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Math Problems
Precalculus
Find the magnitude of a three-dimensional vector
Find the distance between the points
(
7
,
10
)
(7,10)
(
7
,
10
)
and
(
7
,
6
)
(7,6)
(
7
,
6
)
.
\newline
____ units
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Find the distance between the points
(
2
,
6
)
(2,6)
(
2
,
6
)
and
(
10
,
6
)
(10,6)
(
10
,
6
)
.
\newline
_
_
_
_
\_\_\_\_
____
units
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Find the distance between the points
(
4
,
10
)
(4,10)
(
4
,
10
)
and
(
4
,
3
)
(4,3)
(
4
,
3
)
.
\newline
____ units
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Find the distance between the points
(
7
,
8
)
(7,8)
(
7
,
8
)
and
(
7
,
4
)
(7,4)
(
7
,
4
)
.
\newline
____ units
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Find the distance between the points
(
9
,
6
)
(9,6)
(
9
,
6
)
and
(
9
,
2
)
(9,2)
(
9
,
2
)
.
\newline
____ units
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Find the distance between the points
(
8
,
6
)
(8,6)
(
8
,
6
)
and
(
8
,
2
)
(8,2)
(
8
,
2
)
.
\newline
____ units
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Find the distance between the points
(
3
,
4
)
(3,4)
(
3
,
4
)
and
(
10
,
4
)
(10,4)
(
10
,
4
)
.
\newline
____ units
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Find the distance between the points
(
5
,
6
)
(5,6)
(
5
,
6
)
and
(
5
,
2
)
(5,2)
(
5
,
2
)
.
\newline
____ units
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Find the measure of the arc or central angle indicated. Assume that lines which appear to be diameters are actual diameters.
\newline
m
R
S
undefined
m \widehat{RS}
m
RS
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Determine the intersection point of diagonals of triangle
A
B
C
D
ABCD
A
BC
D
, given
A
(
−
5
,
5
)
A(-5,5)
A
(
−
5
,
5
)
,
B
(
4
,
6
)
B(4,6)
B
(
4
,
6
)
,
C
(
7
,
2
)
C(7,2)
C
(
7
,
2
)
, and
D
(
−
6
,
−
4
)
D(-6,-4)
D
(
−
6
,
−
4
)
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Exercise
2
2
2
: Check your understanding of the t-test of independent means:
\newline
1
1
1
. A physical education teacher compared the scores of boys and girls in basketball and obtained the following data: Group (Boys)
9
9
9
,
7
7
7
,
5
5
5
,
10
10
10
,
9
9
9
\newline
Group (Girls)
6
6
6
,
5
5
5
,
7
7
7
,
3
3
3
,
4
4
4
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Use the graph to determine the behavior of the function between the indicated points.
\newline
\begin{tabular}{|c|c|}
\newline
\hline Points & \begin{tabular}{l}
\newline
Behavior of the \\
\newline
function
\newline
\end{tabular} \\
\newline
\hline
A
A
A
and
B
B
B
& \begin{tabular}{l}
\newline
increasing \\
\newline
constant \\
\newline
decreasing
\newline
\end{tabular} \\
\newline
\hline
B
B
B
and
C
C
C
& \begin{tabular}{l}
\newline
increasing \\
\newline
constant \\
\newline
decreasing
\newline
\end{tabular} \\
\newline
\hline
C
C
C
and
D
D
D
& \begin{tabular}{l}
\newline
increasing \\
\newline
constant \\
\newline
decreasing
\newline
\end{tabular} \\
\newline
\hline
D
\mathrm{D}
D
and
E
\mathrm{E}
E
& \begin{tabular}{l}
\newline
increasing \\
\newline
constant \\
\newline
decreasing
\newline
\end{tabular} \\
\newline
\hline
\newline
\end{tabular}
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Determine if each statement is always, sometimes or never true. Explain your reasoni
\newline
7
7
7
. The sum of the two shortest sides of a triangle must be less than the longest side.
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Determine if each statement is always, sometimes or never true. Explain your reasoning
\newline
7
7
7
. The sum of the two shortest sides of a triangle must be less than the longest side.
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Question
\newline
Show Examples
\newline
What is the area, in square inches, of the trapezoid below?
\newline
Answer Attempt
1
1
1
out of
2
2
2
\newline
A
=
A=
A
=
\newline
□
\square
□
in
2
^{2}
2
\newline
Submit Answer
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Solve this system of equations by graphing. Graph the equations, then find the solution.
\newline
y
=
−
1
6
x
−
3
y = -\frac{1}{6}x - 3
y
=
−
6
1
x
−
3
\newline
y
=
x
+
4
y = x + 4
y
=
x
+
4
\newline
Click to select points on the graph.
\newline
\newline
The solution is (
_
,
_
\_, \_
_
,
_
).
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Solve this system of equations by graphing. Graph the equations, then find the solution.
