Domanda del libro di testo
Exercises 57–59 will help you prepare for the material covered in the next section. Subtract:
630
views
Ch. 5 - Systems of Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 6, Problema 57
Find the length and width of a rectangle whose perimeter is 36 feet and whose area is 77 square feet.
Guida verificata passo dopo passo1
Let the length of the rectangle be \(L\) feet and the width be \(W\) feet.
Write the equation for the perimeter of the rectangle: \(2L + 2W = 36\).
Simplify the perimeter equation by dividing both sides by 2: \(L + W = 18\).
Write the equation for the area of the rectangle: \(L \times W = 77\).
Use the perimeter equation to express \(L\) in terms of \(W\): \(L = 18 - W\), then substitute this into the area equation to get \((18 - W) \times W = 77\).
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
4mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Perimeter of a Rectangle
The perimeter of a rectangle is the total distance around it, calculated by adding twice the length and twice the width (P = 2L + 2W). Understanding this formula allows you to set up an equation relating length and width when the perimeter is known.
Area of a Rectangle
The area of a rectangle is the amount of space inside it, found by multiplying the length by the width (A = L × W). This formula helps create a second equation when the area is given, which is essential for solving for both dimensions.
Video consigliato:
6:19
Systems of Inequalities
Solving Systems of Equations
When two equations involve two variables, such as length and width, solving the system means finding values that satisfy both simultaneously. Techniques include substitution or elimination, which are used here to find the rectangle’s dimensions from the perimeter and area equations.
Video consigliato:
5:48Solving Systems of Equations - Substitution
Pratica correlata
Domanda del libro di testo
In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x2+y2<16, y≥2x
488
views
Domanda del libro di testo
Find the value of the objective function z = 2x + 3y at each corner of the graphed region shown. What is the maximum value of the objective function? What is the minimum value of the objective function?
624
views
Domanda del libro di testo
In Exercises 57–59, graph the region determined by the constraints. Then find the maximum value of the given objective function, subject to the constraints. This is a piecewise function. Refer to the textbook.
627
views
Domanda del libro di testo
Exercises 57–59 will help you prepare for the material covered in the next section. Add: (5x−3)/(x2+1) + 2x/(x2+1)2.
675
views
Domanda del libro di testo
Find the length and width of a rectangle whose perimeter is 40 feet and whose area is 96 square feet.
525
views