Write the sum as a product. sin 4x + sin 5x
(a) sin 4x sin 5x
(b) sin 4x cos 5x
(d) sin 4x cos(x / 2)
(e) 2 sin 3x cos(x / 2)
(c) 2 sin(9x / 2)cos(x / 2)
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Write a mathematical expression for the word phrase.Three increased by 31, times 
A. (3 + 31) ÷ 
B. 3 
+ 31
C. (3 + 31)
D. 3 + 31
Write an equation to represent the situation. Then, solve the equation.The triangle in the illustration is such that side a is twice as long as side b, and side c is 2 inches shorter than side a. The perimeter of the triangle is 33 inches. Determine the lengths of sides a, b, and c.
A. 2a + a + (2a - 2) = 33; a = 7 inches, b = 14 inches, c = 5 inches B. 2b + b + (2b - 2) = 33; a = 7 inches, b = 14 inches, c = 5 inches C. 2b + b + (2b - 2) = 33; a = 14 inches, b = 7 inches, c = 12 inches D. 2a + a + (2a - 2) = 33; a = 14 inches, b = 7 inches, c = 12 inches
Simplify the expression.
A. 
B. - 
C. 
D. 
Perform the indicated operation(s). Simplify if possible.
- 
A. 2y B. 0 C. 4y D. 5x