Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

For a given input value
a, the function
f outputs a value
b to satisfy the following equation.

-3a+6b=a+4b
Write a formula for
f(a) in terms of
a.

f(a)=◻

For a given input value $a$ , the function $f$ outputs a value $b$ to satisfy the following equation. $\newline$ $-3a+6b=a+4b$ $\newline$ Write a formula for $f(a)$ in terms of $a$ . $\newline$ $f(a)=\square$

View step-by-step help

View step-by-step help

Write equations of cosine functions using properties

Full solution

Q. For a given input value

a

, the function

f

outputs a value

b

to satisfy the following equation.

\newline

-3a+6b=a+4b

\newline

Write a formula for

f(a)

in terms of

a

.

\newline

f(a)=\square

Isolate $b$ on one side: To solve for $b$ in terms of $a$ , we need to isolate $b$ on one side of the equation. Let's start by moving all terms involving $b$ to one side and all terms involving $a$ to the other side. $\newline$ $-3a + 6b - 4b = a$
Combine like terms: Combine like terms to simplify the equation. $-3a + 2b = a$
Move term involving $a$ : Now, move the term involving $a$ on the left side to the right side by adding $3$ a to both sides of the equation. $\newline$ $2$ b = a + $3$ a
Combine terms involving $a$ : Combine the terms on the right side to get a single term involving $a$ . $\newline$ $2$ b = $4$ a
Divide both sides: Divide both sides by $2$ to solve for $b$ . $\newline$ $b = \frac{4a}{2}$
Simplify the formula: Simplify the right side to get the final formula for $b$ in terms of $a$ . $\newline$ $b = 2a$

More problems from Write equations of cosine functions using properties

Question

Find an equation for a sinusoidal function that has period

2\pi

1

, and contains the point

\left(\pi, -1\right)

\newline

Write your answer in the form

f(x)=A\cos(Bx+C)+D

A

B

C

D

are real numbers.

\newline

f(x)=

Posted 7 months ago

Question

Find an equation for a sinusoidal function that has period

2\pi

1

, and contains the point

\left(-\frac{\pi}{2},-1\right)

. Write your answer in the form

f(x) = A\sin(Bx + C) + D

A

B

C

D

are real numbers. `f(x)` =______

Posted 8 months ago

Question

Find an equation for a sinusoidal function that has period

2\pi

1

, and contains the point

(0,-1)

\newline

Write your answer in the form

f(x) = A\cos(Bx + C) + D

A

B

C

D

are real numbers.

\newline

f(x) =

Posted 8 months ago

Question

Franklin Middle School is having a canned food drive. In Mr. Lao's class, Mr. Lao brought

10

cans of food, and each student brought

2

cans. In Ms. Roger's class, Ms. Rogers did not bring any cans, but each student brought

3

cans of food. Write two equations in slope-intercept form to represent the number of cans of food for each class

y

in terms of the number of students

x

Posted 8 months ago

Question

Franklin Middle School is having a canned food drive. In Mr. Lao's class, Mr. Lao brought

10

cans of food, and each student brought

2

cans. In Ms. Roger's class, Ms. Rogers did not bring any cans, but each student brought

3

cans of food. Write two equations in slope-intercept form to represent the number of cans of food for each class

y

in terms of the number of students

x

Posted 8 months 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

feet long, and each strand of his Christmes lights will wrap around a

70

-inch length of the railing, what is the minimum number of strands Kris needs to completely wrap the porch railing?

\newline

6

\newline

7

\newline

8

\newline

9

Posted 8 months 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

feet long, and each strand of his Christmas lights will wrap around a

70

-inch length of the railing, what is the minimum number of strands Kris needs to completely wrap the porch railing?

\newline

6

\newline

7

\newline

8

\newline

9

Posted 8 months ago

Question

For a given input value

b

f

outputs a value

a

to satisfy the following equation.

\newline

4a+7b=-52

\newline

Write a formula for

f(b)

b

\newline

f(b)=\square

Posted 6 months ago

Question

For a given input value

x

g

outputs a value

y

to satisfy the following equation.

\newline

-4x-6=-5y+2

\newline

Write a formula for

g(x)

x

\newline

g(x)=\square

Posted 9 months ago

Question

You pick a card at random, put it back, and then pick another card at random.

\newline

4

\newline

5

\newline

6

\newline

7

\newline

What is the probability of picking a number greater than

5

and then picking a

4

\newline

Write your answer as a percentage.

Posted 27 days ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant