Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for
r.

{:[(4r)/(5r+6)=(1)/(6)],[r=]:}

Solve for $r$ . $\newline$ $\begin{array}{l} \frac{4 r}{5 r+6}=\frac{1}{6} \\ r=\square \end{array}$

View step-by-step help

View step-by-step help

Composition of linear functions: find a value

Full solution

Q. Solve for

r

.

\newline

\begin{array}{l} \frac{4 r}{5 r+6}=\frac{1}{6} \\ r=\square \end{array}

Set up the equation: Set up the equation. $\newline$ We are given the equation $(\frac{4r}{5r+6}) = \frac{1}{6}$ . We need to solve for $r$ .
Cross-multiply to eliminate the fractions: Cross-multiply to eliminate the fractions. $\newline$ Multiply both sides of the equation by $(5r+6)\cdot 6$ to get rid of the denominators. $\newline$ $\frac{4r}{5r+6} \cdot (5r+6) \cdot 6 = \frac{1}{6} \cdot (5r+6) \cdot 6$
Simplify both sides of the equation: Simplify both sides of the equation. $\newline$ On the left side, $(5r+6)$ cancels out, and on the right side, $6$ cancels out with $\frac{1}{6}$ . $\newline$ $4r \times 6 = 5r + 6$
Distribute the $6$ on the left side: Distribute the $6$ on the left side. $24r = 5r + 6$
Subtract $5r$ from both sides: Subtract $5r$ from both sides to get all $r$ terms on one side. $\newline$ $24r - 5r = 5r - 5r + 6$ $\newline$ $19r = 6$
Divide both sides by $19$ : Divide both sides by $19$ to solve for $r$ . $r = \frac{6}{19}$

More problems from Composition of linear functions: find a value

Question

Find the inverse of the function.

y = x + 3

Write your answer in the form

ax + b

. Simplify any fractions.

y =

Posted 2 months ago

Question

(r \circ s)(x)

\newline

3

\newline

2

5

\newline

Write your answer as a polynomial in simplest form.

\newline

(r \circ s)(x) =

Posted 1 month ago

Question

(f + g)(x)

\newline

f(x) = -3x

\newline

g(x) = 3x + 1

\newline

\newline

Write your answer as a polynomial or a rational function in simplest form.

\newline

\underline{\hspace{3cm}}

\newline

Posted 1 month ago

Question

(f * g)(x)

\newline

f(x) = -x + 4

\newline

g(x) = 4x

\newline

\newline

Write your answer as a polynomial or a rational function in simplest form.

\newline

\underline{\hspace{3em}}

\newline

Posted 1 month ago

Question

What is the domain of

\left(\frac{f}{g}\right)(x)

\newline

f(x) = 2x

\newline

g(x) = -5x + 3

\newline

\newline

[\text{A]All real numbers}

\newline

[\text{B]All real numbers except } \frac{3}{5}

\newline

[\text{C]All real numbers except } -\frac{3}{5}

\newline

[\text{D]All real numbers except } \frac{5}{3}

Posted 2 months ago

Question

Find the inverse of the function.

\newline

-3x

\newline

Write your answer in the form

ax + b

. Simplify any fractions.

\newline

Posted 1 month ago

Question

(f \circ g)(0)

\newline

f(x) = 6x

\newline

g(x) = x^2 + 4x

\newline

(f \circ g)(0) =

Posted 1 month ago

Question

(f \circ g)(x)

\newline

f(x) = x^2 + 5

\newline

g(x) = 4x

\newline

Write your answer as a polynomial in simplest form.

\newline

(f \circ g)(x) =

Posted 1 month ago

Question

f(x)

the inverse function of

g(x)

\newline

f(x) = x

\newline

g(x) = -4x

\newline

\newline

\text{[yes]}

\newline

\text{[no]}

Posted 1 month ago

Question

(f * g)(x)

f(x) = 3x^2 + 9x

g(x) = 3x

Write your answer as a polynomial or a rational function in simplest form. ______

Posted 2 months ago