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Math Problems
Algebra 2
Find the roots of factored polynomials
Complete the point-slope equation of the line through
(
6
,
4
)
(6,4)
(
6
,
4
)
and
(
7
,
2
)
(7,2)
(
7
,
2
)
.
\newline
Use exact numbers.
\newline
y
−
2
=
y-2=
y
−
2
=
Get tutor help
Complete the point-slope equation of the line through
(
−
1
,
6
)
(-1,6)
(
−
1
,
6
)
and
(
1
,
5
)
(1,5)
(
1
,
5
)
.
\newline
Use exact numbers.
\newline
y
−
6
=
y-6=
y
−
6
=
Get tutor help
Complete the point-slope equation of the line through
(
1
,
0
)
(1,0)
(
1
,
0
)
and
(
6
,
−
3
)
(6,-3)
(
6
,
−
3
)
.
\newline
Use exact numbers.
\newline
y
−
(
−
3
)
=
□
y-(-3)=\square
y
−
(
−
3
)
=
□
Get tutor help
Complete the point-slope equation of the line through
(
1
,
−
1
)
(1,-1)
(
1
,
−
1
)
and
(
5
,
2
)
(5,2)
(
5
,
2
)
.
\newline
Use exact numbers.
\newline
y
−
(
−
1
)
=
□
y-(-1)=\square
y
−
(
−
1
)
=
□
Get tutor help
Complete the point-slope equation of the line through
(
8
,
−
8
)
(8,-8)
(
8
,
−
8
)
and
(
9
,
8
)
(9,8)
(
9
,
8
)
.
\newline
Use exact numbers.
\newline
y
−
8
=
y-8=
y
−
8
=
Get tutor help
Complete the point-slope equation of the line through
(
2
,
3
)
(2,3)
(
2
,
3
)
and
(
7
,
4
)
(7,4)
(
7
,
4
)
.
\newline
Use exact numbers.
\newline
y
−
4
=
y-4=
y
−
4
=
Get tutor help
Complete the point-slope equation of the line through
(
−
4
,
8
)
(-4,8)
(
−
4
,
8
)
and
(
4
,
4
)
(4,4)
(
4
,
4
)
. Use exact numbers.
\newline
y
−
4
=
y-4=
y
−
4
=
Get tutor help
Complete the point-slope equation of the line through
(
−
5
,
4
)
(-5,4)
(
−
5
,
4
)
and
(
1
,
6
)
(1,6)
(
1
,
6
)
.
\newline
Use exact numbers.
\newline
y
−
6
=
y-6=
y
−
6
=
Get tutor help
Complete the point-slope equation of the line through
(
−
2
,
6
)
(-2,6)
(
−
2
,
6
)
and
(
1
,
1
)
(1,1)
(
1
,
1
)
. Use exact numbers.
\newline
y
−
6
=
y-6=
y
−
6
=
Get tutor help
Find the zeros of the function. Enter the solutions from least to greatest.
\newline
f
(
x
)
=
(
−
x
−
2
)
(
−
2
x
−
3
)
lesser
x
=
□
greater
x
=
□
\begin{array}{l} f(x)=(−x−2)(−2x−3) \text{lesser } x=\square \text{greater } x=\square \end{array}
f
(
x
)
=
(
−
x
−2
)
(
−2
x
−3
)
lesser
x
=
□
greater
x
=
□
Get tutor help
Ricardo throws a stone off a bridge into a river below.
\newline
The stone's height (in meters above the water),
x
x
x
seconds after Ricardo threw it, is modeled by
\newline
w
(
x
)
=
−
5
(
x
−
8
)
(
x
+
4
)
w(x)=-5(x-8)(x+4)
w
(
x
)
=
−
5
(
x
−
8
)
(
x
+
4
)
\newline
How many seconds after being thrown will the stone reach its maximum height?
\newline
seconds
\text{seconds}
seconds
Get tutor help
A hovercraft takes off from a platform. Its height (in meters),
x
x
x
seconds after takeoff, is modeled by
\newline
h
(
x
)
=
−
(
x
−
11
)
(
x
+
3
)
h(x) = -(x-11)(x+3)
h
(
x
)
=
−
(
x
−
11
)
(
x
+
3
)
\newline
What is the height of the hovercraft at the time of takeoff?
\newline
m
e
t
e
r
s
meters
m
e
t
ers
Get tutor help
The power generated by an electrical circuit (in watts) as a function of its current
x
x
x
(in amperes) is modeled by
\newline
P
(
x
)
=
−
15
x
(
x
−
8
)
P(x)=-15x(x-8)
P
(
x
)
=
−
15
x
(
x
−
8
)
\newline
What is the maximum power possible?
\newline
watts
Get tutor help
The power generated by an electrical circuit (in watts) as a function of its current
x
x
x
(in amperes) is modeled by
\newline
P
(
x
)
=
−
15
x
(
x
−
8
)
P(x)=-15x(x-8)
P
(
x
)
=
−
15
x
(
x
−
8
)
\newline
What current will produce the maximum power?
\newline
amperes
Get tutor help
Ricardo throws a stone off a bridge into a river below.
