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Math Problems
Precalculus
Find the magnitude of a three-dimensional vector
Complete the equation of the line through
(
−
8
,
8
)
(-8, 8)
(
−
8
,
8
)
and
(
1
,
−
10
)
(1, -10)
(
1
,
−
10
)
.
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Find the distance between the points
(
3
,
6
)
(3,6)
(
3
,
6
)
and
(
3
,
2
)
(3,2)
(
3
,
2
)
.
\newline
____ units
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Find the distance between the points
(
2
,
5
)
(2,5)
(
2
,
5
)
and
(
10
,
5
)
(10,5)
(
10
,
5
)
.
\newline
____ units
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Find the distance between the points
(
7
,
10
)
(7,10)
(
7
,
10
)
and
(
7
,
2
)
(7,2)
(
7
,
2
)
.
\newline
____ units
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Find the distance between the points
(
2
,
4
)
(2,4)
(
2
,
4
)
and
(
10
,
4
)
(10,4)
(
10
,
4
)
.
\newline
____ units
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Find the distance between the points
(
3
,
10
)
(3,10)
(
3
,
10
)
and
(
3
,
2
)
(3,2)
(
3
,
2
)
.
\newline
_
_
_
_
\_\_\_\_
____
units
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Find the distance between the points
(
4
,
7
)
(4,7)
(
4
,
7
)
and
(
10
,
7
)
(10,7)
(
10
,
7
)
.
\newline
____ units
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Find the distance between the points
(
4
,
9
)
(4,9)
(
4
,
9
)
and
(
4
,
2
)
(4,2)
(
4
,
2
)
.
\newline
____ units
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Find the distance between the points
(
2
,
7
)
(2,7)
(
2
,
7
)
and
(
8
,
7
)
(8,7)
(
8
,
7
)
.
\newline
____ units
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Find the distance between the points
(
5
,
10
)
(5,10)
(
5
,
10
)
and
(
5
,
2
)
(5,2)
(
5
,
2
)
.
\newline
____ units
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Find the distance between the points
(
2
,
3
)
(2,3)
(
2
,
3
)
and
(
10
,
3
)
(10,3)
(
10
,
3
)
.
\newline
____ units
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Find the distance between the points
(
6
,
9
)
(6,9)
(
6
,
9
)
and
(
6
,
2
)
(6,2)
(
6
,
2
)
.
\newline
_
_
_
_
\_\_\_\_
____
units
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Pick the story that can be modeled by the equation
11
+
x
=
22
11 + x = 22
11
+
x
=
22
.
\newline
Choices:
\newline
(A)Last weekend, Roger biked
11
11
11
miles on Saturday and
x
x
x
times as many miles on Sunday. He biked
22
22
22
miles on Sunday.
\newline
(B)Over the weekend, Roger biked
22
22
22
miles in all. He biked
11
11
11
miles on Saturday and
x
x
x
miles on Sunday.
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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
(
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
(
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
(
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
(
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
(
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
(
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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Determine if each statement is always, sometimes or never true. Explain your reasoning
\newline
The sum of the two shortest sides of a triangle must be less than the longest side.
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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 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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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
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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 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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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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The questions below are posed in order to help you think about how to find the number of degrees in
13
π
18
\frac{13 \pi}{18}
18
13
π
radians.
\newline
What fraction of a semicircle is an angle that measures
13
π
18
\frac{13 \pi}{18}
18
13
π
radians? Express your answer as a fraction in simplest terms.
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The area of a parallelogram is
20
20
20
, and the lengths of its sides are
4
4
4
.
6
6
6
and
9
9
9
.
1
1
1
. Determine, to the nearest tenth of a degree, the measure of the obtuse angle of the parallelogram.
\newline
Answer:
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The area of a parallelogram is
18
18
18
, and the lengths of its sides are
9
9
9
.
2
2
2
and
2
2
2
. Determine, to the nearest tenth of a degree, the measure of the acute angle of the parallelogram.
\newline
Answer:
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The area of a parallelogram is
3
3
3
, and the lengths of its sides are
1
1
1
.
1
1
1
and
4
4
4
.
8
8
8
. Determine, to the nearest tenth of a degree, the measure of the obtuse angle of the parallelogram.
\newline
Answer:
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The area of a parallelogram is
11
11
11
, and the lengths of its sides are
9
9
9
.
6
6
6
and
2
2
2
.
7
7
7
. Determine, to the nearest tenth of a degree, the measure of the obtuse angle of the parallelogram.
\newline
Answer:
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The area of a parallelogram is
22
22
22
, and the lengths of its sides are
8
8
8
.
8
8
8
and
4
4
4
.
6
6
6
. Determine, to the nearest tenth of a degree, the measure of the obtuse angle of the parallelogram.
\newline
Answer:
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The area of a parallelogram is
13
13
13
, and the lengths of its sides are
3
3
3
.
6
6
6
and
5
5
5
.
6
6
6
. Determine, to the nearest tenth of a degree, the measure of the acute angle of the parallelogram.
\newline
Answer:
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The area of a parallelogram is
2
2
2
, and the lengths of its sides are
2
2
2
.
1
1
1
and
1
1
1
.
4
4
4
. Determine, to the nearest tenth of a degree, the measure of the acute angle of the parallelogram.
\newline
Answer:
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Which number represents the probability of an event that is certain to occur?
\newline
39
20
\frac{39}{20}
20
39
\newline
1
1
1
\newline
1
100
\frac{1}{100}
100
1
\newline
83
100
\frac{83}{100}
100
83
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Without dividing, determine if
46
46
46
,
264
264
264
is divisible by
9
9
9
and explain how you know.
\newline
46
,
264
□
46,264 \square
46
,
264
□
divisible by
9
9
9
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Without dividing, determine if
77
77
77
,
269
269
269
is divisible by
2
2
2
and explain how you know.
\newline
77
,
269
□
77,269 \square
77
,
269
□
divisible by
2
2
2
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Find the area. Simplify your answer.
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6
6
6
. The length and breadth of a room are
3
x
2
y
3
3 x^{2} y^{3}
3
x
2
y
3
and
6
x
3
y
2
6 x^{3} y^{2}
6
x
3
y
2
. Find its and area.
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x
+
y
=
3
,
x
−
3
y
=
−
9
\begin{aligned} x+y&=3, \ & x-3y=-9 \end{aligned}
x
+
y
=
3
,
x
−
3
y
=
−
9
\newline
What is the solution
(
x
,
y
)
(x,y)
(
x
,
y
)
to the given system of equations?
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Find the distance between
P
(
4
,
4
)
P(4,4)
P
(
4
,
4
)
and
Q
(
9
,
7
)
Q(9,7)
Q
(
9
,
7
)
.
\newline
The distance between
P
P
P
and
Q
Q
Q
is
□
\square
□
.
\newline
(Simplify your answer. Type an exact answer using radicals as need
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Write the equation of the line that passes through the points
(
−
1
,
−
4
)
(-1,-4)
(
−
1
,
−
4
)
and
(
6
,
−
8
)
(6,-8)
(
6
,
−
8
)
. Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
\newline
Answer:
\newline
Submit Answer
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Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an
(
x
,
y
)
(x, y)
(
x
,
y
)
point.
\newline
y
=
−
2
x
2
−
18
y=-2 x^{2}-18
y
=
−
2
x
2
−
18
\newline
Answer:
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1
2
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