Download Math 125 EXAM 1 Determine whether the statement is true or false

Math 125
EXAM 1
Determine whether the statement is true or false.
1) - 7 2 < 6 2 - 9 2
- 49 < 36 - 81
- 49 < - 45
True
Decide if the statement is true or false.
2) - 11 - -13
-11 -13
True
*Evaluate the expression for the given values. If necessary, round to the nearest tenth.
3) 7x 2 - 2y - x 2 - y3 x = -4, y = -3
7 -4 2 - 2 -3 - -4 2 - -3 3
7 16 + 6 - 16 - (-27)
112 - 10 + 27
129
State the phrase as a mathematical expression. Use x to represent the variable.
4) The quotient of a number less than four and twice a number
4-x
2x
Provide an appropriate response
5) Give an example of an expression which includes the use of distributive property and at least one fraction.
3 x+
1
2
6) Give an example of the inverse property of multiplication using a negative number, and identify the
multiplicative inverse by its commonly used name.
-4-
1
=1
4
-
1
is the reciprocal
4
Conplete the problem to illustrate the commutative property of addition.
7) 2 + (x + 7) = 2 + (7 + x)
Tell whether the statement is true or false. If the statement is false, explain why and give an example of a number that
makes it false.
8) Some integers are irrational numbers.
False, no integer is irrational.
ex. 5
9) Some real numbers are integers.
True
1
*Identify the composite integer(s) from the set below.
10) {-2, 0, - .3,
5, -24,
7
1
26
, - 1 , 9.2, , 4, - 7, 1}
8
7
13
4
Find the measure of each marked angle.
11)
(2x + 45)°
(5x + 6)°
2x + 45 = 5x + 6
39 = 3x
13 = x
2 13 + 45
26 + 45
71
both angles are 71°
Find each unit cost to two decimal places. Tell which brand is the better buy.
12) Brand A 24 oz for $18.96 Brand B 21 oz for $15.96
Brand A
$18.96
= $ .79/oz
24oz
Brand B
$15.96
= $ .76/oz
21oz
Simplify the expression.
4
1
7
1
3
y+2
13) - (z + 12) - z - y - 6 +
3
6
9
12
8
-
4
1
28
3
19
z - 16 - z y-6+
y+
3
6
36
36
8
-
8
1
25
19
z - 22 - z y+
6
6
36
8
-
9
176 25
19
zy+
6
8
36
8
-
3
157 25
zy
2
8
36
Solve the equation. If it is an identity or contradiction, then indicate so.
14) 6(x + 2) - (6x + 12) = 0
6x + 12 - 6x - 12 = 0
0=0
, )
identity
2
15) -
-
1
3
1
y - (y - ) =
( y - 4)
3
8
72
1
3
1
1
y-y+ =
y3
8 72
18
72 -
1
3
1
1
y - y+
y72
=
3
8
72
18
- 24y - 72y + 27 = y - 4
-96y + 27 = y - 4
31 = 97y
31
=y
97
16)
5 3x + 10
=
2
7x
5 7x = 2 3x + 10
35x = 6x + 20
29x = 20
20
x=
29
Use a proportion to solve the following problem.
17) A tree casts a shadow 28 m long. At the same time, the shadow cast by a 61-cm tall statue is 92 cm long. Find
the height of the tree. Round results to the nearest unit.
28m 92cm
=
xm
61cm
92x = 61 28
1708
x=
92
x
19m
Write an equation and use it to solve the problem.
18) Find the measure of an angle, if its supplement measures 41° more than twice its complement.
180 - x = 2 90 - x + 41
180 - x = 180 - 2x + 41
x = 41
19) A square plywood platform has a perimeter which is 10 times the length of a side, decreased by 42. Find the
perimeter.
4x = 10x - 42
-6x = - 42
x=7
P = 4(7) = 28
20) A bag of fertilizer covers 500 square feet of lawn. Find how many bags of fertilizer should be purchased to
cover a rectangular lawn 310 feet by 140 feet. (think carefully about your final answer.)
500sqft 310 140
=
1 bag
x bags
500x = 43400
x = 86.8
87 bags
3
21) In a chemistry class, 8 liters of a 4% silver iodide solution must be mixed with a 12% solution to get a 6%
solution. How many liters of the 12% solution are needed? round answer to the nearest tenth, if necessary.
8 .04 + .12x = .06 x + 8
.32 + .12x = .06x + .48
.06x = .16
x 2.7 liters
22) A paint mixture contains 29 gallons of base for every gallon of color. In 1470 gallons of paint, how many gallons
of color are there?
base + color = paint mixture
29c + c = 1470
30c = 1470
c = 49 gallons
23) Roberto invested some money at 8%, and then invested $2000 more than twice this amount at 11%. His total
annual income from the two investments was $3520. How much was invested at 11%?
.08x + .11 2x + 2000 = 3520
.08x + .22x + 220 = 3520
.30x = 3300
x = 11,000
2 11,000 + 2000
22,000 + 2000
$24,000
24) From a point on a straight road, John and Fred ride bicycles in opposite directions. John rides 32 miles in the
same amount of time that Fred rides 48 miles. John rides 4 miles per hour slower than Fred. Find John's rate.
John
Fred
32 = r - 4 t
32
=t
r- 4
48 = rt
48
=t
r
32
48
=
r- 4
r
32r = 48 r - 4
32r = 48r - 192
192 = 16r
r = 12
12 - 4 = 8mph is John's rate
Bonus. Write an equation and use it to solve the problem. (10 points)
25) If three times the smaller of two consecutive integers is added to four times the larger, the result is 46. Find the
smaller integer.
3x + 4 x + 1 = 46
3x + 4x + 4 = 46
7x = 42
x=6
4