According to the first law of thermodynamics, the energy given off in a chemical reaction can be converted into heat, work, or a mixture of heat and work.
Questions Eliciting Thinking Can you reread the first sentence of the second problem? A difference is described between two values.
What are these two values? What is the difference? Do you know whether or not the temperature on the first day of the month is greater or less than 74 degrees? Why is it necessary to use absolute value symbols to represent the difference that is described in the second problem?
Instructional Implications Model using absolute value to represent differences between two numbers. For example, represent the difference between x and 12 as x — 12 or 12 — x. Emphasize that each expression simply means the difference between x and Evaluate the expression x — 12 for a sample of values some of which are less than 12 and some of which are greater than 12 to demonstrate how the expression represents the difference between a particular value and Guide the student to write an equation to represent the relationship described in the second problem.
Ask the student to solve the equation and provide feedback.
Then explain why the equation the student originally wrote does not model the relationship described in the problem. Ask the student to consider these two solutions in the context of the problem to see if each fits the condition given in the problem i.
Provide additional opportunities for the student to write and solve absolute value equations. Examples of Student Work at this Level The student: Finds only one of the solutions of the first equation.
Writes the solutions of the first equation using absolute value symbols. Questions Eliciting Thinking How many solutions can an absolute value equation have? Do you think you found all of the solutions of the first equation? What are the solutions of the first equation?
Should you use absolute value symbols to show the solutions? Instructional Implications Provide feedback to the student concerning any errors made. If needed, clarify the difference between an absolute value equation and the statement of its solutions.
Got It The student provides complete and correct responses to all components of the task. Examples of Student Work at this Level The student correctly writes and solves the first equation:Algebra Examples. Step-by-Step Examples. Write in Standard Form.
Multiply by to make the denominator of real. Combine. Expand using the FOIL Method. Tap for more steps Apply the distributive property. Apply the distributive property. Apply the distributive property. Remove parentheses. Standard Form; Writing Equations of Lines; Linear Inequalities with Two Variables; using the symmetry of absolute value functions to our advantage.
We know (5, 3) is one point to the right of the vertex; if we go one point to the left of the vertex, Write an equation of the graph shown.
The vertex is (0, 3). This means the beginning of. IntroductionOver the last decade numerous accounting papers investigate the empirical relation between stock market values (or changes in values) and particular accounting numbers for the purpose of assessing or providing a basis of assessing those numbers’ use or proposed use in an accounting standard.
We can use the absolute value's symmetry to find another point: x = 0 is one step to the right of the vertex, so one step to the left of the vertex (x = -2) will also equal.
Looking at our graph, we totally could have picked x = 4 to multiply the fraction away, making everything a zillion times easier. Solving absolute value equations and inequalities.
$$\left | a \right |$$ And represents the distance between a and 0 on a number line. An absolute value equation is an equation that contains an absolute value expression. The equation Writing linear equations using the point-slope form and the standard form; Parallel and perpendicular.
Given a circle on the coordinate plane, Sal finds its standard equation, which is an equation in the form (x-a)²+(y-b)²=r².