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Math Problems
Algebra 1
Convert a recursive formula to an explicit formula
A frisbee-golf club recorded the ages of its members and used the results to construct this histogram.
\newline
Find the number of members
30
30
30
years of age or younger
\newline
□
\square
□
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Sketch graph of polynomial functions using the left-and right-hand behaviour and their turning points.
f
(
x
)
=
−
x
3
+
1
f(x)=-x^3+1
f
(
x
)
=
−
x
3
+
1
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DIRECTIONS: Use this information to answer Parts A and B.
\newline
A right Triangle
X
Y
Z
X Y Z
X
Y
Z
has Vertices
X
(
−
2
,
−
1
)
X(-2,-1)
X
(
−
2
,
−
1
)
and
Y
(
1
,
1
)
Y(1,1)
Y
(
1
,
1
)
and a right angle at Vertex
Z
Z
Z
.
\newline
Part A
\newline
What could the coordinates of Vertex
Z
Z
Z
be?
\newline
Enter the correct answers in the boxes.
\newline
Show Hints
\newline
□
\square
□
\newline
□
\square
□
or
□
\square
□
\newline
□
\square
□
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Final Test Chapters
1
1
1
−
9
-9
−
9
\newline
NAME
\qquad
\newline
Draw the line (or lines) of symmetry for each figure.
\newline
a
\newline
b
\newline
35
35
35
.
\newline
c
\newline
d
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Use the initial term and the recursive formula to find an explicit formula for the sequence
a
a
a
. Write your answer in simplest form.
\newline
a
=
36
a = 36
a
=
36
\newline
a
=
a
+
17
a = a + 17
a
=
a
+
17
\newline
a
=
a =
a
=
______
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Use the initial term and the recursive formula to find an explicit formula for the sequence
a
a
a
. Write your answer in simplest form.
\newline
a
=
1
a = 1
a
=
1
\newline
a
=
a
−
10
a = a - 10
a
=
a
−
10
\newline
a = ______
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Use the initial term and the recursive formula to find an explicit formula for the sequence
a
a
a
. Write your answer in simplest form.
\newline
a
=
23
a = 23
a
=
23
\newline
a
=
a
+
17
a = a + 17
a
=
a
+
17
\newline
a
=
a =
a
=
______
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Find the sum of the first
35
35
35
terms of the following series, to the nearest integer.
\newline
11
,
17
,
23
,
…
11,17,23, \ldots
11
,
17
,
23
,
…
\newline
Answer:
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In an arithmetic sequence, the first term,
a
1
a_{1}
a
1
, is equal to
5
5
5
, and the sixth term,
a
6
a_{6}
a
6
, is equal to
15
15
15
. Which number represents the common difference of the arithmetic sequence?
\newline
d
=
2
d=2
d
=
2
\newline
d
=
3
d=3
d
=
3
\newline
d
=
4
d=4
d
=
4
\newline
d
=
5
d=5
d
=
5
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In an arithmetic sequence, the first term,
a
1
a_{1}
a
1
, is equal to
9
9
9
, and the fourth term,
a
4
a_{4}
a
4
, is equal to
39
39
39
. Which number represents the common difference of the arithmetic sequence?
\newline
d
=
9
d=9
d
=
9
\newline
d
=
10
d=10
d
=
10
\newline
d
=
11
d=11
d
=
11
\newline
d
=
12
d=12
d
=
12
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In an arithmetic sequence, the first term,
a
1
a_{1}
a
1
, is equal to
8
8
8
, and the fifth term,
a
5
a_{5}
a
5
, is equal to
20
20
20
. Which number represents the common difference of the arithmetic sequence?
\newline
d
=
2
d=2
d
=
2
\newline
d
=
3
d=3
d
=
3
\newline
d
=
4
d=4
d
=
4
\newline
d
=
5
d=5
d
=
5
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In an arithmetic sequence, the first term,
a
1
a_{1}
a
1
, is equal to
4
4
4
, and the seventh term,
a
7
a_{7}
a
7
, is equal to
40
40
40
. Which number represents the common difference of the arithmetic sequence?
\newline
d
=
5
d=5
d
=
5
\newline
d
=
6
d=6
d
=
6
\newline
d
=
7
d=7
d
=
7
\newline
d
=
8
d=8
d
=
8
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In an arithmetic sequence, the first term,
a
1
a_{1}
a
1
, is equal to
5
5
5
, and the seventh term,
a
7
a_{7}
a
7
, is equal to
29
29
29
. Which number represents the common difference of the arithmetic sequence?
\newline
d
=
4
d=4
d
=
4
\newline
d
=
5
d=5
d
=
5
\newline
d
=
6
d=6
d
=
6
\newline
d
=
7
d=7
d
=
7
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In an arithmetic sequence, the first term,
a
1
a_{1}
a
1
, is equal to
9
9
9
, and the sixth term,
a
6
a_{6}
a
6
, is equal to
24
24
24
. Which number represents the common difference of the arithmetic sequence?
\newline
d
=
2
d=2
d
=
2
\newline
d
=
3
d=3
d
=
3
\newline
d
=
4
d=4
d
=
4
\newline
d
=
5
d=5
d
=
5
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In a geometric sequence, the first term,
a
1
a_{1}
a
1
, is equal to
1
1
1
, and the fourth term,
a
4
a_{4}
a
4
, is equal to
27
27
27
. Which number represents the common ratio of the geometric sequence?
\newline
r
=
1
r=1
r
=
1
\newline
r
=
2
r=2
r
=
2
\newline
r
=
3
r=3
r
=
3
\newline
r
=
4
r=4
r
=
4
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In an arithmetic sequence, the first term,
a
1
a_{1}
a
1
, is equal to
5
5
5
, and the sixth term,
a
6
a_{6}
a
6
, is equal to
30
30
30
. Which number represents the common difference of the arithmetic sequence?
\newline
d
=
4
d=4
d
=
4
\newline
d
=
5
d=5
d
=
5
\newline
d
=
6
d=6
d
=
6
\newline
d
=
7
d=7
d
=
7
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Use the initial term and the recursive formula to find an explicit formula for the sequence
a
n
a_n
a
n
. Write your answer in simplest form.
\newline
a
1
=
1
a_1 = 1
a
1
=
1
\newline
a
n
=
a
n
−
1
+
14
a_n = a_{n - 1} + 14
a
n
=
a
n
−
1
+
14
\newline
a
n
=
a_n =
a
n
=
______
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