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Math Problems
Algebra 1
Convert an explicit formula to a recursive formula
3
x
2
+
a
x
−
5
=
0
3x^{2}+ax-5=0
3
x
2
+
a
x
−
5
=
0
\newline
In the given equation,
a
a
a
is a constant. If the equation has the solutions
x
=
−
5
x=-5
x
=
−
5
and
\newline
x
=
1
3
x=\frac{1}{3}
x
=
3
1
, what is the value of
a
a
a
?
\newline
◻
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The graph of a sinusoidal function has a maximum point at
(
0
,
7
)
(0,7)
(
0
,
7
)
and then intersects its midline at
(
3
,
3
)
(3,3)
(
3
,
3
)
.
\newline
Write the formula of the function, where
x
x
x
is entered in radians.
\newline
f
(
x
)
=
f(x)=
f
(
x
)
=
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A function is invertible if it is
\newline
a) surjective
\newline
b) bijective
\newline
c) injective
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Which of the following are true statements about the expression
6
+
(
−
6
)
?
6+(-6) ?
6
+
(
−
6
)?
\newline
Choose
2
2
2
answers:
\newline
(A) The expression describes the number that is
6
6
6
to the left of
6
6
6
on the number line.
\newline
(B) The expression describes the number that is
6
6
6
to the right of
6
6
6
on the number line.
\newline
(C) The expression equals
0
0
0
.
\newline
(D) The expression equals
12
12
12
.
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Which of the following are true statements about the expression
7
−
(
−
7
)
?
7-(-7) ?
7
−
(
−
7
)?
\newline
Choose
2
2
2
answers:
\newline
(A) The expression describes the number that is
7
7
7
to the left of
7
7
7
on the number line.
\newline
(B) The expression describes the number that is
7
7
7
to the right of
7
7
7
on the number line.
\newline
(C) The expression equals
0
0
0
.
\newline
(D) The expression equals
14
14
14
.
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Which of the following are true statements about the expression
7
+
(
−
7
)
?
7+(-7) ?
7
+
(
−
7
)?
\newline
Choose
2
2
2
answers:
\newline
(A) The expression describes the number that is
7
7
7
to the left of
7
7
7
on the number line.
\newline
(B) The expression describes the number that is
7
7
7
to the right of
7
7
7
on the number line.
\newline
(C) The expression equals
0
0
0
.
\newline
(D) The expression equals
14
14
14
.
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Which of the following are true statements about the expression
5
+
(
−
5
)
?
5+(-5) ?
5
+
(
−
5
)?
\newline
Choose
2
2
2
answers:
\newline
(A) The expression describes the number that is
5
5
5
to the left of
5
5
5
on the number line.
\newline
(B) The expression describes the number that is
5
5
5
to the right of
5
5
5
on the number line.
\newline
(C) The expression equals
0
0
0
.
\newline
(D) The expression equals
10
10
10
.
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Which of the following are true statements about the expression
6
−
(
−
6
)
?
6-(-6) ?
6
−
(
−
6
)?
\newline
Choose
2
2
2
answers:
\newline
(A) The expression describes the number that is
6
6
6
to the left of
6
6
6
on the number line.
\newline
(B) The expression describes the number that is
6
6
6
to the right of
6
6
6
on the number line.
\newline
(C) The expression equals
0
0
0
.
\newline
(D) The expression equals
12
12
12
.
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The expression
1
2
b
h
\frac{1}{2} b h
2
1
bh
gives the area of a triangle where
b
b
b
is the base of the triangle and
h
h
h
is the height of the triangle.
\newline
What is the area of a triangle with a base of
7
c
m
7 \mathrm{~cm}
7
cm
and a height of
4
c
m
4 \mathrm{~cm}
4
cm
?
\newline
c
m
2
\mathrm{cm}^{2}
cm
2
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Consider the expression
1
2
b
h
\frac{1}{2} b h
2
1
bh
.
\newline
Complete
2
2
2
descriptions of the parts of the expression.
\newline
1
1
1
. The entire expression is the product of
□
\square
□
.
\newline
2
2
2
. In this context,
1
2
\frac{1}{2}
2
1
is a
□
\square
□
.
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What happens to the value of the expression
2
t
t
\frac{2 t}{t}
t
2
t
as
t
t
t
decreases?
\newline
Choose
1
1
1
answer:
\newline
(A) It increases.
\newline
(B) It decreases.
\newline
(C) It stays the same.
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w
=
6
+
3
x
y
75
w=6+\frac{3 x y}{75}
w
=
6
+
75
3
x
y
\newline
The equation gives the quantity
w
w
w
in terms of the quantities
x
x
x
and
y
y
y
. Which of the following equations correctly expresses
y
y
y
in terms of
w
w
w
and
x
x
x
?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
25
w
x
−
6
y=\frac{25 w}{x}-6
y
=
x
25
w
−
6
\newline
(B)
y
=
25
w
+
150
x
y=\frac{25 w+150}{x}
y
=
x
25
w
+
150
\newline
(C)
y
=
25
w
−
150
x
y=\frac{25 w-150}{x}
y
=
x
25
w
−
150
\newline
(D)
y
=
25
w
−
2
x
y=\frac{25 w-2}{x}
y
=
x
25
w
−
2
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If
j
k
=
4
5
\frac{j}{k}=\frac{4}{5}
k
j
=
5
4
, which of the following correctly expresses
k
k
k
in terms of
j
j
j
?
\newline
Choose
1
1
1
answer:
\newline
(A)
k
=
4
5
j
k=\frac{4}{5 j}
k
=
5
j
4
\newline
(B)
k
=
5
4
j
k=\frac{5}{4 j}
k
=
4
j
5
\newline
(C)
k
=
4
j
5
k=\frac{4 j}{5}
k
=
5
4
j
\newline
(D)
k
=
5
j
4
k=\frac{5 j}{4}
k
=
4
5
j
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If
6
p
t
=
11
\frac{6}{p t}=11
pt
6
=
11
, which of the following correctly expresses
p
p
p
in terms of
t
t
t
?
\newline
Choose
1
1
1
answer:
\newline
(A)
p
=
6
t
11
p=\frac{6 t}{11}
p
=
11
6
t
\newline
(B)
p
=
66
t
p=\frac{66}{t}
p
=
t
66
\newline
(C)
p
=
11
6
t
p=\frac{11}{6 t}
p
=
6
t
11
\newline
(D)
p
=
6
11
t
p=\frac{6}{11 t}
p
=
11
t
6
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Use the explicit formula to find a recursive formula for the sequence
a
n
a_n
a
n
. Write your answer in simplest form.
\newline
The recursive formula should depend on
a
n
−
1
a_{n - 1}
a
n
−
1
.
\newline
a
n
=
14
n
−
23
a_n = 14n - 23
a
n
=
14
n
−
23
\newline
a
n
=
a_n =
a
n
=
______
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