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¶ … linear equation and a linear inequality be solved in the same way? Explain why. What makes them different? Team B
A linear equation and a linear inequality can be solved the same except for very specific scenarios: one flips the inequality sign whenever multiplying or dividing by a negative (Staples, 2012). What makes them different is that the answer will not be a single number, but a range of numbers.
Stapel, E. (2012). Solving inequalities: An overview. Retrieved November 11, 2013 from Purplemath.com website: http://www.purplemath.com/modules/ineqsolv.htm
What are the four steps for solving a problem? Should any other factors be accounted for when solving a problem? Should any factors be accounted for when explaining how to solve a problem? Explain your answer.
The four steps for solving a problem are to: remove grouping symbols, clear fractions, isolate the unknown variable on one side, and check the answer. Removing grouping signals involves combining like terms. Clearing fractions involves finding the lowest common denominator and multiplying by it through the entire equation. Isolating the unknown variable means getting the variable (generally an x) on its own on one side of the equation, generally through a combination of addition, subtraction, multiplication, or division. Finally, one...
What does the slope of this line represent? How is this graph useful? Provide another example for your colleagues to explain. Team B
The slope of the line represented by (x, y) (hours, feet) would be the rise (change in y) over the run (change in x). Therefore, the line would represent the change in feet over the change in hours. Feet over hours represents the speed of the person walking in terms of feet per hour. Another example would be to represent as y the calories burned in Kcal a person burns per x minute of a particular aerobic activity.
If a line has no y-intercept, what can you say about the line? What if a line has no x-intercept? Think of a real-life situation where a graph would have no x- or y-intercept. Will what you say about the line always be true in that situation? Team B
If a line has no y-intercept, then the line does not cross the y-axis. It is therefore a vertical line and the equation for the line will be x=some number, but that number will not be zero. If a line has no x-intercept, then the line does not cross the x-axis. It is therefore a horizontal…
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
Math Inequalities Ozark furniture has 3000 board feet of lumber to manufacture their rockers. The classic rocker (C) takes 15 board feet of lumber. The modern rocker (M) takes 12 board feet of lumber. The linear inequality that results when one combines these two variables with the amount of lumber available to Ozark furnitures is: 15C + 12M
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
They must also solve polynomial, exponential and logarithmic equations both analytically and graphically. Standard 4: Students must be able to understand and use matrices to perform basic operations. This includes addition, subtraction, multiplication and inversion of matrices. They must also be able to identify the appropriate methods and technology to accomplish this. In addition, students must demonstrate the ability to find the inverses of two-by-two matrices without only with the
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
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