/*! 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 27 Find a number \(t\) such that th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 27

Find a number \(t\) such that the point \((t, 2 t)\) is on the line containing the points (3,-7) and (5,-15) .

Short Answer

Expert verified
The value of \(t\) that makes the point \((t, 2t)\) lie on the line containing the points (3,-7) and (5,-15) is \(t = \frac{5}{6}\).

Step by step solution

01

Find the equation of the line

To find the equation of the line, we'll first find the slope, which is given by the formula: \[m = \frac{y_2 - y_1}{x_2 - x_1}\] So, the slope of the line passing through (3,-7) and (5,-15) is calculated as: \[m = \frac{-15 - (-7)}{5 - 3} = \frac{-8}{2} = -4\] Now, let's use the point-slope form of the equation of a line, which is given by: \[y - y_1 = m(x - x_1)\] Using the point (3, -7) and the calculated slope -4, the equation of the line is: \[y - (-7) = -4(x - 3)\]
02

Simplify the equation

Let's simplify the equation to put it in the slope-intercept form (y = mx + b): \[y + 7 = -4(x - 3)\] \[y + 7 = -4x + 12\] \[y = -4x + 12 - 7\] \[y = -4x + 5\]
03

Substitute the coordinates of point \((t, 2t)\)

Now, let's substitute the coordinates of the point \((t, 2t)\) into the equation \(y = -4x + 5\): \[2t = -4t + 5\]
04

Solve for \(t\)

Now, let's solve the equation \(2t = -4t + 5\) for \(t\): \[2t + 4t = 5\] \[6t = 5\] \[t = \frac{5}{6}\] So, the value of \(t\) we are looking for is \(\frac{5}{6}\), and the point \((t, 2t)\) becomes \(\left(\frac{5}{6}, \frac{10}{6}\right)\), which lies on the line containing the points (3,-7) and (5,-15).

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

Write the indicated expression as a ratio of polynomials, assuming that $$ r(x)=\frac{3 x+4}{x^{2}+1}, \quad s(x)=\frac{x^{2}+2}{2 x-1}, \quad t(x)=\frac{5}{4 x^{3}+3} $$. $$ (r s)(x) $$

Find a number \(b\) such that 3 is a zero of the polynomial \(p\) defined by $$ p(x)=1-4 x+b x^{2}+2 x^{3} $$.

Find a polynomial \(p\) of degree 3 such that \(-2,-1,\) and 4 are zeros of \(p\) and \(p(1)=2\).

Explain why the composition of two polynomials is a polynomial.

Write the indicated expression as a ratio of polynomials, assuming that $$ r(x)=\frac{3 x+4}{x^{2}+1}, \quad s(x)=\frac{x^{2}+2}{2 x-1}, \quad t(x)=\frac{5}{4 x^{3}+3} $$. $$ (r \circ t)(x) $$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

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.