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°)

Which is the most efficient first step to solve x in the equation 3.7x - 18 = -4.3x -34 a. add 3.7x to both sides of the equation. b. add 4.3x to both sides of the equation. c. subtract 18 from both sides of the equation. d. subtract 34 from both sides of the equation.

Find the area and perimeter of each composite figure. use 3.14 for π. round your answer to the nearest tenth. a square and a right triangle share a common side. image long description a 3-meter by 0.5-meter rectangle has triangles attached like wings to the 3-meter sides. the other two sides of both triangles measure 2.5 meters. the height of each triangle is 2 meters. a 6-inch by 4-inch rectangle has 2 half-circles attached like wings to the 6-inch sides. the radius of each half-circle is 3 inches. find the surface area and volume of each figure. use 3.14 for π. round your answer to the nearest tenth. a right circular cylinder has a base radius of 6 yards and a height of 20 yards. a rectangular prism has a base that is 9 centimeters long and 7 centimeters wide. the height is 2 centimeters. a rectangular prism has a base that measures 11 millimeters by 11 millimeters. the height is 11 millimeters.

It takes an ant farm 3 days to consume 1/2 of an apple. at that rate, in how many days will the ant farm consume 3 apples