the value of x:

x = 180 - (62 + 53) = 65°

therefore, the value of x in this triangle is 65°.

false

step-by-step explanation:

the reason i say this is because for a certain length of sides you can pick any two and the length is wither equal or greater than the third side and in this case it's not.

3 + 5 = 8

8 is smaller than 9 which is the third side.

hope this : )