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Math Problems
Algebra 2
Pythagorean Theorem and its converse
The length of a rectangle is
3
3
3
inches longer than it is wide. If the area is
130
130
130
square inches, what are the dimensions of the rectangle?
\newline
The width, or shorter side is
□
\square
□
inches
\newline
The length, or longer side is
□
\square
□
inches
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A basketball game was scheduled to last
60
60
60
minutes, including the breaks between quarters. Several timeouts were used throughout the game, resulting in the game lasting a total of
72
72
72
minutes, including breaks. If each timeout was
90
90
90
seconds, how many total timeouts were used during the game?
\newline
□
\square
□
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5
5
5
years ago a man was
7
7
7
times as old as his son. After
5
5
5
years the father will be
3
3
3
time as old as his son. Find their present age.
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Raggedy Rugs is holding their annual rug blowout sale this weekend! Since rugs will only be
$
6
\$6
$6
per square foot, Katie is going to get a new rug for her apartment. The rug is shaped like a rectangle with a width of
8
8
8
feet and a diagonal length of
17
17
17
feet. How much will the rug cost?
\newline
$
\$
$
____
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Every day, Gabrielle bicycles
3.6
3.6
3.6
miles due east from her house to school. After school, she bicycles due north from school to her friend Quinn's house, and then she bicycles home on a bike path that goes straight from Quinn's house to her own house. If the distance along the path from Quinn's house to Gabrielle's house is
8.9
8.9
8.9
miles, how far does Gabrielle bicycle each day? If necessary, round your answer to the nearest tenth.
\newline
____ miles
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Hugo and Brenda are mountain climbing and want to climb up an
8
8
8
-meter vertical rock face. Hugo goes first while Brenda stands a few steps back from the rock face. When Hugo reaches the top, she is
10
10
10
meters away from Brenda. How far away from the rock face is Brenda standing?
\newline
_____ meters
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After school, Brandon skateboards directly from school to a movie theater and then from the movie theater to an ice cream parlor. The movie theater is \(5\) kilometers south of the school and the ice cream parlor is \(12\) kilometers east of the movie theater. What is the straight-line distance between the school and the ice cream parlor?______________kilometers
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Hazel has two cubes. The smaller cube has a volume of
27
27
27
cubic units. The larger cube's sides are twice as long as those of the small cube. What is the volume of the second cube?
\newline
____ cubic units
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Malik walked up and back down an empty
\newline
18
m
18\,\text{m}
18
m
long escalator at a constant rate. Since the escalator was going up at the time, it took him only
\newline
22.5
s
22.5\,\text{s}
22.5
s
. Going down took Malik
\newline
90
s
90\,\text{s}
90
s
. Assume the escalator speed is constant.
\newline
What was Malik's walking speed?
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Estelle is helping at a community food drive by boxing up cans of soup. There are two sizes of boxes, large and small. Estelle fills
3
3
3
large boxes and
5
5
5
small boxes with
170
170
170
soup cans total. The boy working next to her fills
4
4
4
large boxes and
4
4
4
small boxes with
184
184
184
soup cans total.
\newline
How many cans does each small box hold?
\newline
_
_
_
_
\_\_\_\_
____
cans
\newline
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3
3
3
. A number exceeds
37684955
37684955
37684955
by
3615045
3615045
3615045
. What is that number?
\newline
4
4
4
. There were three candidates in an election. They received
687905
687905
687905
votes,
495086
495086
495086
votes and
93756
93756
93756
votes respectively. The number of invalid votes was
13849
13849
13849
. If
25467
25467
25467
persons did not vote. Ind how many votes were registered.
\newline
5
5
5
. A survey conducted on an Indian state shows that
1623546
1623546
1623546
people have only primary education:
9768678
9768678
9768678
people have secondary education:
6837954
6837954
6837954
people have higher
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Jane is going to walk once around the edge of a rectangular park. The park is
200
200
200
yards long and
300
300
300
feet wide. How far will Jane walk?
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Background
\newline
Layout
\newline
Theme
\newline
Trans
\newline
Question
131
131
131
:
\newline
To get from the pooi to home, Fred can either take a bike path through the rectangular park or ride his bike along the two sides of the park.
