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Geometry
Sine and cosine of complementary angles
Select the expressions that are equivalent to
4
h
+
5
h
4h + 5h
4
h
+
5
h
.
\newline
Multi-select Choices:
\newline
(A)
3
h
+
7
h
3h + 7h
3
h
+
7
h
\newline
(B)
h
×
9
h \times 9
h
×
9
\newline
(C)
h
+
9
h + 9
h
+
9
\newline
(D)
9
h
9h
9
h
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Calculate the following:
\newline
8
+
3
×
2
=
10
−
6
÷
2
=
\begin{array}{l} 8+3 \times 2= \\ 10-6 \div 2= \end{array}
8
+
3
×
2
=
10
−
6
÷
2
=
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Solve for
c
c
c
.
\newline
2
c
−
2
=
4
c
=
\begin{array}{l} 2 c-2=4 \\ c= \end{array}
2
c
−
2
=
4
c
=
\newline
Submit
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Solve for
h
h
h
.
\newline
15.3
+
1
h
=
1.3
−
1
h
h
=
\begin{array}{l} 15.3+1 h=1.3-1 h \\ h= \end{array}
15.3
+
1
h
=
1.3
−
1
h
h
=
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\newline
−
5
x
+
y
=
6
−
10
x
+
8
y
=
18
\begin{array}{l} -5 x+y=6 \\ -10 x+8 y=18 \end{array}
−
5
x
+
y
=
6
−
10
x
+
8
y
=
18
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Solve for
x
,
y
x, y
x
,
y
, and
z
z
z
\newline
x
+
6
y
−
z
=
−
5
−
2
x
−
5
y
+
2
z
=
3
x
−
4
5
y
+
z
=
19
5
\begin{array}{l} x+6 y-z=-5 \\ -2 x-5 y+2 z=3 \\ x-\frac{4}{5} y+z=\frac{19}{5} \end{array}
x
+
6
y
−
z
=
−
5
−
2
x
−
5
y
+
2
z
=
3
x
−
5
4
y
+
z
=
5
19
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The homework for English class was to write a poem. The teacher wants to ask
4
4
4
students,
2
2
2
boys and
2
2
2
sirls, to read their poems for the class. If there are
10
10
10
boys and
15
15
15
girls, how many different combinations of
2
2
2
boys and
2
2
2
girls can the teacher select?
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Solve the system.
\newline
{
x
+
3
y
−
z
=
−
6
−
2
x
−
y
+
z
=
10
x
−
y
+
3
z
=
2
\begin{cases} x+3y-z&=-6 \ -2x-y+z&=10 \ x-y+3z&=2 \end{cases}
{
x
+
3
y
−
z
=
−
6
−
2
x
−
y
+
z
=
10
x
−
y
+
3
z
=
2
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For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).
\newline
4
x
−
1
,
3
x
−
1
,
2
x
−
1
,
..
4 x-1, \quad 3 x-1, \quad 2 x-1, \quad \text {.. }
4
x
−
1
,
3
x
−
1
,
2
x
−
1
,
..
\newline
1
1
1
\newline
−
x
-x
−
x
\newline
x
x
x
\newline
−
1
-1
−
1
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For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).
\newline
7
,
−
35
,
175
,
…
7,-35,175, \ldots
7
,
−
35
,
175
,
…
\newline
−
5
-5
−
5
\newline
−
42
-42
−
42
\newline
−
1
5
-\frac{1}{5}
−
5
1
\newline
42
42
42
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Solve the system:
\newline
x
+
6
y
=
17
−
x
+
3
y
=
−
8
\begin{array}{c} x+6 y=17 \\ -x+3 y=-8 \end{array}
x
+
6
y
=
17
−
x
+
3
y
=
−
8
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Click and drag like terms onto each other to simplify fully.
\newline
−
1
−
4
y
3
−
2
x
3
+
5
x
+
2
−
7
−
x
3
-1-4 y^{3}-2 x^{3}+5 x+2-7-x^{3}
−
1
−
4
y
3
−
2
x
3
+
5
x
+
2
−
7
−
x
3
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Click and drag like terms onto each other to simplify fully.
\newline
1
−
6
y
+
5
+
6
x
−
5
x
+
4
1-6 y+5+6 x-5 x+4
1
−
6
y
+
5
+
6
x
−
5
x
+
4
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Jack, Tom, Beth, and Ruth each have a number of marbles. Jack has
10
10
10
marbles, the least, while Tom has
27
27
27
marbles, the highest. Which of the following could be the average of the number of marbles present with all of them, given that no two of them has the same number of marbles?
\newline
A
)
$
13
A)\ \$13
A
)
$13
\newline
B
)
$
17
B)\ \$17
B
)
$17
\newline
C
)
$
23
C)\ \$23
C
)
$23
\newline
D
)
$
26
D)\ \$26
D
)
$26
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In an election between two candidates Joseph and Judith,
60
%
60\%
60%
of the total number of voters did not vote for Joseph and
50
%
50\%
50%
of the total number of voters did not vote for Judith. If it is known that each voter can vote for only one candidate, what percentage of voters did not cast their votes? [With calculator]
\newline
(A)
5
5
5
\newline
(B)
10
10
10
\newline
(C)
20
20
20
\newline
(D)
30
30
30
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Factor
28
+
56
t
+
28
w
28+56 t+28 w
28
+
56
t
+
28
w
to identify the equivalent expressions.
\newline
Choose
2
2
2
answers:
\newline
A
2
(
56
+
112
t
+
56
w
)
2(56+112 t+56 w)
2
(
56
+
112
t
+
56
w
)
\newline
B
28
(
1
+
2
t
+
w
)
28(1+2 t+w)
28
(
1
+
2
t
+
w
)
\newline
c
4
(
7
+
13
t
+
7
w
)
4(7+13 t+7 w)
4
(
7
+
13
t
+
7
w
)
\newline
D
7
(
4
+
8
t
+
4
w
)
7(4+8 t+4 w)
7
(
4
+
8
t
+
4
w
)
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Which is equal to
sin
7
5
∘
\sin 75^\circ
sin
7
5
∘
?
\newline
Choices:
\newline
(A)
cos
2
5
∘
\cos 25^\circ
cos
2
5
∘
\newline
(B)
cos
1
5
∘
\cos 15^\circ
cos
1
5
∘
\newline
(C)
sin
2
5
∘
\sin 25^\circ
sin
2
5
∘
\newline
(D)
sin
1
5
∘
\sin 15^\circ
sin
1
5
∘
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