Domanda del libro di testo
Determine whether each equation defines y as a function of x. 2x + y^2 = 6
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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 7
Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (-2, -6) and (3, −4)
Guida verificata passo dopo passo1
Identify the coordinates of the two points: Point 1 is \((-2, -6)\) and Point 2 is \((3, -4)\).
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:
\[d = \sqrt{(3 - (-2))^2 + (-4 - (-6))^2}\]
Simplify inside the parentheses:
\[d = \sqrt{(3 + 2)^2 + (-4 + 6)^2}\]
which becomes
\[d = \sqrt{5^2 + 2^2}\]
Calculate the squares and write the expression under the square root:
\[d = \sqrt{25 + 4}\]
Then simplify the radical if possible, and finally round the result to two decimal places.
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Distance Formula
The distance formula calculates the length between two points in the coordinate plane. It is derived from the Pythagorean theorem and is given by √[(x2 - x1)² + (y2 - y1)²]. This formula helps find the straight-line distance between points (x1, y1) and (x2, y2).
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Solving Quadratic Equations Using The Quadratic Formula
Simplifying Radical Expressions
Simplifying radicals involves expressing a square root in its simplest form by factoring out perfect squares. This makes the answer more exact and easier to interpret before rounding. For example, √50 can be simplified to 5√2 by factoring 50 into 25 × 2.
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Rounding Decimal Numbers
Rounding is the process of approximating a number to a specified number of decimal places for clarity or practicality. In this problem, after simplifying the radical, the distance should be rounded to two decimal places to provide a clear, usable numerical answer.
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