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## Lesson 2 Homework Practice Numerical Expressions Answers Fixed

Lesson 2 Homework Practice Numerical Expressions Answers Fixed

As a group, students can also generate factorizations of expressions: (x + 2)(x + 3) = (x + 6)x + 2x + 9. In fact, they can do this with the quadratic equation a x2 + b x 2 + c = 0, which is the case for expressions a = 3, b = 7, and c = -2. Adding the constant to the variable, they can factor x out to get x(a x 2 + b x 2 + c = 0). When students use expressions to factor and then replace that factor with x, the resulting expression is equal to a x2 + b x 2 + c. Once students grasp this, they should be able to use it to factor and simplify other expressions. For example, they could factor the quadratic, with a = 2 and b = 3, to get x(x2 + c) = x(x2 + 9) = x(x2 + 3)(x + 3), and then replace x with -3 to get x(-3)(x2 + 9) = x(-3)2 + 3x - 27, and finally replace the 2 with x so that it becomes 3x - 27.

To make this concrete, we will construct an expression that is not equivalent to any other expression. Students will evaluate the expressions for the same input value. When they are done, they will be able to compare the expressions, but not to replicate the expressions. Once they have a concrete understanding of the concept, they will be able to explain that a variable is really about position, and that, because the expressions are different, the variable must be different.

At some point, students will decide to compare expressions visually. They will want to compare the two expressions by inserting the same number into each. They will realize that the expressions are equivalent, which will make them reflect on the role of the variable. In doing so, they will begin to see that the value of a variable is not just a number, but a vector. The value is not really about the number, but about the position of the value of the variable in the expression. The position of the value of the variable in the expression is what determines the meaning of the expression.

Peer Group Questions – Think about the size of the private equity firm and the industry you are applying to. How did the firm decide to go with that size? Can you think of a situation where a firm would consider a different size? What kind of questions would you ask to determine whether a particular size or industry is right for you?

To decide which one should you opt for, one needs to look at the business as a whole. Doing so will give a better understanding of how the business functions, how profitable it is, how the management team is doing and what problems it might face in the future. It also helps to determine if there are any other reasons as to why you should or shouldn’t be interested in the company. Companies with a higher ROE are considered more attractive as well as have a higher Return on invested capital (ROIC). This helps determine if you need to invest in the company. 827ec27edc