C Challenge
-
Reasoning Devise a plan to find the value of x.
x
=
2
+
2
+
2
+
⋯
x equals . square root of 2 plus . square root of 2 plus , square root of 2 plus math axis ellipsis end root end root end root
For each set of values, determine which is greater without using a calculator.
-
6
or
2
+
1
square root of 6 , or , square root of 2 plus 1
-
3
+
11
or
5
square root of 3 plus square root of 11 , or , 5
-
10
or
2
+
3
square root of 10 , or , square root of 2 plus square root of 3
-
19
+
3
or
5
+
13
square root of 19 plus square root of 3 , or , square root of 5 plus square root of 13
Standardized Test Prep
SAT/ACT
- What is the solution of
(
x
+
2
)
3
4
=
27
?
open , x plus 2 , close super 3 fourths end super . equals 27 question mark
-
x
=
27
x equals 27
-
x
=
79
x equals 79
-
x
=
81
x equals 81
-
x
=
83
x equals 83
- A problem on a test asked students to solve a fifth-degree polynomial equation with rational coefficients. Adam found the following roots:
−
11.5
,
2
,
2
i
+
6
2
,
−
2
negative , 11.5 , comma square root of 2 comma . fraction 2 i plus 6 , over 2 end fraction . comma negative square root of 2 and
3
−
i
.
3 minus i . His teacher wrote that four of these roots are correct, and one is incorrect. Which root is incorrect?
-
−
11.25
negative , 11.25
-
2
square root of 2
-
2
i
+
6
2
fraction 2 i plus 6 , over 2 end fraction
-
3
−
i
3 minus i
- Which expression represents the solution of the equation
x
y
=
c
a
+
b
x over y , equals . fraction c , over eh plus b end fraction solved for a?
-
c
b
−
x
y
c over b , minus , x over y
-
y
c
a
+
b
fraction y c , over eh plus b end fraction
-
y
c
x
+
b
fraction y c , over x end fraction , plus b
-
y
c
−
x
b
x
fraction y c minus x b , over x end fraction
Short Response
- To rationalize the denominator of
4
25
4
,
the fourth , root of 4 twenty fifths end root , , comma by what number would you multiply the numerator and denominator of the fraction?
Mixed Review
See Lesson 6-4.
Simplify each number.
-
81
1
4
81 super and 1 fourth end super
-
4
1
2
4 super and 1 half end super
-
125
⋅
125
1
3
125 dot . 125 super and 1 third end super
-
32
⋅
256
1
2
32 dot . 256 super and 1 half end super
-
100
−
3
2
100 super negative 3 over 2 end super
-
64
2
3
64 super and 2 thirds end super
-
25
1.5
25 to the 1.5
-
6
1
2
⋅
12
1
2
6 super and 1 half end super , dot , 12 super and 1 half end super
See Lesson 4-5.
Solve each equation by factoring. Check your answers.
-
x
2
−
7
x
+
12
=
0
x squared , minus 7 x plus 12 equals 0
-
x
2
−
8
x
+
15
=
0
x squared , minus 8 x plus 15 equals 0
-
x
2
+
9
x
+
20
=
0
x squared , plus 9 x plus 20 equals 0
-
3
x
2
+
8
x
+
4
=
0
3 x squared , plus 8 x plus 4 equals 0
-
9
x
2
+
15
x
+
4
=
0
9 x squared , plus 15 x plus 4 equals 0
-
4
x
2
+
11
x
+
6
=
0
4 x squared , plus 11 x plus 6 equals 0
Get Ready! To prepare for Lesson 6-6, do Exercises 91-96.
See Lesson 2-1.
Find the domain and range of each relation, and determine whether it is a function.
- {
(
0
,
−
5
)
,
(
2
,
−
3
)
,
(
4
,
−
1
)
open 0 comma negative 5 close comma open 2 comma negative 3 close comma open 4 comma negative 1 close }
- {(
−
2
,
2
)
,
negative 2 comma 2 close comma (0, 0), (1, 1)}
- {(
−
2
,
−
2
negative 2 comma negative 2 ), (0, 0), (1, 1)}
- {
(
3
,
−
1
)
,
(
4
,
−
1
)
,
(
5
,
−
1
)
open 3 comma negative 1 close comma open 4 comma negative 1 close comma open 5 comma negative 1 close }
- {(0, 0), (1, 0), (2, 1), (2, 2)}
- {
(
0
,
−
2
)
,
open 0 comma negative 2 close comma (0, 0), (0, 2)}
