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Math Problems
Grade 6
Which word problem matches the one-step equation?
Consider the following system of equations,
\newline
−
2
x
−
9
y
=
12
−
2
x
−
7
y
=
8
\begin{array}{l} -2 \mathrm{x}-9 \mathrm{y}=12 \\ -2 \mathrm{x}-7 \mathrm{y}=8 \end{array}
−
2
x
−
9
y
=
12
−
2
x
−
7
y
=
8
\newline
The value of
x
x
x
is
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near functions:
C
\mathrm{C}
C
\newline
a
−
1
-1
−
1
-fl-best/x
91
91
91
c
6
6
6
a
5
5
5
a
4
4
4
a
9698230
9698230
9698230
:analyzing-linear-functions/x
91
91
91
c
6
6
6
a
5
5
5
a
4
4
4
a
9698230
9698230
9698230
:using-slope-...
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4599328675
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Google Classroom
\newline
Graph a line that contains the point
(
3
,
−
6
)
(3,-6)
(
3
,
−
6
)
and has a slope of
−
1
2
-\frac{1}{2}
−
2
1
.
\newline
Do
6
6
6
problems
\newline
。
\newline
Skip
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Q
3
3
3
A. Consider the Control Process \begin{pmatrix}x\ y\ z\end{pmatrix}^' = \begin{pmatrix}0 & 1 & 0\ 0 & 0 & 1\ -2 & -4 & 1\end{pmatrix}\begin{pmatrix}x\ y\ z\end{pmatrix} + \begin{pmatrix}1 & 0\ 0 & 1\ -1 & 1\end{pmatrix}\begin{pmatrix}u_1\left(t\right)\ u_2\left(t\right)\end{pmatrix}. Is this system globally null controllable? Q
3
3
3
B. Is this system in Q
3
3
3
A globally null controllable under the additional contraint
∣
∣
(
u
1
(
t
)
u
2
(
t
)
)
∣
∣
≤
2
||\begin{pmatrix}u_1\left(t\right)\ u_2\left(t\right)\end{pmatrix}|| \le 2
∣∣
(
u
1
(
t
)
u
2
(
t
)
)
∣∣
≤
2
? Use Analysis to solve the question completely
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The painting shown at the right has an area of
360
i
n
2
360 \mathrm{in}^{2}
360
in
2
. What is the value of
x
x
x
?
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MCR
3
3
3
U - OPTIONAL ASSIGNMENT
\newline
Part A : choose one
\newline
1
1
1
. A culture has
570
570
570
bacteria. The number of bacteria doubles every
12
h
12 \mathrm{~h}
12
h
. How long will it take to have
2152
2152
2152
bacteria in the culture?
\newline
2
x
2
−
3
x
2 x^{2}-3 x
2
x
2
−
3
x
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A student solved the equation
x
2
=
123
x^{2}=123
x
2
=
123
to find the length of the diagonal of a square in inches. What is the measurement of
x
x
x
, the length of the diagonal of the square, rounded to the nearest tenth?
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7
7
7
. A certain amount of money is shared between Rui Feng and Vishal in the ratio
5
:
9
5: 9
5
:
9
. If Rui Feng gets
$
44
\$ 44
$44
less than Vishal, find the total amount of money that is shared between the two boys.
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Get ready for equations Unit test
\newline
Let
p
=
x
2
−
2
p=x^{2}-2
p
=
x
2
−
2
.
\newline
Which equation is equivalent to
(
x
2
−
2
)
2
+
18
=
9
x
2
−
18
\left(x^{2}-2\right)^{2}+18=9 x^{2}-18
(
x
2
−
2
)
2
+
18
=
9
x
2
−
18
in terms of
p
p
p
?
