Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The Pool Company installs custom-built swimming pools. One of its customers would like a rectangular pool with a sidewalk of equal width around the entire perimeter. To fit in the backyard, the pool and sidewalk together will have to be 1818 feet by 3636 feet.\newlineThe area of the pool in square feet can be modeled by the expression (18−2x)(36−2x)(18 - 2x)(36 - 2x), where xx is the width of the sidewalk in feet.\newlineWhat does the quantity 36−2x36 - 2x represent in the expression?\newlineChoices:\newline(A)the perimeter around the outside of the pool in feet\newline(B)the area of the pool in square feet\newline(C)the area of the sidewalk in square feet\newline(D)the length of the pool in feet

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Interpret parts of quadratic expressions: word problemsright chevron icon

Full solution

Q. The Pool Company installs custom-built swimming pools. One of its customers would like a rectangular pool with a sidewalk of equal width around the entire perimeter. To fit in the backyard, the pool and sidewalk together will have to be 1818 feet by 3636 feet.\newlineThe area of the pool in square feet can be modeled by the expression (18−2x)(36−2x)(18 - 2x)(36 - 2x), where xx is the width of the sidewalk in feet.\newlineWhat does the quantity 36−2x36 - 2x represent in the expression?\newlineChoices:\newline(A)the perimeter around the outside of the pool in feet\newline(B)the area of the pool in square feet\newline(C)the area of the sidewalk in square feet\newline(D)the length of the pool in feet
  1. Identify Area Expression: The expression for the area of the pool is (18−2x)(36−2x)(18 - 2x)(36 - 2x). We need to identify what 36−2x36 - 2x represents.
  2. Dimensions of Pool and Sidewalk: The dimensions of the pool and sidewalk together are 1818 feet by 3636 feet. The width of the sidewalk is xx feet on all sides.
  3. Find Pool Length: To find the length of just the pool, we subtract the sidewalk's width from both sides of the total length, which is 3636 feet. So we do 36−x−x36 - x - x or 36−2x36 - 2x.
  4. Length of Pool Representation: Therefore, 36−2x36 - 2x represents the length of the pool in feet, not the perimeter or the area of the pool or sidewalk.

More problems from Interpret parts of quadratic expressions: word problems

Question
Solve by completing the square.\newlinem2−10m−29=0m^2 - 10m - 29 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newline`m` = ____ or `m` = _____
Get tutor helpright-arrow

Posted 1 month ago

Question
Find g(x) g(x) , where g(x) g(x) is the translation 5 5 units up of f(x)=x2 f(x)=x^2 .\newlineWrite your answer in the form a(x–h)2+k a(x–h)^2+k , where a a , h h , and k k are integers.\newlineg(x)= g(x)= ____
Get tutor helpright-arrow

Posted 1 month ago

Question
What is the range of this quadratic function?\newliney=x2−4x+4y = x^2 - 4x + 4\newlineChoices:\newline{y∣y≥2}\left\{y \mid y \geq 2\right\}\newline{y∣y≤0}\left\{y \mid y \leq 0\right\}\newline{y∣y≥0}\left\{y \mid y \geq 0\right\}\newlineall real numbers\text{all real numbers}
Get tutor helpright-arrow

Posted 1 month ago

Question
Write the equation of the parabola that passes through the points (1,0)(1,0), (2,0)(2,0), and (3,–16)(3,\text{–}16). Write your answer in the form y=a(x–p)(x–q)y = a(x – p)(x – q), where aa, pp, and qq are integers, decimals, or simplified fractions.\newline______
Get tutor helpright-arrow

Posted 1 month ago

Question
Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinef2+8f+_____f^2 + 8f + \_\_\_\_\_
Get tutor helpright-arrow

Posted 1 month ago

Question
Solve for h h .\newlineh2+39h=0 h^2 + 39h = 0 \newline\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlineh= h = ____\newline
Get tutor helpright-arrow

Posted 1 month ago

Question
Write a quadratic function with zeros −9-9 and −7-7.\newlineWrite your answer using the variable xx and in standard form with a leading coefficient of 11.\newlinef(x)=_____f(x) = \_\_\_\_\_
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the equation of the axis of symmetry for the parabola y=x2y = x^2. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline‾\underline{\hspace{3cm}}
Get tutor helpright-arrow

Posted 2 months ago

Question
Find g(x)g(x), where g(x)g(x) is the translation 88 units up of f(x)=x2f(x) = x^2.\newlineWrite your answer in the form a(x–h)2+ka(x – h)^2 + k, where aa, hh, and kk are integers.\newlineg(x)=g(x) = ______\newline
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve for xx.\newlinex2=1x^2 = 1\newline\newlineWrite your answer in simplified, rationalized form.\newlinex=x = ______ or x=x = ______\newline
Get tutor helpright-arrow

Posted 2 months ago

View all (159)