Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Raggedy Rugs is holding their annual rug blowout sale this weekend! Since rugs will only be $\$6$ per square foot, Katie is going to get a new rug for her apartment. The rug is shaped like a rectangle with a width of $8$ feet and a diagonal length of $17$ feet. How much will the rug cost? $\newline$ $\$$ ____

View step-by-step help

View step-by-step help

Pythagorean Theorem and its converse

Full solution

Q. Raggedy Rugs is holding their annual rug blowout sale this weekend! Since rugs will only be

\$6

per square foot, Katie is going to get a new rug for her apartment. The rug is shaped like a rectangle with a width of

8

feet and a diagonal length of

17

feet. How much will the rug cost?

\newline

\$

____

Calculate Rug Length: Calculate the length of the rug using the Pythagorean theorem. Given the diagonal ( $17$ feet) and the width ( $8$ feet), we need to find the length. $\newline$ $8^2 + \text{length}^2 = 17^2$ $\newline$ $64 + \text{length}^2 = 289$ $\newline$ $\text{length}^2 = 225$ $\newline$ $\text{length} = 15 \text{ feet}$
Calculate Rug Area: Calculate the area of the rug using the dimensions found. The rug is a rectangle with a width of $8$ feet and a length of $15$ feet. $\newline$ $\text{Area} = \text{width} \times \text{length}$ $\newline$ $\text{Area} = 8 \times 15$ $\newline$ $\text{Area} = 120 \text{ square feet}$
Calculate Rug Cost: Calculate the cost of the rug by multiplying the area by the price per square foot. The price per square foot is $\(6\).\(\newline\)\[ \text{Cost} = \text{Area} \times \text{price per square foot} \]\(\newline\)\[ \text{Cost} = 120 \times 6 \]\(\newline\)\[ \text{Cost} = 720 \text{ dollars} \]

More problems from Pythagorean Theorem and its converse

Question

Find all solutions with

0^\circ \leq \theta \leq 180^\circ

. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.

\newline

\cos(\theta) = -1

\newline

\underline{\hspace{2em}}^\circ

Posted 1 month ago

Question

Kimi's school is

15

kilometers west of her house and

8

kilometers south of her friend Franklin's house. Every day, Kimi bicycles from her house to her school. After school, she bicycles from her school to Franklin's house. Before dinner, she bicycles home on a bike path that goes straight from Franklin's house to her own house. How far does Kimi bicycle each day?

\newline

\_\_\_\_\_

Posted 1 month ago

Question

Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth.

\newline

\cos 35^\circ =

Posted 1 month ago

Question

Find all solutions with

-90^\circ \leq \theta \leq 90^\circ

. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.

\newline

\csc(\theta) = -1

\newline

\_\_\_\_\,^\circ

Posted 1 month ago

Question

Evaluate. Write your answer in simplified, rationalized form. Do not round.

\newline

\cot 30^\circ =

Posted 1 month ago

Question

The terminal side of an angle

\theta

in standard position intersects the unit circle at

(\frac{84}{85}, \frac{13}{85})

\cos(\theta)

\newline

Write your answer in simplified, rationalized form.

\newline

Posted 1 month ago

Question

-90^\circ < \theta < 90^\circ

. Find the value of

\theta

\newline

\tan(\theta) = 0

\newline

Write your answer in simplified, rationalized form. Do not round.

\newline

\theta =

^\circ

\newline

Posted 2 months ago

Question

Evaluate. Write your answer in simplified, rationalized form. Do not round.

\newline

\csc 60^\circ =

Posted 1 month ago

Question

\theta

is an acute angle. Find the value of

\theta

\newline

\sec(\theta) = \sqrt{2}

\newline

\theta =

\degree

Posted 1 month ago

Question

Evaluate. Write your answer in simplified, rationalized form. Do not round.

\newline

\cos 90^\circ =

Posted 2 months ago