\newline
y
=
7
4
x
−
1
y = \frac{7}{4}x - 1
y
=
4
7
x
−
1
\newline
y
=
1
2
x
+
4
y = \frac{1}{2}x + 4
y
=
2
1
x
+
4
\newline
Click to select points on the graph.
\newline
\newline
The solution is
(
_
,
_
)
(\_, \_)
(
_
,
_
)
.
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Suppose we want to choose
5
5
5
objects, without replacement, from
15
15
15
distinct objects.
\newline
(a) How many ways can this be done, if the order of the choices does not matter?
\newline
(b) How many ways can this be done, if the order of the choices matters?
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Test
\newline
2
2
2
. Find the volume of the prism.
\newline
4
4
4
. Find the surface area and volume o regular pyramid. Round your answ
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Find the area of each figure depicted or describe
\newline
1
1
1
. A triangle with a height of
10
m
10 \mathrm{~m}
10
m
and a base of
22
m
22 \mathrm{~m}
22
m
.
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Suppose that a function
f
(
x
)
f(x)
f
(
x
)
is defined for all real values of
x
x
x
except
x
=
c
x=c
x
=
c
. Can anything be said about the existence of
lim
x
→
c
f
(
x
)
\lim_{x \rightarrow c}f(x)
lim
x
→
c
f
(
x
)
? Give reasons.
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5
5
5
. The pyramids are similar.
\newline
a. Find the missing dimension.
\newline
b. Find the surface area of the red pyramid.
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(
5
5
5
) Razona la necesidad de la existencia de procesos de apoptosis en las células de un organismo pluricelular.
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Slart Over
\newline
startover
\newline
View Results
\newline
Read Explanation
\newline
Skip Questio
\newline
Question Number
7
7
7
of
20
20
20
- Geometry
\newline
Which of the following constructions is illustrated?
\newline
(E) The bisector of a given angle
\newline
(G) The perpendicular bisector of a given segment
\newline
[
1
1
1
] The bisector of a given segment
\newline
(
1
1
1
) An angle congruent to a given angle
\newline
That's My Final Answer!
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14
14
14
) The line graph below shows the temperature in a city over a week. Whatwas the temperature on Wednesday?
\newline
(a)
0
0
0
.
5
5
5
\newline
(c)
1
1
1
.
25
25
25
\newline
(b)
1
1
1
\newline
(d)
1
1
1
.
5
5
5
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Find the center and radius of a circle in steps with answer being center being
(
8
,
0
)
(8, 0)
(
8
,
0
)
and radius
(
2
3
)
(2 \sqrt{3})
(
2
3
)
the problem is
(
x
−
8
)
2
+
y
2
=
12
(x-8)^2+y^2=12
(
x
−
8
)
2
+
y
2
=
12
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Find the distance between the two points.
\newline
(
8
,
−
8
)
(8,-8)
(
8
,
−
8
)
and
(
−
5.2
,
−
8
)
(-5.2,-8)
(
−
5.2
,
−
8
)
\newline
Write an optional reasoning for your answer:
\newline
7
7
7
\newline
A
A
A
\newline
B
B
B
\newline
I
I
I
\newline
Q
(
0
)
Q_{(0)}
Q
(
0
)
\newline
s
s
s
\newline
(
2
)
(2)
(
2
)
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Find the distance between the two points.
\newline
(
8
,
−
8
)
and
(
−
5.2
,
−
8
)
(8,-8) \text { and }(-5.2,-8)
(
8
,
−
8
)
and
(
−
5.2
,
−
8
)
\newline
Answer:
\newline
Write an optional reasoning for your answer:
\newline
7
7
7
\newline
A
\newline
B
\newline
I
\newline
Q
0
Q_{0}
Q
0
\newline
sis
\newline
(
2
2
2
)
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In the diagram below,
Q
R
‾
\overline{Q R}
QR
is parallel to
N
O
‾
\overline{N O}
NO
. If
Q
R
=
30
,
P
O
=
28
Q R=30, P O=28
QR
=
30
,
PO
=
28
, and
P
R
=
20
P R=20
PR
=
20
, find the length of
N
O
‾
\overline{N O}
NO
. Figures are not necessarily drawn to scale.
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id the perimeter, area, a
\newline
Find the perimeter
&
\&
&
area:
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Find the area of
\newline
the curved trapezoid bounded by the lines
y
=
3
x
+
6
y=3x+6
y
=
3
x
+
6
,
y
=
0
y=0
y
=
0
,
x
=
−
1
x=-1
x
=
−
1
,
x
=
2
x=2
x
=
2
.
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7
7
7
. Is there enough information in the diagram below to determine whether the polygons are similar? If so, explain why, write a similarity statement, and find the scale factor. If not, explain your reasoning. (
4
4
4
pts)
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(
3
3
3
) Determine the value of
x
x
x
so that the square and the rectangle shown have equal perimeters
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cavenger Hunt
\newline
Name
\newline
Task
\newline
Type
(
4
5
)
2
\left(4^{5)^{2}}\right.
