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Give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. (x+3)² + (y - 2)² = 4
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Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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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 3, Problema 45
After a 30% price reduction, you purchase a 50″ 4K UHD TV for \$245. What was the television's price before the reduction?
Guida verificata passo dopo passo1
Let the original price of the television be represented by the variable \(P\).
Since the price was reduced by 30%, the sale price is 70% of the original price. This can be written as the equation: \(0.70 \times P = 245\).
To find the original price \(P\), divide both sides of the equation by 0.70: \(P = \frac{245}{0.70}\).
Simplify the right side of the equation to express \(P\) in terms of a numerical value (do not calculate the final number).
The result from the previous step will give you the original price of the television before the 30% reduction.
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Percentage Decrease
A percentage decrease represents how much a quantity is reduced relative to its original amount, expressed as a percent. In this problem, a 30% price reduction means the new price is 70% of the original price, since 100% - 30% = 70%.
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Original Price Calculation
To find the original price before a percentage decrease, divide the reduced price by the remaining percentage (expressed as a decimal). Here, dividing $245 by 0.70 gives the original price before the 30% reduction.
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Decimal and Percentage Conversion
Percentages are often converted to decimals for calculations by dividing by 100. For example, 30% becomes 0.30, and 70% becomes 0.70. This conversion is essential for multiplying or dividing when solving percentage problems.
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