Reflect about what you have learned from today's lesson as you answer the following question in your Learning Log. Title this entry "Representing Expressions on an Expression Mat" and include today's date . Using an Expression Mat, find two different ways to represent $x -1- (2x - 3)$ . Sketch the different representations and write a few sentences to describe the differences in the ways you built each representation.

"Rocket man" has a propulsion unit strapped to his back. He starts from rest on the ground, fires the unit, and is propelled straight upward. At a height of 16 m, his speed is 5.0 m/s. His mass, including the propulsion unit, has the approximately constant value of 136 kg. Find the work done by the force generated by the propulsion unit.

Solve each equation below. $\frac{5 x+4}{3}=\frac{2 x+1}{5}$

Determine whether the given value is a solution of the equation.

$$\frac{36}{x}=9 ; x=4$$

The line y = 7 is the perpendicular bisector of the segment with endpoints A(2,10) and B(2,k). What is the value of k? Explain your reasoning.

Find the volume of the solid E whose boundaries are given in rectangular coordinates. E is bounded by the circular cone $z=\sqrt{x^{2}+y^{2}}$ and z=1.

A local appliance store has decided on an advertising campaign utilizing newspaper and radio. Each dollar spent on newspaper advertising is expected to reach 50 people in the “Under $25,000” and 40 in the “Over$25,000” bracket. Each dollar spent on radio advertising is expected to reach 70 people in the “Under $25,000” and 20 people in the “Over$25,000” bracket. If the store wants to reach at least 100,000 people in the “Under $25,000” and at least 120,000 in the “Over$25,000” bracket, how should it proceed so that the cost of advertising is minimized? (a) Formulate a linear programming problem that models the problem. Be sure to identify all variables used. (b) Solve the linear programming problem. (c) Analyze the solution

Simplify each expression. $\left(\dfrac{3t^2}{5}\right)^2$

Estimate the value of each expression. $5\dfrac{1}{12}-2\dfrac{7}{9}$

use the quotient rule to derive $\frac{d}{d x}(\sec x)=\sec x \tan x$

What statement do you have to have in a value-returning function?

Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve

$$y = e ^ { x }$$

, and the line x = ln 2 about the line x = ln 2.

Members of Congress have from time to time argued in favor of a constitutional amendment that would require the federal government to maintain a balanced budget except in times of war. Discuss whether you think this would be a good idea. Be sure to explain the reasons for your point of view.

Quan and Kystal earned the same number of points playing the same video game. Quan played for 45 minutes and Krystal played for 30 minutes. Whose rate of points earned per minute was higher? Explain.