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Math Problems
Algebra 2
Identify properties of logarithms
Trigonometric Identities and Equations
\newline
Sum and difference identities: Problem type
1
1
1
: Degrees
\newline
Find the exact value of
\newline
cos
10
5
∘
\cos 105^\circ
cos
10
5
∘
by using a sum or difference formula.
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When solving an equation, Gabrielle's first step is shown below. Which property justifies Gabrielle's first step?
\newline
Original Equation:
\newline
2
(
x
+
1
)
=
4
2(x+1)=4
2
(
x
+
1
)
=
4
\newline
First Step:
\newline
2
x
+
2
=
4
2 x+2=4
2
x
+
2
=
4
\newline
addition property of equality
\newline
associative property of multiplication
\newline
distributive property of multiplication over addition
\newline
commutative property of addition
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When solving an equation, Gabrielle's first step is shown below. Which property justifies Gabrielle's first step?
\newline
Original Equation:
\newline
−
x
−
4
=
−
4
-x-4=-4
−
x
−
4
=
−
4
\newline
First Step:
\newline
−
x
=
0
-x=0
−
x
=
0
\newline
distributive property of multiplication over addition
\newline
associative property of multiplication
\newline
addition property of equality
\newline
commutative property of multiplication
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When solving an equation, Francesca's first step is shown below. Which property justifies Francesca's first step?
\newline
Original Equation:
\newline
−
2
x
=
−
10
-2 x=-10
−
2
x
=
−
10
\newline
First Step:
\newline
x
=
5
x=5
x
=
5
\newline
addition property of equality
\newline
commutative property of addition
\newline
associative property of addition
\newline
division property of equality
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When solving an equation, Gabrielle's first step is shown below. Which property justifies Gabrielle's first step?
\newline
Original Equation:
\newline
−
5
x
=
−
20
-5 x=-20
−
5
x
=
−
20
\newline
First Step:
\newline
x
=
4
x=4
x
=
4
\newline
subtraction property of equality
\newline
division property of equality
\newline
associative property of multiplication
\newline
associative property of addition
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When solving an equation, Francesca's first step is shown below. Which property justifies Francesca's first step?
\newline
Original Equation:
\newline
x
+
4
=
−
2
x+4=-2
x
+
4
=
−
2
\newline
First Step:
\newline
x
=
−
6
x=-6
x
=
−
6
\newline
multiplication property of equality
\newline
division property of equality
\newline
commutative property of addition
\newline
subtraction property of equality
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When solving an equation, Carmen's first step is shown below. Which property justifies Carmen's first step?
\newline
Original Equation:
\newline
−
1
4
x
=
1
-\frac{1}{4} x=1
−
4
1
x
=
1
\newline
First Step:
\newline
x
=
−
4
x=-4
x
=
−
4
\newline
commutative property of addition
\newline
associative property of multiplication
\newline
multiplication property of equality
\newline
distributive property of multiplication over addition
Get tutor help
When solving an equation, Gabrielle's first step is shown below. Which property justifies Gabrielle's first step?
\newline
Original Equation:
\newline
−
3
x
−
4
=
−
1
-3 x-4=-1
−
3
x
−
4
=
−
1
\newline
First Step:
\newline
−
3
x
=
3
-3 x=3
−
3
x
=
3
\newline
addition property of equality
\newline
distributive property of multiplication over addition
\newline
commutative property of multiplication
\newline
multiplication property of equality
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When solving an equation, Gabrielle's first step is shown below. Which property justifies Gabrielle's first step?
\newline
Original Equation:
\newline
1
3
x
=
3
\frac{1}{3} x=3
3
1
x
=
3
\newline
First Step:
\newline
x
=
9
x=9
x
=
9
\newline
addition property of equality
\newline
multiplication property of equality
\newline
commutative property of multiplication
\newline
subtraction property of equality
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When solving an equation, Drew's first step is shown below. Which property justifies Drew's first step?
\newline
Original Equation:
\newline
−
4
x
+
x
2
+
5
=
0
-4 x+x^{2}+5=0
−
4
x
+
x
2
+
5
=
0
\newline
First Step:
\newline
x
2
−
4
x
+
5
=
0
x^{2}-4 x+5=0
x
2
−
4
x
+
5
=
0
\newline
commutative property of addition
\newline
distributive property of multiplication over addition
\newline
associative property of multiplication
\newline
addition property of equality
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Which of the following functions are continuous for all real numbers?
\newline
h
(
x
)
=
log
(
x
)
h(x)=\log (x)
h
(
x
)
=
lo
g
(
x
)
\newline
g
(
x
)
=
cot
(
x
)
g(x)=\cot (x)
g
(
x
)
=
cot
(
x
)
\newline
Choose
1
1
1
answer:
\newline
(A)
h
h
h
only
\newline
(B)
g
g
g
only
\newline
(C) Both
h
h
h
and
g
g
g
\newline
(D) Neither
h
h
h
nor
g
g
g
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Which property of logarithms does this equation demonstrate?
\newline
log
3
3
+
log
3
6
=
log
3
18
\log_3 3 + \log_3 6 = \log_3 18
lo
g
3
3
+
lo
g
3
6
=
lo
g
3
18
\newline
Choices:
\newline
(A)
Product Property
\text{Product Property}
Product Property
\newline
(B)
Power Property
\text{Power Property}
Power Property
\newline
(C)
Quotient Property
\text{Quotient Property}
Quotient Property
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