\newline
The stone's height (in meters above the water),
x
x
x
seconds after Ricardo threw it, is modeled by
\newline
w
(
x
)
=
−
5
(
x
−
8
)
(
x
+
4
)
w(x)=-5(x-8)(x+4)
w
(
x
)
=
−
5
(
x
−
8
)
(
x
+
4
)
\newline
What is the maximum height that the stone will reach?
\newline
m
e
t
e
r
s
meters
m
e
t
ers
Get tutor help
Guillermo is a professional deep water free diver. His altitude (in meters relative to sea level),
x
x
x
seconds after diving, is modeled by
\newline
g
(
x
)
=
1
20
x
(
x
−
100
)
g(x)=\frac{1}{20}x(x-100)
g
(
x
)
=
20
1
x
(
x
−
100
)
\newline
What is the lowest altitude Guillermo will reach? meters relative to sea level
Get tutor help
The number of mosquitoes in Brooklyn (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled by
\newline
m
(
x
)
=
−
x
(
x
−
4
)
m(x)=-x(x-4)
m
(
x
)
=
−
x
(
x
−
4
)
\newline
What is the maximum possible number of mosquitoes?
\newline
million mosquitoes
Get tutor help
The number of mosquitoes in Brooklyn (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled by
\newline
m
(
x
)
=
−
x
(
x
−
4
)
m(x)=-x(x-4)
m
(
x
)
=
−
x
(
x
−
4
)
\newline
What amount of rainfall results in the maximum number of mosquitoes?
\newline
centimeters
\text{centimeters}
centimeters
Get tutor help
Guillermo is a professional deep water free diver. His altitude (in meters relative to sea level),
x
x
x
seconds after diving, is modeled by
g
(
x
)
=
1
20
x
(
x
−
100
)
g(x) = \frac{1}{20}x(x-100)
g
(
x
)
=
20
1
x
(
x
−
100
)
How many seconds after diving will Guillermo reach his lowest altitude?
seconds
\text{seconds}
seconds
Get tutor help
Find the zeros of the function. Enter the solutions from least to greatest.
\newline
f
(
x
)
=
(
x
−
3
)
(
2
x
−
8
)
f(x) = (x - 3)(2x - 8)
f
(
x
)
=
(
x
−
3
)
(
2
x
−
8
)
,
lesser
x
=
□
\text{lesser } x = \square
lesser
x
=
□
,
greater
x
=
□
\text{greater } x = \square
greater
x
=
□
Get tutor help
A hovercraft takes off from a platform. Its height (in meters),
x
x
x
seconds after takeoff, is modeled by
h
(
x
)
=
−
(
x
−
11
)
(
x
+
3
)
h(x) = -(x-11)(x+3)
h
(
x
)
=
−
(
x
−
11
)
(
x
+
3
)
How many seconds after takeoff will the hovercraft land on the ground?
seconds
\text{seconds}
seconds
Get tutor help
Amir stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground),
x
x
x
seconds after Amir threw it, is modeled by
\newline
h
(
x
)
=
−
(
x
+
1
)
(
x
−
7
)
h(x) = -(x+1)(x-7)
h
(
x
)
=
−
(
x
+
1
)
(
x
−
7
)
\newline
How many seconds after being thrown will the ball reach its maximum height?
\newline
seconds
\text{seconds}
seconds
Get tutor help
Ana dives into a pool off of a springboard high dive. Her height (in meters above the water),
x
x
x
seconds after diving, is modeled by
\newline
h
(
x
)
=
−
5
(
x
+
1
)
(
x
−
3
)
h(x)=-5(x+1)(x-3)
h
(
x
)
=
−
5
(
x
+
1
)
(
x
−
3
)
\newline
What is the height of Ana above the water at the time of diving?
meters
\text{meters}
meters
Get tutor help
Simon has
160
160
160
meters of fencing to build a rectangular garden.
\newline
The garden's area (in square meters) as a function of the garden's width
\newline
x
x
x
(in meters) is modeled by
\newline
A
(
x
)
=
−
x
(
x
−
80
)
A(x)=-x(x-80)
A
(
x
)
=
−
x
(
x
−
80
)
\newline
What width will produce the maximum garden area?
\newline
meters
\text{meters}
meters
Get tutor help
Simon has
160
160
160
meters of fencing to build a rectangular garden.
\newline
The garden's area (in square meters) as a function of the garden's width
\newline
x
x
x
(in meters) is modeled by
\newline
A
(
x
)
=
−
x
(
x
−
80
)
A(x)=-x(x-80)
A
(
x
)
=
−
x
(
x
−
80
)
\newline
What is the maximum area possible?
\newline
square meters
Get tutor help
Amir stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground),
x
x
x
seconds after Amir threw it, is modeled by
\newline
h
(
x
)
=
−
(
x
+
1
)
(
x
−
7
)
h(x) = -(x+1)(x-7)
h
(
x
)
=
−
(
x
+
1
)
(
x
−
7
)
\newline
What is the maximum height that the ball will reach?
\newline
m
e
t
e
r
s
meters
m
e
t
ers
Get tutor help
Find the zeros of the function. Enter the solutions from least to greatest.
\newline
h
(
x
)
=
(
−
4
x
−
5
)
(
−
x
+
5
)
h(x) = (-4x - 5)(-x + 5)
h
(
x
)
=
(
−
4
x
−
5
)
(
−
x
+
5
)
,
lesser
x
=
□
\text{lesser } x = \square
lesser
x
=
□
,
greater
x
=
□
\text{greater } x = \square
greater
x
=
□
Get tutor help
Find the zeros of the function. Enter the solutions from least to greatest.
\newline
g
(
x
)
=
(
x
−
2
)
(
3
x
+
3
)
g(x) = (x - 2)(3x + 3)
g
(
x
)
=
(
x
−
2
)
(
3
x
+
3
)
,
lesser
x
=
□
\text{lesser } x = \square
lesser
x
=
□
,
greater
x
=
□
\text{greater } x = \square
greater
x
=
□
Get tutor help
Find the zeros of the function. Enter the solutions from least to greatest.
\newline
h
(
x
)
=
(
−
2
x
+
3
)
(
−
x
+
3
)
h(x) = (-2x + 3)(-x + 3)
h
(
x
)
=
(
−
2
x
+
3
)
(
−
x
+
3
)
,
lesser
x
=
□
\text{lesser } x = \square
lesser
x
=
□
,
greater
x
=
□
\text{greater } x = \square
greater
x
=
□
Get tutor help
Find the zeros of the function. Enter the solutions from least to greatest.
\newline
g
(
x
)
=
(
−
5
x
−
1
)
(
2
x
+
8
)
g(x) = (-5x - 1)(2x + 8)
g
(
x
)
=
(
−
5
x
−
1
)
(
2
x
+
8
)
,
lesser
x
=
□
\text{lesser } x = \square
lesser
x
=
□
,
greater
x
=
□
\text{greater } x = \square
greater
x
=
□
Get tutor help
An object is launched from a platform.
\newline
Its height (in meters),
x
x
x
seconds after the launch, is modeled by
\newline
h
(
x
)
=
−
5
(
x
+
1
)
(
x
−
9
)
h(x)=-5(x+1)(x-9)
h
(
x
)
=
−
5
(
x
+
1
)
(
x
−
9
)
\newline
How many seconds after launch will the object hit the ground?
\newline
seconds
\text{seconds}
seconds
Get tutor help
A certain company's main source of income is a mobile app.
\newline
The company's annual profit (in millions of dollars) as a function of the app's price (in dollars) is modeled by
\newline
P
(
x
)
=
−
2
(
x
−
3
)
(
x
−
11
)
P(x)=-2(x-3)(x-11)
P
(
x
)
=
−
2
(
x
−
3
)
(
x
−
11
)
\newline
Which app prices will result in
$
0
\$0
$0
annual profit?
\newline
Enter the lower price first.
\newline
Lower price:
dollars
\text{dollars}
dollars
\newline
Higher price:
dollars
\text{dollars}
dollars
Get tutor help
Ana dives into a pool off of a springboard high dive. Her height (in meters above the water),
x
x
x
seconds after diving, is modeled by
\newline
h
(
x
)
=
−
5
(
x
+
1
)
(
x
−
3
)
h(x) = -5(x+1)(x-3)
h
(
x
)
=
−
5
(
x
+
1
)
(
x
−
3
)
\newline
How many seconds after diving will Ana hit the water?
\newline
seconds
\text{seconds}
seconds
Get tutor help
An object is launched from a platform. Its height (in meters),
x
x
x
seconds after the launch, is modeled by
\newline
h
(
x
)
=
−
5
(
x
+
1
)
(
x
−
9
)
h(x)=-5(x+1)(x-9)
h
(
x
)
=
−
5
(
x
+
1
)
(
x
−
9
)
\newline
What is the height of the object at the time of launch?
meters
\text{meters}
meters
Get tutor help
A certain company's main source of income is a mobile app.
\newline
The company's annual profit (in millions of dollars) as a function of the app's price (in dollars) is modeled by
\newline
P
(
x
)
=
−
2
(
x
−
3
)
(
x
−
11
)
P(x)=-2(x-3)(x-11)
P
(
x
)
=
−
2
(
x
−
3
)
(
x
−
11
)
\newline
What would be the company's profit if the app price is
0
0
0
dollars?
\newline
million dollars
\text{million dollars}
million dollars
Get tutor help
Complete the point-slope equation of the line through
(
−
5
,
7
)
(-5,7)
(
−
5
,
7
)
and
(
−
4
,
0
)
(-4,0)
(
−
4
,
0
)
. Use exact numbers.
\newline
y
−
7
=
y-7=
y
−
7
=
Get tutor help
Find the roots of the factored polynomial.
\newline
(
x
+
7
)
(
x
+
4
)
(x + 7)(x + 4)
(
x
+
7
)
(
x
+
4
)
\newline
Write your answer as a list of values separated by commas.
\newline
x
=
x =
x
=
____
Get tutor help
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