Technical Math

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

e-mail Joanne Smith

Joanne Smith
University of Massachusetts Boston