Download Math 0361 Test 2 Review Definitions: 1. Equation

Math 0361
Test 2 Review
Definitions:
1. Equation- A statement asserting that two algebraic expressions are equal.
2. Solution- A number that makes the equation true when it replaces the variable.
3. Equivalent equations- Equations with exactly the same solution sets.
4. Conditional equation- An equation with exactly one solution.
5. Identity- An equation with both sides exactly the same and has solution set as {all real numbers}.
6. Contradiction- The equation has no solution because the variable disappears and both sides of
equation are not equal. We can also say the solution set is an empty set or Ø.
7. Consecutive Integers- Two integers that differ by 1. When they are unknown in applied
problems, we can represent consecutive integers by x, x+1, x+2, x+3,…
8. Consecutive Even/Odd Integers- Two integers that differ by 2. When they are unknown in
applied problems, we can represent consecutive even/odd integers by x, x+2, x+4, x+6,…
9. Complementary Angles- Two angles whose sum is 90°. (90-x represents the complement also.)
10. Supplementary Angles- Two angles whose sum is 180°. (180-x represents the complement also.)
11. Right angle- An angle that measures 90°.
12. Straight angle- An angle that measures 180°.
13. Acute angle – An angle that measures less than 90°.
14. Obtuse angle- An angle that measures more than 180°.
15. Formula- An equation in which variables are used to describe a relationship.
16. Area- A measure of the surface covered by the figure.
17. Perimeter- The distance around the figure.
18. Vertical Angles- Angles that are opposite each other and have the same angle measure.
19. Equilateral Triangle – A triangle in which all three sides are equal.
20. Isosceles Triangle – A triangle in which two sides and two angles are equal.
21. Scalene Triangle – A triangle in which all three sides are not equal.
Helpful Charts:
Types of Equation:
Steps to Solving an Applied Problem:
Step 1: Read the problem carefully.
Step 2: Assign a variable to represent the unknown value. Express any
other unknown values in terms of the variable.
Step 3: Write an equation using the variable expression(s).
Step 4: Solve the equation.
Step 5: State the answer. Label it appropriately. Does it seem
reasonable?
Step 6: Check the answer in the words of the original problem.
Finding Consecutive Integers:
If x = the lesser integer, then, for any
two consecutive integers, use
x, x+1
two consecutive even integers, use
x, x+2
two consecutive odd integers, use
x, x+2
Types of Angles:
Area:
Perimeter:
P  2L  2W
Rectangle
P = 4s
Square
Vertical Angles:
and
are a pair of vertical angles.
and
are another pair of vertical angles.
Phrases to look for when translating word phrases to inequalities:
Problems:
1. Use the addition property of equality to solve the equation.
n-27 = -34
2. Solve the equation using the addition property of equality.
4x+2 = 3x
3. Solve the equation.
2
5
w 2 w
3
3
4. Solve.
4.9 r – 5 = 3.9 r -5
5. Solve.
3
1 2 4
2
x   x
7
2 5 7
5
6. Solve.
-3 (8p + 2) – 2 (2- 20p) – 3 (6+5p) = 0
The solution set is {
}.
7. Write an equation using the information in the problem. Then solve the equation.
Five times a number is 12 more than four times the number.
________________________
The solution set is {
}.
8. Write an equation using the information given in the problem. Use x as the variable.
If two times a number is subtracted from three times the number, the result is -4.
_________________________
9. Solve the equation you wrote in #8.
10. The equation 3x = 12 can be solved by completing what step first?
_____________________________
11. Determine the number by which both sides of this equation must be multiplied or divided to
obtain just x on the left side.
3
x  17
8
12. Use the multiplicative property to solve for x.
-9x = 7
13. Solve.
4
x 2
5
14. Solve.
-x = 25
15. Solve.
1
1
k  (k  2)  (k  4)
2
4
16. Solve.
0.30 x + 0.05 (2 – x) = 0.10 (-14)
17. The numbers on two consecutively numbered gym lockers have a sum of 147. What are the
locker numbers?
18. Find two consecutive even integers such that the smaller added to three times the larger gives a
sum of 22.
19. Find the measure of an angle whose complement is seventeen times its measure.
The measure of the angle is ________ degrees.
20. Find the measure of an angle whose supplement measures fourteen times its measure.
The measure of the angle is ________ degrees.
21. A minor league baseball team plays 75 games in a season. If the team won 15 more than twice
as many games as they lost, how many wins and losses did the team have?
22. The U.S. Senate has 100 members. After a certain election, there were 20 more Democrats than
Republicans, with no other parties represented. How many members of each party were there
in the Senate?
23. If 1 is added to a number and the sum is tripled, the result is 13 more than the number. Find the
number.
24. If Planet I is 31.1 million miles farther from the sun than Planet II, then Planet III is 23.8 million
miles farther from the sun than Planet I. When the total of the distances for these three planets
from the sun is 188.0 million miles, how far away from the sun is Planet II?
25. Joe earns 10 dollars a day at the soup kitchen. He works there 3 days a week. How much does
he earn in 5 weeks?
26. Use the formula to find the value of the remaining variable.
P = 2L + 2W; L = 50, W = 125
27. Solve for the specified variable.
C = 2πr;
r (This means to solve the equation for r.)
28. The perimeter of a standard-sized rectangular rug is 24 ft. The length is 2 ft longer than the
width. Find the dimensions.
Width = __________
Length = ___________
29. A flower bed is in the shape of a triangle with one side twice the length of the shortest side, and
the third side is 18 feet more than the length of the shortest side. Find the dimensions if the
perimeter is 126 feet.
30. The area of a triangle sign is 72 ft2. If the base of the sign is 12 feet, what is the height of the
sign? (You will be provided with a formula sheet on the test.)
31. Find the measurements of each angle.
32. Find the measurements of the angles.
33. Find the measures of the angles.
34. Solve for m.
D=
25m
r
35. Solve the equation for the specified variable.
U = Y (r+A), for r.
36. Solve the inequality and write your answer in interval notation.
X+6˂7
37. Solve the inequality and write solution in interval notation.
4x + 3 ˃ 3x + 6
38. Write the inequality in interval notation and graph the interval.
-3 ˂ x ˂ 3