\newline
What measurement is closest to the distance of the bike path?
\newline
A.
2.45
mi
2.45\,\text{mi}
2.45
mi
\newline
B.
3.4
mi
3.4\,\text{mi}
3.4
mi
\newline
C.
1.45
mi
1.45\,\text{mi}
1.45
mi
\newline
D.
0.7
mi
0.7\,\text{mi}
0.7
mi
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8
8
8
. During a storm, a tree breaks
9
9
9
feet above the ground and falls to form a right trian
\newline
If the top of the tree rests
12
12
12
feet from the base of the tree, approximately how ta storm (round to the nearest foot)?
\newline
A.
19
19
19
feet
\newline
B.
21
21
21
feet
\newline
C.
24
24
24
feet
\newline
D.
27
27
27
feet
\newline
Module
9
9
9
-Test Form A
164
164
164
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Question
\newline
Watch Video
\newline
Show Examples
\newline
The length of a cell phone is
1
1
1
.
4
4
4
inches and the width is
4
4
4
.
2
2
2
inches. The company making the cell phone wants to make a new version whose length will be
1
1
1
.
75
75
75
inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?
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Malik walked up and back down an empty
18
m
18\,\text{m}
18
m
long escalator at a constant rate. Since the escalator was going up at the time, it took him only
22.5
s
22.5\,\text{s}
22.5
s
. Going down took Malik
90
s
90\,\text{s}
90
s
. Assume the escalator speed is constant.
\newline
What was Malik's walking speed?
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DeltaMath Student Application
\newline
3010254
/
23346821
/
d
c
5986
c
636
e
2
a
375955
c
422635
d
1
c
e
4
d
3010254 / 23346821 / d c 5986 c 636 e 2 a 375955 c 422635 d 1 c e 4 d
3010254/23346821/
d
c
5986
c
636
e
2
a
375955
c
422635
d
1
ce
4
d
\newline
hagorean Theorem Word Problems
\newline
ore:
0
/
10
0 / 10
0/10
\newline
Penalty:
1
1
1
off
\newline
Question
\newline
Show Examples
\newline
An altitude is drawn from the vertex of an isosceles triangle, forming a right angle and twc congruent triangles. As a result, the altitude cuts the base into two equal segments. The length of the altitude is
26
26
26
inches, and the length of the base is
9
9
9
inches. Find the triangle's perimeter. Round to the nearest tenth of an inch.
\newline
Answer Attempt
1
1
1
out of
2
2
2
\newline
□
\square
□
in.
\newline
Submit Answer
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5
5
5
. A center-pivot or circle sprinkler is used on large farms to irrigate crops. The sprinkler rotates an irrigation arm
36
0
∘
360^{\circ}
36
0
∘
from a fixed center. The outside of the irrigation arm travels
3
3
3
,
140
140
140
yards with each rotation. Determine the length of the irrigation arm in yards.
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33
33
33
David has just finished building his tree house and still needs to buy a ladder to be attached to the ledge of the treehouse and anchored at a point on the ground, as modeled below. David is standing
1
1
1
.
3
3
3
meters from the stilt supporting the treehouse. This is the point on the ground where he has decided to anchor the ladder. The angle of elevation from his eye level to the bottom of the treehouse is
56
56
56
degrees. David's eye level is
1
1
1
.
5
5
5
meters above the ground. Determine and state the minimum length ladder, to the nearest tenth of a meter, that David will need to buy for his treehouse.
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Whitney is making a strawberry cake for her brother's birthday. The cake pan is a right rectangular prism
20
cm
20\,\text{cm}
20
cm
wide by
28
cm
28\,\text{cm}
28
cm
long. Whitney puts
1848
cm
3
1848\,\text{cm}^{3}
1848
cm
3
of batter into the pan.
\newline
How deep is the cake batter?
\newline
□
cm
\square\,\text{cm}
□
cm
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Jaquan passed a checkpoint jogging at a constant speed of
9
9
9
km
h
\frac{\text{km}}{\text{h}}
h
km
. Then,
2
2
2
minutes later, Odalis passed the same checkpoint.
\newline
If Odalis runs at a constant speed of
12
12
12
km
h
\frac{\text{km}}{\text{h}}
h
km
then how far past the checkpoint will Odalis be when they catch up to Jaquan?
\newline
□
km
\square \,\text{km}
□
km
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Aspen has
306
306
306
green beads and
210
210
210
silver beads. For every
5
cm
5\,\text{cm}
5
cm
of a belt that Aspen sews, they use
40
40
40
green beads and
24
24
24
silver beads.
\newline
After how many centimeters of the belt will Aspen have equal numbers of green and silver beads left?
\newline
□
\square
□
cm
\text{cm}
cm
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The tires of a go-kart are
1
m
1 \mathrm{~m}
1
m
in circumference. The tires revolve
15
15
15
times per second.
\newline
What is the distance the go-kart travels in
40
40
40
seconds?
\newline
□
\square
□
m
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Brookfield Street, which is
16
16
16
meters wide, intersects with Greenville Avenue, which is
12
12
12
meters wide. Eduardo walks his dog across Brookfield Street and then turns and walks across Greenville Avenue. Suddenly, Eduardo's dog runs diagonally across the intersection back to the corner they started on. How far does Eduardo's dog travel in all?
\newline
\newline
cent;____ meters
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Jasper takes a sheet of paper and makes a diagonal cut from one corner to the opposite corner, making two triangles. The cut he makes is
85
85
85
inches long and the width of the paper is
51
51
51
inches. What is the paper's length?
\newline
_
_
_
_
_
_
_
_
_
\_\_\_\_\_\_\_\_\_
_________
inches
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Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled
28
kilometers
28\,\text{kilometers}
28
kilometers
, and the eastbound airplane has traveled
96
kilometers
96\,\text{kilometers}
96
kilometers
. How far apart are the two airplanes?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
kilometers
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A gopher has dug holes in opposite corners of a rectangular yard. One length of the yard is
24
24
24
meters and the distance between the gopher's holes is
26
26
26
meters. How wide is the yard?
\newline
_
_
_
\_\_\_
___
meters
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The area of an extra large circular pizza from Gambino's Pizzeria is
484
π
c
m
2
484 \pi \mathrm{cm}^{2}
484
π
cm
2
.
\newline
What is the diameter of an extra large pizza from Gambino's Pizzeria?
\newline
□
\square
□
c
m
\mathrm{cm}
cm
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Lila takes a
52
52
52
-centimeter by
39
39
39
-centimeter rectangle of plywood and uses a table saw to cut from one corner of the piece of plywood to the diagonally opposite corner. Now Lila has two equally sized triangles of plywood. What is the perimeter of each triangle?
\newline
_____ centimeters
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After school, Tyler skateboards directly from school to a game store and then from the game store to a movie theater. The game store is
12
12
12
kilometers south of the school and the movie theater is
5
5
5
kilometers east of the game store. What is the straight-line distance between the school and the movie theater?
\newline
_
_
_
_
\_\_\_\_
____
kilometers
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Camilla is building a skateboarding ramp by propping the end of a piece of wood on a cinder block. If the ramp starts
44
44
44
inches from the cinder block and the piece of wood is
55
55
55
inches long, how tall is the cinder block?
\newline
_
_
_
_
\_\_\_\_
____
inches
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A rake is leaning against a wall. The top of the rake hits the wall
63
63
63
inches above the ground and the bottom of the rake is
16
16
16
inches away from the base of the wall. A beetle crawls from the bottom of the rake to the top of the rake. Then the beetle climbs down to the base of the wall and back to the bottom of the rake. How far does the beetle travel in all?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
inches
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Tanvi is building a skateboarding ramp by propping the end of a piece of wood on a cinder block. If the ramp begins
45
45
45
inches from the block and the block is
28
28
28
inches tall, how long is the piece of wood?
\newline
_____ inches
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A flying squirrel's nest is
10
10
10
feet high in a tree. From its nest, the flying squirrel glides
26
26
26
feet to reach an acorn that is on the ground. How far is the acorn from the base of the tree?
