Textbook Question
In Exercises 11–26, determine whether each equation defines y as a function of x. x + y = 16
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Ch. 2 - Functions and Graphs
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 3, Problem 11
Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (3.5, 8.2) and (-0.5, 6.2)
Verified step by step guidance1
Identify the coordinates of the two points: Point 1 is (3.5, 8.2) and Point 2 is (-0.5, 6.2).
Recall the distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]
Substitute the given coordinates into the formula:
\[d = \sqrt{(-0.5 - 3.5)^2 + (6.2 - 8.2)^2}\]
Simplify the expressions inside the parentheses:
Calculate \((-0.5 - 3.5)\) and \((6.2 - 8.2)\), then square each result.
Add the squared values and take the square root of the sum to find the distance. If possible, simplify the radical before rounding to two decimal places.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Distance Formula
The distance formula calculates the length between two points in the coordinate plane. It is derived from the Pythagorean theorem and given by d = √[(x2 - x1)² + (y2 - y1)²], where (x1, y1) and (x2, y2) are the coordinates of the points.
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Simplified Radical Form
Simplified radical form means expressing a square root in its simplest form by factoring out perfect squares. This helps present answers in an exact form before approximating decimals, ensuring clarity and precision in mathematical solutions.
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Rounding Decimals
Rounding decimals involves approximating a number to a specified number of decimal places. In this problem, answers are rounded to two decimal places, which means keeping two digits after the decimal point and adjusting the last digit based on the next digit.
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Related Practice
Textbook Question
Use the graph of y = f(x) to graph each function g.
g(x) = ½ f(x)
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Textbook Question
Find the domain of each function. f(x) = 1/(x2+1) - 1/(x2-1)
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Textbook Question
Use the given conditions to write an equation for each line in point-slope form and general form. Passing through (4, −7) and perpendicular to the line whose equation is x − 2y – 3 = 0
Textbook Question
The functions in Exercises 11-28 are all one-to-one. For each function, a. Find an equation for f-1(x), the inverse function. b. Verify that your equation is correct by showing that f(ƒ-1 (x)) = = x and ƒ-1 (f(x)) = x. f(x) = x +3
Textbook Question
Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope = 2, passing through (3, 5)