An airplane started at point X, traveled 320 miles to point Y, adjusted its route, and traveled another 400 miles to point Z. If the airplane is currently 599 miles from its starting position at point X, by how many degrees did it adjust its route at point Y?

67.88°

Step-by-step explanation:

If three sides of a triangle are known and you want to determine one angle, this can be done using cosine rule.

Given sides x, y, and z and the angle Y is opposite to side y, the cosine formula is given as:

y² = x² + z² - 2xzcosY

For this problem, x = 400 miles, y = 599 miles, z = 320 miles.

Using the cosine formula:

Degree to adjust its route at point Y = 180° - 112.12° = 67.88°

It needs to adjust by 67.88° at point Y

go and ask your mom to you

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.