Simplify: (4 – 5) – (13 – 18 + 2).
By following the order of operations (PEMDAS) we can see in a few steps: = (4 – 5) – (13 – 18 + 2). = -1-(13+2-18). solved first parentheses = -1-(15-18). solved first expression in the second set of parentheses = -1-(-3). solved the second set of parentheses = -1+3. distributed the subtraction sign to the negative 3. = 2. added the two remaining terms.
Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
Let the 1st paycheck be x (integer). Mrs. Rodger got a weekly raise of $ 145. So after completing the 1st week she will get $ (x+145). Similarly after completing the 2nd week she will get $ (x + 145) + $ 145. = $ (x + 145 + 145) = $ (x + 290) So in this way end of every week her salary will increase by $ 145.
The radius of a cylindrical gift box is (3x+4) inches. The height of the gift box is twice the radius. What is the surface area of the cylinder?
The surface area of a cylinder A = 2*pi*r*h (lateral) + 2*pi*r^2 (end caps), where r is the radius and h is the height. Given: r = 3x+4; h = 2*r -> h = 2(3x+4) A = 2*pi(2(3x+4)^2 + (3x+4)^2) = 2*pi*(3(3x+4)^2) = 6*pi*(3x+4)^2 I leave it as an exercise for you to expand and express in standard form.