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The numbers are converted into a point, and that point is used as a test point to see if they fall within the shaded area of the graph. If the test point is in shaded area, the combination can fit. If the test point is outside of the shaded area, then the combination will not work. This can also be determined by plugging the numbers into the equation for the linear equality, which can provide more precise answers than a quick visual assessment from a graph, particularly if the point is close to the line created by the linear inequality.
The first question asked is: will the truck hold 71 refrigerators and 118 TVs? Those numbers are plugged into the equation y = ? -3x + 330. The number sentence resulting is: 118 ? -3(71) + 330? Simplified, that sentence reads 118 ? 117. Clearly that is false. Therefore, the truck cannot hold that combination of TVs and refrigerators. Instead, if there are 71 refrigerators, the truck can hold up to 117 TVs, but not 118.
Next, the text asks whether the truck will hold 51 refrigerators and 176 TVs? The resulting number sentence becomes 176 ? -3(51) + 330. Simplified, that reads 176 ? 177. This is a true...
Therefore, the truck will hold that combination of TVs and refrigerators.
The next question asks how many TVs it could buy if the Buy More will purchase a maximum of 60 refrigerators. The order will contain between 0 and 60 refrigerators. The maximum number of TVs would be based on 0 refrigerators in the shipment and would be 330, as determined in the first paragraph. The maximum number of TVs that would ship if Buy More purchased its stated maximum number of refrigerators for this order would be based on using 60 refrigerators. The answer for that is 150 TVs. This would not change the graph of the linear inequality, but it would cause a line, parallel to the y-axis to drop down from the point where x-60 to indicate that no answers beyond that line where within the solution set for the new conditions.
If the Burbank Buy More orders a minimum of 200 TVs, the maximum number of refrigerators is not figured by looking at a zero order, but by setting 200 as the new minimum. The resulting number sentence reads: 200 ? -3x + 330. Solving for x yields 43.3, but refrigerators are shipped as whole units, providing an…
Equation Examples Solving Linear Equations subtract divide by Solving Linear Equations (including fractions) (1/2)x = 4 + x multiply by (2/1) or x = 8 + 2x subtract subtract x -8 = x, or x = -8 Solving Inequalities 4x > divide by Intro to Functions f (x) = 7x + 9 evaluate for x = 3 solve arithmetic f (3) = 30 Finding Slope A line passes through (-5, 7) and (10, 17) Find the rise (y2 -- y1) Find the run (x2 -- x1) Slope = rise/run Finding the Equation
Students will present their findings to the class. 2. In groups, students will graph population growth and predict future trends using exponential functions (Ormond 2010). A data set is available at: http://serc.carleton.edu/files/quantskills/events/NAGT02/quantskillsworldpop.pdf. Students will discuss the political and environmental implications of their findings. 3. Students will perform an exercise using exponential functions graphing increases in atmospheric CO2 concentrations (Ormond 2010). A data set is available at: http://serc.carleton.edu/files/quantskills/events/NAGT02/co2moe2edit.pdf Students will discuss the political
At which point, the students would begin studying composition of functions to verify each other. There will be a brief period of one day, to review the information that was covered during the quarter. (Cox, 2006) In the first week of August, is when a comprehensive review will take place, covering everything that was presented in the year and preparing students, for their achievement as well as quarterly examinations. At
National and State Subject Matter Content Standards for Math According to the California standards for high school students, the geometry curriculum contains six critical components: "to establish criteria for congruence of triangles based on rigid motions; establish criteria for similarity of triangles based on dilations and proportional reasoning; informally develop explanations of circumference, area, and volume formulas; apply the Pythagorean Theorem to the coordinate plan; prove basic geometric theorems; and
Synthetic Financial Instruments The price of a reset strike call when the initial value of the stock is a is greater than or equal to a vanilla European strike call and the price of a reset strike put when the initial value of the stock is a is greater than or equal to a vanilla European strike put (as expressed in the cited equation) for all values of S. The style of
Once the concept of factoring is understood, technology can be used to assist the students with solving quadratic equations and equalities. The website (http://www.coolmath.com/algebra/) will be references, but the students will have to write explanations showing that they understand how at least two homework problems were solved. 4. By the time we are ready to learn inverse functions, students will have a review of everything learned during the school year