(
4
5
)
2
into the calculator.
\newline
Which does it match?
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Chapter
\newline
10
10
10
\newline
Test A
\newline
You randomly choose one shape from the bag. (a) Find the number of ways the event can occur.
\newline
(b) Find the favorable outcomes of the event.
\newline
1
1
1
. Choosing a square
\newline
2
2
2
. Choosing a circle
\newline
3
3
3
. Not choosing a star
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Assume
A
A
A
is located at
(
2
,
4
)
,
B
(2,4), B
(
2
,
4
)
,
B
is located at
(
5
,
1
)
(5,1)
(
5
,
1
)
and James is travelling from
A
A
A
to
B
B
B
with a constant speed of
1
m
/
s
1 \mathrm{~m} / \mathrm{s}
1
m
/
s
. The point
C
C
C
represents his position at some point in time during the trip.
\newline
(a) (
2
2
2
marks) Calculate the location of
C
C
C
after he travelled for
3
3
3
seconds.
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Solve the following equation for
x
x
x
. Express your answer in the simplest form.
\newline
5
x
+
1
2
(
6
x
−
10
)
=
−
(
−
8
x
+
4
)
−
1
5 x+\frac{1}{2}(6 x-10)=-(-8 x+4)-1
5
x
+
2
1
(
6
x
−
10
)
=
−
(
−
8
x
+
4
)
−
1
\newline
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Find the area
(
A
)
(A)
(
A
)
and perimeter
(
P
)
(P)
(
P
)
of the enclosed figures.
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nd the area of each composite figur rectar
\newline
it into two figures**
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Consider a parallel-plate capacitor with capacitance
C
C
C
, what happens when we double the separation between the plates and halve the area of each plate?
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(iv)
3
×
1000000
+
4
×
100000
+
6
×
1000
+
5
×
100
+
7
×
1
3 \times 1000000+4 \times 100000+6 \times 1000+5 \times 100+7 \times 1
3
×
1000000
+
4
×
100000
+
6
×
1000
+
5
×
100
+
7
×
1
\newline
Find the difference between the place values of the two nines in
79520986
79520986
79520986
.
\newline
Find the difference between the place value and the face value of
7
7
7
in
27650934
27650934
27650934
.
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(a) Find the coordinates of points
A
,
B
,
C
A, B, C
A
,
B
,
C
.
\newline
(b) Find the equations of lines
A
B
,
B
C
A B, B C
A
B
,
BC
, and
A
C
A C
A
C
in the diagram.
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Complete the equation of the line through
(
3
,
−
8
)
(3,-8)
(
3
,
−
8
)
and
(
6
,
−
4
)
(6,-4)
(
6
,
−
4
)
.
\newline
Use exact numbers.
\newline
y
=
y=
y
=
\newline
□
\square
□
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Find the slope of the line containing the points
(
6
,
−
5
)
(6,-5)
(
6
,
−
5
)
and
(
−
8
,
8
)
(-8,8)
(
−
8
,
8
)
.
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What is the total number of different
10
10
10
-letter arrangements that can be formed using the letters in the word STATISTICS?
\newline
Answer:
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Reflect
(
−
7
,
−
6
)
(-7,-6)
(
−
7
,
−
6
)
across the
y
y
y
-axis.
\newline
Then reflect the result across the
x
x
x
-axis.
\newline
What are the coordinates of the final point?
\newline
(___ , ___)
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Evaluate the expression.
\newline
5
729
3
−
24
=
_
_
_
_
_
5 \sqrt[3]{729}-24= \_\_\_\_\_
5
3
729
−
24
=
_____
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Part
3
3
3
-Algebra Practice. Directions: Multiply the binomials
\newline
21
21
21
) a)
(
x
−
4
)
(
x
+
9
)
(x-4)(x+9)
(
x
−
4
)
(
x
+
9
)
\newline
In Exercises
14
14
14
and
15
15
15
, find the length of
A
B
‾
\overline{A B}
A
B
.
\newline
14
14
14
.
\newline
15
15
15
.
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The coordinates of the point
E
E
E
are
(
1
,
4
)
(1,4)
(
1
,
4
)
and the coordinates of point
F
F
F
are
(
1
,
−
5
)
(1,-5)
(
1
,
−
5
)
. What is the distance, in units, between the point
E
E
E
and point
F
F
F
?
\newline
Answer:
□
\square
□
units
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The questions below are posed in order to help you think about how to find the number of degrees in
π
6
\frac{\pi}{6}
6
π
radians.
\newline
What fraction of a semicircle is an angle that measures
π
6
\frac{\pi}{6}
6
π
radians? Express your answer as a fraction in simplest terms.
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1
2
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