Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Q. 20 (page 171)

In Problems 7–22, solve each inequality.

25x2+16<40x

Short Answer

Expert verified

The inequality has no solution.

Step by step solution

01

Step 1. Given information

The given inequality is25x2+16<40x.

02

Step 2. Find the Intercepts and Vertex

  • Express the inequality in standard form.

25x2-40x+16<0

  • Factor the function f(x)=25x2-40x+16.

localid="1646159236427" f(x)=(5x-4)2

  • So, the x-intercept of the function is 45,0.
  • The value of f(0)=16.
  • So, the y-intercept is (0,16).
  • Find x -coordinate of the vertex by using the formulax=-b2a.

x=4050=45

  • The value of f45=0.
  • So, the vertex of the parabola is45,0.
03

Step 3. Graph the function

  • Plot f(x)on a graph by using the intercepts and the vertex.

04

Step 4. Find the region below x-axis

The function f(x)is on or above the horizontal axis, so the given inequality has no solution.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

In Problems 25–32, use the given functions f and g.

(a)f(x)=0(b)g(x)=0(c)f(x)=g(x)(d)f(x)>0

(e)g(x)≤0(f)f(x)>g(x)(g)f(x)≥1

f(x)=-x2+3g(x)=-3x+3

Graph the function fby starting with the graph of y=x2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.

f(x)=(x+2)2-2

The graph of a quadratic function is called a _________.

Make up a quadratic function that opens down and has only one x-intercept. Compare yours with others in the class. What are the similarities? What are the differences?

If g(x)=5x-4,then

(a) Determine the slope and y-intercept of each function.

(b) Use the slope and y-intercept to graph the linear function.

(c) Determine the average rate of change of each function.

(d) Determine whether the linear function is increasing, decreasing, or constant
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

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.

Sign-up for free