/*! 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 12 Isabel said it would take her at... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 12

Isabel said it would take her at least an hour and a half, but no more than 2 hours, to finish her homework. Write an inequality to express the number of hours, \(h\), Isabel thinks it will take to do her homework.

Short Answer

Expert verified
\[ 1.5 \leq h \leq 2 \]

Step by step solution

01

- Understand the Range of Time

Isabel believes it will take her between 1.5 hours and 2 hours to finish her homework. This means we need to establish these two values as the bounds within which the time required lies.
02

- Define the Variable

Let the variable representing the number of hours Isabel will spend on her homework be denoted by the symbol 'h'.
03

- Write the Inequality

To represent that the homework time 'h' is at least 1.5 hours and no more than 2 hours, use the inequality: \[ 1.5 \leq h \leq 2 \]

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

solving inequalities
represents 'less than or equal to').
range of values
The range of values is the set of all possible numbers that a variable can take. In the context of inequalities, this range is determined by the boundaries set by the inequality. For the exercise, Isabel estimates her homework will take between 1.5 and 2 hours. This means the range of values for the variable \(h\) (time) falls within this window.

Specifically, \(1.5 \leq h \leq 2\) indicates:
  • The smallest possible value for \(h\) is 1.5 hours.
  • The largest possible value for \(h\) is 2 hours.
Understanding the range of values helps us see all the possible times that satisfy the condition. It鈥檚 crucial to include the boundary values (using \(\leq\)) if they are part of the solution.
algebraic expressions
Algebraic expressions are combinations of numbers, variables, and operators. In our inequality, the algebraic expression is \(1.5 \leq h \leq 2\). This expression tells us how the variable \(h\) (homework time) is related to the bounds. Here, the variable \(h\) represents the hours Isabel will spend on homework, and \(\leq\) represents 'less than or equal to'.

When forming algebraic expressions for inequalities:
  • Identify the variable that represents the unknown (in this case, \(h\)).
  • Determine the bounds or limits based on the problem鈥檚 context.
  • Combine them into a logical statement (inequality).
Well-formed algebraic expressions make it easier to grasp the essence of the problem and solve it effectively.
mathematics education
Mathematics education is all about helping students understand and apply various mathematical concepts. Algebra and inequalities are core components that build a foundation for more advanced topics. By learning to solve inequalities, students develop critical thinking and problem-solving skills.

In the context of this exercise, understanding how to form and manipulate inequalities:
  • Teaches how to translate real-world scenarios into mathematical statements.
  • Provides a structured approach to find solutions within given constraints.
  • Promotes analytical thinking by analyzing the range of possible values.
Educators should emphasize these concepts using similar, relatable problems to enhance students' comprehension and keep them engaged in mathematics.

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

Solve each equation by backtracking. (Backtrack mentally if you can.) Check your solutions. $$ 3\left(\frac{m}{6}-4\right)=12 $$

An object that is dropped, like one thrown upward, will be pulled downward by the force of gravity. However, its initial velocity will be \(0 .\) If air resistance is ignored, you can estimate the object's height \(h\) at time \(t\) with the formula \(h=s-16 t^{2},\) where \(s\) is the starting height in feet. a. If a baseball is dropped from a height of 100 \(\mathrm{ft}\) , what equation would you solve to determine the number of seconds that would pass before the baseball hits the ground? b. Solve your equation.

For each table, tell whether the relationship between x and y could be linear, quadratic, or an inverse variation, and write an equation for the relationship. $$ \begin{array}{|c|c|c|c|c|c|}\hline x & {0.5} & {2} & {4} & {5} & {20} \\\ \hline y & {5} & {1.25} & {0.625} & {0.5} & {0.125} \\ \hline\end{array} $$

Physical Science A ball is launched straight upward from ground level with an initial velocity of 50 feet per second. Its height \(h\) in feet above the ground \(t\) seconds after it is thrown is given by the formula \(h=50 t-16 t^{2} .\) a. Draw a graph of this formula with time on the horizontal axis and height on the vertical axis. Show \(0 \leq t \leq 4\) and \(0 \leq h \leq 40 .\) b. What is the approximate value of \(t\) when the ball hits the ground? c. About how high does the ball go before it starts falling? d. After approximately how many seconds does the ball reach its maximum height?

Solve each inequality. $$5(e-2)>10$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Mechanics 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.