\newline
Choose
1
1
1
answer:
\newline
(a)
p
2
+
9
p
+
36
=
0
p^{2}+9 p+36=0
p
2
+
9
p
+
36
=
0
\newline
()
p
2
+
9
p
+
18
=
0
p^{2}+9 p+18=0
p
2
+
9
p
+
18
=
0
\newline
(c)
p
2
−
9
p
+
36
=
0
p^{2}-9 p+36=0
p
2
−
9
p
+
36
=
0
\newline
(C)
p
2
−
9
p
+
18
=
0
p^{2}-9 p+18=0
p
2
−
9
p
+
18
=
0
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Solve the following:
\newline
a. Mr. Doers is going to remove all of the ceramic tiles in his kitchen in order to replace them with new ones. There are
18
18
18
tiles along the width of the kitchen and
21
21
21
tiles along the length. How many tiles will he have to remove?
\newline
b. The kitchen floor is
168
168
168
square feet. New ceramic tiles will cost
$
7.50
\$ 7.50
$7.50
per square foot. How much will it cost to replace the kitchen floor?
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The circle has center
O
O
O
, and the central angle of the shaded sector measures
18
0
∘
180^{\circ}
18
0
∘
. The area of the shaded sector is what fraction of the area of the circle?
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Without dividing, determine if
10
10
10
,
769
769
769
is divisible by
9
9
9
and explain how you know.
\newline
10
,
769
□
10,769 \square
10
,
769
□
divisible by
9
9
9
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if
a
π
a \pi
aπ
radians is equal to
900
900
900
degrees, what is the value of
a
a
a
? (The number of degrees of arc in a circle is
360
360
360
. The number of radians of arc in a circle is
2
π
2 \pi
2
π
.)
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m
+
p
=
23
m
−
7
=
p
\begin{array}{l} m+p=23 \\ m-7=p \end{array}
m
+
p
=
23
m
−
7
=
p
\newline
The given system of equations relates
m
m
m
, the number of shirts Mara owns, and
p
p
p
, the number of shirts Phil owns. Which of the following is the best interpretation of the number
7
7
7
in the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Mara owns
7
7
7
more shirts than Phil does.
\newline
(B) Phil owns
7
7
7
more shirts than Mara does.
\newline
(C) Mara owns
7
7
7
shirts.
\newline
(D) Phil owns
7
7
7
shirts.
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The sum of two consecutive odd numbers is
2012
2012
2012
. What is the larger number?
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\begin{cases} m+p=23 \\\newline m-7=p \end{cases}
\newline
The given system of equations relates
m
m
m
, the number of shirts Mara owns, and
p
p
p
, the number of shirts Phil owns.
\newline
Which of the following is the best interpretation of the number
7
7
7
in the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Mara owns
7
7
7
more shirts than Phil does.
\newline
(B) Phil owns
7
7
7
more shirts than Mara does.
\newline
(C) Mara owns
7
7
7
shirts.
\newline
(D) Phil owns
7
7
7
shirts.
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Mara is
m
m
m
years old, and her younger brother Kyle is
k
k
k
years old. If Mara is
3
3
3
years older than Kyle, which of the following correctly expresses
k
k
k
in terms of
m
m
m
? Choose
1
1
1
answer:
\newline
(A)
k
=
m
+
3
k=m+3
k
=
m
+
3
\newline
(B)
k
=
m
−
3
k=m-3
k
=
m
−
3
\newline
(C)
k
=
3
m
k=3m
k
=
3
m
\newline
(D)
k
=
3
−
m
k=3-m
k
=
3
−
m
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Question
\newline
Watch Vi
\newline
Find all vertical asymptotes of the following function.
\newline
f
(
x
)
=
2
x
+
10
x
2
−
16
f(x)=\frac{2 x+10}{x^{2}-16}
f
(
x
)
=
x
2
−
16
2
x
+
10
\newline
Answer Attempt
1
1
1
out of
3
3
3
\newline
No Vertical Asymptotes
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m
+
p
=
23
m+p=23
m
+
p
=
23
\newline
m
−
7
=
p
m-7=p
m
−
7
=
p
\newline
The given system of equations relates
m
m
m
, the number of shirts Mara owns, and
p
p
p
, the number of shirts Phil owns. Which of the following is the best interpretation of the number
7
7
7
in the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Mara owns
7
7
7
more shirts than Phil does.
\newline
(B) Phil owns
7
7
7
more shirts than Mara does.
\newline
(C) Mara owns
7
7
7
shirts.
\newline
(D) Phil owns
7
7
7
shirts.
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