Triangle D E F is shown. Angle D E F is 140 degrees. The length of D E is 11, the length of E F is 9, and the length of D F is e. In ΔDEF, DE = 11, EF = 9, and angle E = 140°.

Which equation correctly uses the law of cosines to solve for the third side?

e2 = 112 + 92 − 2(11)(9)cos(140°)
112 = e2 + 92 − 2e(9)cos(140°)
92 = e2 + 112 − 2e(11)cos(140°)
e = 11 + 9 − 2(11)(9)cos(140°)

Select all the correct answers.natalie buys a new car. in the first month, the odometer on the car records 800 miles. from past experience, she expects to drive 900 miles per monthselect all the functions that can be used to find the number of miles, f(n), recorded on the odometer after n months.of(n) = 800n + 100f(n) = 9001 - 100f(n) = 900n + 800(1) = 800; }(n) = f(n - 1) + 900, for n > 2f(1) = 800; 1(n) = f(n − 1) + 100, for n > 2(1) = 900; }(n) = f(n - 1) + 800, for n > 2

If the simple annual interest rate on a loan is 6, what is the interest rate in percentage per month?

Astudent draws two parabolas on graph paper. both parabolas cross the x-axis at (–4, 0) and (6, 0). the y-intercept of the first parabola is (0, –12). the y-intercept of the second parabola is (0, –24). what is the positive difference between the a values for the two functions that describe the parabolas? write your answer as a decimal rounded to the nearest tenth