The parallelogram shown in the figure below has a perimeter of 44 cm and an area of 64 cm2. Find angle T in degrees. http://cdn-1.analyzemath.com/high_school_math/grade_10/graphs/geometry_g10_2.gif

44 = 2(3x + 2) + 2(5x + 4) , solve for x x = 2 height = area / base = 64 / 14 = 32/7 cm sin(T) = (32/7) / 8 = 32/56 = 4/7, T = arcsin(4/7) = 34.8 degrees

Sales for a business were 3 million dollars more the second year than the first, and sales for the third year were double the sales for the second year. If sales for the third year were 38 million dollars, what were sales, in millions of dollars, for the first year?

First, we divide the sales for the third year by 2. Then, we subtract the 3 million increase for the second year. Therefore, sales for the first year are 16.

In triangle ABC, the measure of ∠B is 90°, BC=16, and AC=20. Triangle DEF is similar to triangle ABC, where vertices D, E, and F correspond to vertices A, B, and C, respectively, and each side of triangle DEF is 13 the length of the corresponding side of triangle ABC. What is the value of sinF?

Triangle ABC is a right triangle with its right angle at B. Therefore, AC is the hypotenuse of right triangle ABC, and AB and BC are the legs of right triangle ABC. Here, the Pythagorean theorem will be used and plugged in. Since triangle DEF is similar to triangle ABC, with vertex F corresponding to vertex C, the measure of angle ∠F equals the measure of angle ∠C. Therefore, sinF = sinC. And then, we find out that sinF = 3/5, and the final answer is 3/5 (or 0.6).