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Chapter 3: Q. 19 (page 171)

In Problems 7–22, solve each inequality.

4x2+9<6x

Short Answer

Expert verified

The given inequality has no solution.

Step by step solution

01

Step 1. Given Information

The given inequality is4x2+9<6x.

02

Step 2. Find the Intercepts

  • Rewrite the inequality in standard form.

4x2+9-6x<0

  • There are no real roots of 4x2+9-6x=0, so, there are no x-intercepts of the curve.
  • The value of f(0)=9.
  • So, the y-intercept is (0,9).
  • Find x=-b2a to find the x - intercept of the vertex of parabola.

x=68

  • The value of f68=274.
  • So, the vertex is68,274.
03

Step 3. Plot the Graph

  • Plot the parabola on a graph using the vertex and intercepts calculated in the previous step.

04

Step 4. Find the region below x-axis

  • From the graph, there is no region that lies below the x-axis.
  • So, the given inequality has no solution.

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Most popular questions from this chapter

In Problems 21–28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line .

xy=f(x)
-2-4
-10
04
18
212

Match each graph to one the following functions.

f(x)=x2-2x+1

Graph the function fby starting with the graph of y=x2and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.

Hint: If necessary, write fin the form f(x)=a(x-h)2+k.

f(x)=3x2+6x

For the graph of the linear function f(x)=mx+bmis the_______

and bis the_______.

In Problems 21–28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.

xy=f(x)
-2-4
-1-3.5
0-3
1-2.5
2-2
See all solutions

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