\newline
_____ feet
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The diameter of a circle is
16
16
16
units.
\newline
What is the radius of the circle?
\newline
□
\square
□
units
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The radius of a circle is
1
1
1
units.
\newline
What is the diameter of the circle?
\newline
□
\square
□
units
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The radius of a circle is
5
5
5
units.
\newline
What is the diameter of the circle?
\newline
□
\square
□
units
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The radius of a circle is
3
3
3
units.
\newline
What is the diameter of the circle?
\newline
□
\square
□
units
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The diameter of a circle is
4
4
4
units.
\newline
What is the radius of the circle?
\newline
□
\square
□
units
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The diameter of a circle is
2
2
2
units.
\newline
What is the radius of the circle?
\newline
□
\square
□
units
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A circle has a circumference of
11
11
11
,
304
304
304
units.
\newline
What is the diameter of the circle? Use
3
3
3
.
14
14
14
for
π
\pi
π
and enter your answer as a decimal.
\newline
□
\square
□
units
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A circle has a circumference of
7
7
7
,
850
850
850
units.
\newline
What is the radius of the circle? Use
3
3
3
.
14
14
14
for
π
\pi
π
and enter your answer as a decimal.
\newline
□
\square
□
units
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The diameter of a circle is
6
6
6
units.
\newline
What is the radius of the circle?
\newline
□
\square
□
units
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The radius of a circle is
8
8
8
units.
\newline
What is the diameter of the circle?
\newline
□
\square
□
units
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The diameter of a circle is
10
10
10
units.
\newline
What is the radius of the circle?
\newline
□
\square
□
units
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11
11
11
) Alan drives from his house to his mother's house in
20
20
20
hours. He drives at an average speed of
66
66
66
miles per hour. What is the distance from Alan's house to his mother's house?
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1
1
1
:
13
13
13
PM Sun Apr
14
14
14
\newline
⋯
\cdots
⋯
\newline
HAlg
11
11
11
.
5
5
5
B Mid-Point Formula
\newline
SHORT RESPONSE The point of no return in aviation is the farthest point to which a plane can fly and still have enough fuel to return to its starting place or to fly to an alternative landing destination. After a plane passes the point of no return, it must fly to its planned destination. The distance between consecutive grid lines represents
50
50
50
nautical miles.
\newline
The flight path of a plane is from airport A to airport B. The plane is currently at the midpoint of the flight path. How far away is the plane from airport A? Round your answer to the nearest nautical mile.
\newline
□
\square
□
\newline
The plane's point of no return is calculated to be
200
200
200
nautical miles.
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A pedestrian underpass is constructed beneath a roadway using a cylindrical pipe with radius
1.8
m
1.8 \mathrm{~m}
1.8
m
. The bottom of the pipe will be filled and paved. The headroom at the centre of the path is
2.8
m
2.8 \mathrm{~m}
2.8
m
. How wide is the path?
\newline
ake It Further
\newline
A spherical fish bowl has diameter
26
c
m
26 \mathrm{~cm}
26
cm
. The surface of the water in the bowl is a
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Question
8
8
8
\newline
Joe was trying to determine the distance across a point, so he made the measurements shown below.
\newline
All images created for VVA,
2022
2022
2022
'
\newline
Which is closest to the distance from
M
\mathrm{M}
M
to
N
\mathrm{N}
N
?
\newline
48.2
m
48.2 \mathrm{~m}
48.2
m
\newline
33.2
m
33.2 \mathrm{~m}
33.2
m
\newline
59.3
m
59.3 \mathrm{~m}
59.3
m
\newline
22.4
m
22.4 \mathrm{~m}
22.4
m
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mae mowed two lawns. One of them measured
10
m
10 \, \text{m}
10
m
by
13
m
13 \, \text{m}
13
m
and the other
15
m
15 \, \text{m}
15
m
by
10
m
10 \, \text{m}
10
m
. Keili's rate is
$
3
\$3
$3
per
10
m
2
10\,\text{m}^2
10
m
2
. How much money did she get for the two lawns?
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1
2
3
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