Solving Word Problems with Proportions and Relative Comparisons These word problems are set-up where the dependent variable is not provided as is, but rather as a part of an operation. You will have to set-up each side of the equality with its own operations. Example 1: “Shelley finished x number of her math homework problems before dinner. Had she finished 3 more, she would have... read more
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Word Problems with Multiple Variables and Given Values This type of problem will be presented such that you'll have to set-up the equation or relation between the variables. Additionally, you will be given the value of one or more variables. On all of these problems you are not asked to solve the problem, only set-up the equation. Example 1: “A weather balloon is launched from a height of 100... read more
Writing Expressions Involving Rate of Change These real-world problems can be best translated when broken down into their components (variables and operations). When you see the words “is” or “are”, this is the points where you set-up the equality. Whenever you see the word “per”, “each” the implication is a multiplication. This indicates the rate of change between the variables. The... read more
Solving Proportions By definition, ratios must be the same in order for them to be proportionate. Using the process of cross-multiplication we are able to prove if any given set of fractions are proportionate. In solving proportions, you use the same process. In these problems, you are trying to find the value which makes the fractions proportionate. Example 1: 3/n and 5/15 Step... read more
DEFINITIONS When given two ratios (in the form x:y) or two relations (in the form of fractions), if the ratios of each element are the same they're said to be proportionate. Example: 3/6 and 1/2 are proportionate because 3 out 6 is the same as 1 out of two (half). PROVING PROPORTIONALITY When given two fractions to prove as proportionate, such as 1 and 3 2 6 you... read more
Algebra Word Problems, Part II: Real World Problems. In this type of world situations, you will need to establish every variable in the situation as well as all fixed values. You generally will be given a relationship between the variable or variables. Example 1: “Richard wants to buy a shirt that is on sale for 20% off the regular price. Write the expression which represents... read more
Algebra Word Problems: Translating simple comparisons. In this first entry, I will cover the simplest of problems presented to students. These are usually expressed as comparisons between two numbers involving one or more operations. Example 1: “Two more than three times a number”. Translating these is best done by breaking each element of the phrase. Visualize this using parentheses: “ Two more... read more
DEFINITIONS DOMAIN describes all the independent values in a function. RANGE describes all the dependent values in a function. DISCRETE FUNCTIONS Discrete functions are derived from sets of data which have gaps in them. As such they are described by sets of ordered pairs (x, y). The domain and range of these functions are described in brackets with each individual... read more
what is x+y=2 2x=y=-1 (answer)
I'm assuming your system looks like this (since you have two = signs on the right) : x + y = 2 and 2x - y = - 1 To solve this, you need to find the point where both equations meet. SOLVING THROUGH ELIMINATION When solving through elimination, you want to make sure the variables...
Do the equations x = 4y + 1 and x = 4y – 1 have the same solution? How might you explain your answer to someone who has not learned algebra? (answer)
They do not. The last operation in each function (add one; and, subtract one) are different, creating different results for solutions. i.e. if you select begin with y = 0, then the solutions for each are as follows: x = 4y + 1 x = 4y - 1 x = 4(0) + 1...
To answer Nataliya's question regarding the difference between "Slope Intercept Form" and "Point-Slope Form": They're the same thing; only written differently. Let's work the problem using Point-Slope Form. Start with slope formula m = (y2 - y1) / (x2 - x1 ). m = ( 2 - 1 ) / ( 4...
factor 5x cubed minus 45x (answer)
Start with: 5x3 - 45x. You can factor out every term starting with constants; in this case 5. 5 ( x3 - 9x) Next step, factor out the x so 5x (x2 - 9) Using FOIL, you can then factor out the term in the parenthesis (x2 - 9). Note there is no x term...