In a right triangle ABC, tan(A) = 3/4. Find sin(A) and cos(A).
Sin = Opposite/Hypotenuse; Cos = Adjacent/Hypotenuse; Tan = Opposite/Adjacent If Tan(A) = 3/4, you know the Opposite = 3 and Adjacent = 4. Use Pythagorean Theorem to find the hypotenuse. a^2 + b^2 = c^2 so, 3^2 + 4^2 = c^2. Solve. 9 + 16 = 25, find the square root of 25 which is 5. Sin(A) = 3/5, and Cos(A) = 4/5
Solve this linear inequality for b. -94–3b < -100
Linear inequality is -94 - 3b < -100 Treat the inequality sign as an equal sign, as if you were solving an equation. Add 94 to both sides. -94 + 94 - 3b < -100 + 94 Left side cancels out, so you end up with -3b < -6 Solve for b. In a normal equation, you would divide 3 on both sides. In an inequality, if you multiply/divide on both sides, you need to change the direction of the inequality sign. Therefore, b > 2
Use the following function rule to find f(1). f(x) = [(7)^x] + 11
Plus in 1 to the function of x. f(1) = [(7)^1] + 11 Any number to the first power equals itself, so seven to the first power equals seven. f(1) = 7 + 11 Add and solve. f(1) = 18