Textbook Question
In Exercises 21–28, divide and express the result in standard form. 5i/(2 - i)
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Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- 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
Chapter 2, Problem 25
A rectangular soccer field is twice as long as it is wide. If the perimeter of the soccer field is 300 yards, what are its dimensions?
Verified step by step guidance1
Let the width of the soccer field be represented by \(w\) yards.
Since the length is twice the width, express the length as \$2w$ yards.
Recall the formula for the perimeter of a rectangle: \(P = 2 \times (\text{length} + \text{width})\).
Substitute the given perimeter and expressions for length and width into the formula: \(300 = 2 \times (2w + w)\).
Simplify the equation and solve for \(w\), then use the value of \(w\) to find the length \$2w$.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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 is essential to relate the given perimeter to the dimensions of the soccer field.
Algebraic Representation of Relationships
Translating the problem's conditions into algebraic expressions is crucial. Here, the length is twice the width, so L = 2W. This relationship allows substitution into the perimeter formula to form an equation with one variable.
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Solving Linear Equations
Once the equation is set up, solving for the unknown variable involves combining like terms and isolating the variable. This step yields the width, which can then be used to find the length, providing the field's dimensions.
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Related Practice
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Solve each equation in Exercises 15–34 by the square root property.
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Textbook Question
Solve and check each linear equation. 25 - [2 + 5y - 3(y + 2)] = - 3(2y - 5) - [5(y - 1) - 3y + 3]
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Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 2x/3 = 6 - x/4
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In Exercises 15–26, use graphs to find each set. [3, ∞) ⋃ (6, ∞)
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Divide and express the result in standard form. 8i/(4 - 3i)
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