Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The area of a rectangle is
x^(2)+6x-16. Its width is
x-2. What is a simplified expression for its length?

The area of a rectangle is $x^{2}+6 x-16$ . Its width is $x-2$ . What is a simplified expression for its length?

View step-by-step help

View step-by-step help

Solve quadratic equations: word problems

Full solution

Q. The area of a rectangle is

x^{2}+6 x-16

. Its width is

x-2

. What is a simplified expression for its length?

Calculate Area Divided by Width: To find the length of the rectangle, we need to divide the area by the width. The area of the rectangle is given by the expression $x^2 + 6x - 16$ , and the width is given by $x - 2$ .
Perform Polynomial Long Division: Perform the division of the area by the width. This can be done by polynomial long division or synthetic division. We will use polynomial long division here.
Set Up Division: Set up the division: x^2 + 6x - 16) \div (x - 2)\. We will divide \$x^2 by $x$ to get $x$ , and then multiply $x$ by $x - 2$ to subtract from the original polynomial.
Subtract Result: After multiplying $x$ by $(x - 2)$ , we get $x^2 - 2x$ . We subtract this from $x^2 + 6x$ to get $8x - 16$ .
Divide Again: Next, we divide $8x$ by $x$ to get $8$ , and multiply $8$ by $(x - 2)$ to subtract from $8x - 16$ .
Check Remainder: After multiplying $8$ by $(x - 2)$ , we get $8x - 16$ . We subtract this from $8x - 16$ to get a remainder of $0$ .
Finalize Length: Since the remainder is $0$ , the division is exact, and the quotient $x + 8$ is the simplified expression for the length of the rectangle.

More problems from Solve quadratic equations: word problems

Question

Solve by completing the square.

\newline

m^2 - 10m - 29 = 0

\newline

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

\newline

`m` = ____ or `m` = _____

Posted 8 months ago

Question

g(x)

g(x)

is the translation

5

f(x)=x^2

\newline

Write your answer in the form

a(x–h)^2+k

a

h

k

\newline

g(x)=

Posted 7 months ago

Question

What is the range of this quadratic function?

\newline

y = x^2 - 4x + 4

\newline

\newline

\left\{y \mid y \geq 2\right\}

\newline

\left\{y \mid y \leq 0\right\}

\newline

\left\{y \mid y \geq 0\right\}

\newline

\text{all real numbers}

Posted 5 months ago

Question

Write the equation of the parabola that passes through the points

(1,0)

(2,0)

(3,\text{–}16)

. Write your answer in the form

y = a(x – p)(x – q)

a

p

q

are integers, decimals, or simplified fractions.

\newline

Posted 5 months ago

Question

Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.

\newline

f^2 + 8f + \_\_\_\_\_

Posted 5 months ago

Question

h

\newline

h^2 + 39h = 0

\newline

\newline

Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

\newline

h =

\newline

Posted 5 months ago

Question

Write a quadratic function with zeros

-9

-7

\newline

Write your answer using the variable

x

and in standard form with a leading coefficient of

1

\newline

f(x) = \_\_\_\_\_

Posted 5 months ago

Question

Find the equation of the axis of symmetry for the parabola

y = x^2

\newline

Simplify any numbers and write them as proper fractions, improper fractions, or integers.

\newline

\underline{\hspace{3cm}}

Posted 4 months ago

Question

g(x)

g(x)

is the translation

8

f(x) = x^2

\newline

Write your answer in the form

a(x – h)^2 + k

a

h

k

\newline

g(x) =

\newline

Posted 4 months ago

Question

x

\newline

x^2 = 1

\newline

\newline

Write your answer in simplified, rationalized form.

\newline

x =

x =

\newline

Posted 5 months ago

Related topics

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