Resources
Testimonials
Plans
Sign in
Sign up
Resources
Testimonials
Plans
AI tutor
Welcome to Bytelearn!
Let’s check out your problem:
(
3
x
2
−
7
x
)
+
(
5
x
2
+
13
)
\left(3 x^{2}-7 x\right)+\left(5 x^{2}+13\right)
(
3
x
2
−
7
x
)
+
(
5
x
2
+
13
)
\newline
The given expression can be written as
a
x
2
+
b
x
+
c
a x^{2}+b x+c
a
x
2
+
b
x
+
c
, where
a
,
b
a, b
a
,
b
, and
c
c
c
are constants. What is the value of
a
a
a
?
View step-by-step help
Home
Math Problems
Algebra 2
Write equations of cosine functions using properties
Full solution
Q.
(
3
x
2
−
7
x
)
+
(
5
x
2
+
13
)
\left(3 x^{2}-7 x\right)+\left(5 x^{2}+13\right)
(
3
x
2
−
7
x
)
+
(
5
x
2
+
13
)
\newline
The given expression can be written as
a
x
2
+
b
x
+
c
a x^{2}+b x+c
a
x
2
+
b
x
+
c
, where
a
,
b
a, b
a
,
b
, and
c
c
c
are constants. What is the value of
a
a
a
?
Combine like terms:
Combine like terms by adding the coefficients of the
x
2
x^2
x
2
terms from both expressions.
(
3
x
2
+
5
x
2
)
=
8
x
2
(3x^{2} + 5x^{2}) = 8x^{2}
(
3
x
2
+
5
x
2
)
=
8
x
2
Identify coefficient:
Identify the coefficient of the
x
2
x^2
x
2
term in the simplified expression.
\newline
The coefficient of
x
2
x^2
x
2
is
8
8
8
.
Find value of
a
a
a
:
The value of
a
a
a
is the coefficient of the
x
2
x^2
x
2
term in the expression.
\newline
Therefore,
a
=
8
a = 8
a
=
8
.
More problems from Write equations of cosine functions using properties
Question
Find an equation for a sinusoidal function that has period
2
π
2\pi
2
π
, amplitude
1
1
1
, and contains the point
(
π
,
−
1
)
\left(\pi, -1\right)
(
π
,
−
1
)
.
\newline
Write your answer in the form
f
(
x
)
=
A
cos
(
B
x
+
C
)
+
D
f(x)=A\cos(Bx+C)+D
f
(
x
)
=
A
cos
(
B
x
+
C
)
+
D
, where
A
A
A
,
B
B
B
,
C
C
C
, and
D
D
D
are real numbers.
\newline
f
(
x
)
=
f(x)=
f
(
x
)
=
Get tutor help
Posted 1 year ago
Question
Find an equation for a sinusoidal function that has period
2
π
2\pi
2
π
, amplitude
1
1
1
, and contains the point
(
−
π
2
,
−
1
)
\left(-\frac{\pi}{2},-1\right)
(
−
2
π
,
−
1
)
. Write your answer in the form
f
(
x
)
=
A
sin
(
B
x
+
C
)
+
D
f(x) = A\sin(Bx + C) + D
f
(
x
)
=
A
sin
(
B
x
+
C
)
+
D
, where
A
A
A
,
B
B
B
,
C
C
C
, and
D
D
D
are real numbers. `f(x)` =______
Get tutor help
Posted 1 year ago
Question
Find an equation for a sinusoidal function that has period
2
π
2\pi
2
π
, amplitude
1
1
1
, and contains the point
(
0
,
−
1
)
(0,-1)
(
0
,
−
1
)
.
\newline
Write your answer in the form
f
(
x
)
=
A
cos
(
B
x
+
C
)
+
D
f(x) = A\cos(Bx + C) + D
f
(
x
)
=
A
cos
(
B
x
+
C
)
+
D
, where
A
A
A
,
B
B
B
,
C
C
C
, and
D
D
D
are real numbers.
\newline
f
(
x
)
=
f(x) =
f
(
x
)
=
_____
Get tutor help
Posted 1 year ago
Question
Franklin Middle School is having a canned food drive. In Mr. Lao's class, Mr. Lao brought
10
10
10
cans of food, and each student brought
2
2
2
cans. In Ms. Roger's class, Ms. Rogers did not bring any cans, but each student brought
3
3
3
cans of food. Write two equations in slope-intercept form to represent the number of cans of food for each class
y
y
y
in terms of the number of students
x
x
x
.
Get tutor help
Posted 1 year ago
Question
Franklin Middle School is having a canned food drive. In Mr. Lao's class, Mr. Lao brought
10
10
10
cans of food, and each student brought
2
2
2
cans. In Ms. Roger's class, Ms. Rogers did not bring any cans, but each student brought
3
3
3
cans of food. Write two equations in slope-intercept form to represent the number of cans of food for each class
y
y
y
in terms of the number of students
x
x
x
.
Get tutor help
Posted 1 year ago
Question
Kris is wrapping Christmas lights around the railing that runs around three sides of his square porch If one side of his porch is
12
12
12
feet long, and each strand of his Christmes lights will wrap around a
70
70
70
-inch length of the railing, what is the minimum number of strands Kris needs to completely wrap the porch railing?
\newline
A)
6
6
6
\newline
B)
7
7
7
\newline
C)
8
8
8
\newline
D)
9
9
9
Get tutor help
Posted 1 year ago
Question
Kris is wrapping Christmas lights around the railing that runs around three sides of his square porch If one side of his porch is
12
12
12
feet long, and each strand of his Christmas lights will wrap around a
70
70
70
-inch length of the railing, what is the minimum number of strands Kris needs to completely wrap the porch railing?
\newline
A)
6
6
6
\newline
B)
7
7
7
\newline
C)
8
8
8
\newline
D)
9
9
9
Get tutor help
Posted 1 year ago
Question
For a given input value
b
b
b
, the function
f
f
f
outputs a value
a
a
a
to satisfy the following equation.
\newline
4
a
+
7
b
=
−
52
4a+7b=-52
4
a
+
7
b
=
−
52
\newline
Write a formula for
f
(
b
)
f(b)
f
(
b
)
in terms of
b
b
b
.
\newline
f
(
b
)
=
□
f(b)=\square
f
(
b
)
=
□
Get tutor help
Posted 10 months ago
Question
For a given input value
x
x
x
, the function
g
g
g
outputs a value
y
y
y
to satisfy the following equation.
\newline
−
4
x
−
6
=
−
5
y
+
2
-4x-6=-5y+2
−
4
x
−
6
=
−
5
y
+
2
\newline
Write a formula for
g
(
x
)
g(x)
g
(
x
)
in terms of
x
x
x
.
\newline
g
(
x
)
=
□
g(x)=\square
g
(
x
)
=
□
Get tutor help
Posted 1 year ago
Question
For a given input value
a
a
a
, the function
f
f
f
outputs a value
b
b
b
to satisfy the following equation.
\newline
−
3
a
+
6
b
=
a
+
4
b
-3a+6b=a+4b
−
3
a
+
6
b
=
a
+
4
b
\newline
Write a formula for
f
(
a
)
f(a)
f
(
a
)
in terms of
a
a
a
.
\newline
f
(
a
)
=
□
f(a)=\square
f
(
a
)
=
□
Get tutor help
Posted 1 year ago
Related topics
Algebra - Order of Operations
Algebra - Distributive Property
`X` and `Y` Axes
Geometry - Scalene Triangle
Common Multiple
Geometry - Quadrant