/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 7 Find the distance between each p... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 7

Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places. $$(-2,-6) \text { and }(3,-4)$$

Short Answer

Expert verified
The distance between the points \((-2,-6)\) and \((3,-4)\) is approximately 5.39 units.

Step by step solution

01

Understand the Distance Formula

The Distance Formula is derived from the Pythagorean theorem and is used to find the distance between two points in a plane. The formula is \(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\) where \((x_1,y_1)\) and \((x_2,y_2)\) are the coordinates of the two points.
02

Apply the Distance Formula

Substitute the given points into the formula. For the points \((-2,-6)\) and \((3,-4)\), the formula becomes \(d = \sqrt{(3-(-2))^2 + ((-4)-(-6))^2}\). Simplifying inside the brackets gives \(d = \sqrt{(5)^2 + (2)^2}\).
03

Simplify the Expression

The expression under the square root becomes \(d = \sqrt{25 + 4}\), which simplifies to \(d = \sqrt{29}\).
04

Express the Answer in Decimal Form

To express the distance in decimal form, calculate the square root of 29 to get \(d 鈮� 5.39\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. To avoid sign errors when finding h and k, I place parentheses around the numbers that follow the subtraction signs in a circle鈥檚 equation.

How is the standard form of a circle鈥檚 equation obtained from its general form?

Give an example of a circle鈥檚 equation in standard form. Describe how to find the center and radius for this circle.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I have two functions. Function \(f\) models total world population \(x\) years after 2000 and function \(g\) models population of the world's more-developed regions \(x\) years after \(2000 .\) I can use \(f-g\) to determine the population of the world's less-developed regions for the years in both function's domains.

Express the given function \(h\) as \(a\) composition of two functions \(f\) and \(g\) so that \(h(x)=(f \circ g)(x)\). $$h(x)=(3 x-1)^{4}$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.