Technical Math
 Practice for the MIDTERM Test Express each as an algebraic expression: 1. subract 7 from X 2. subtyract X from 7 3. Four times V minus 12 4. Divide X by the product of 25 and Y 5. incease A by the square of B Substitute the given numbers for the variables and compute the value of each expression. Round your answer to two decimal places if needed. e = 8 and f = 4 1. 3ef + 9 2. 5f + ef 3. 5e + f(e/4) 4. (10e - 6f)/8 5. 12e /(2f + 2) Perform the operations indicated: 1. -37 - (-31) 2. (-3)(-3)(-3) 3. 24/(-3) 4. (-21)/(-7) 5. (-4)^2 6. (-4)^3 7. [6(9+3)]/[7(11-6)-5] Simplify each expression: 1. 5x - 6x - x - 8x 2. (5a + 6b) + (4a + 8b) 3. (6R - 5R^2) - (4R - 8R^2) 4. (-12a)(-5a^2) 5. 5x^2(x + x^2y) 6. (16y^2)/8y Solve each equation: 1. m + 7 = 22 2. y - 7 = -20 3. 5x = 55 4. (1/2)E = 6 5. 12X - 9 = 39 6. 18/(x+7) = 10 7. 4x - 7 = x + 14 Solve the following system of equations using substitution: 6x + 5y = 13 3x + 4y = 14 WORD PROBLEMS 1. The area of a triangle is one-half the product of the base(b)and the height(h). Write the formula for area (A) as an algebraic sentence. If the base=2x+1 and the height=x+5, write an expression for the area. 2. Use the Pythagorean Theorem to solve the following: A carpenter is completing the corner of a room/ He wants to make sure his corner is square or 90 degrees. A 6 ft length is marked on one wall. An 8 ft length is marked on the other wall. What should be the measurement length between the two marks? 3. Use a proportion to solve the following: A machine produces 280 pieces in 3.5 hours. How long does it take to produce a run of 720 pieces? A tank 6 meters high contains 7200 gallons of water when full. How many gallons of water does it contain when the water is 2 meters high? 4. Use the quadratic formula to solve the following: One side of a window is four less than the length of the other side. Three times the product of their lengths is 231. Find both numbers. (Hint: Use substitution to write a quadratic equation in the form ax^2+bx+c=0. Determine a, b, and c. Substitute these values into the quadratic formula and solve.) [-b +/- SQRT(b^2-4ac)]/2a Joanne Smith University of Massachusetts Boston