# Tutor profile: Josephine P.

## Questions

### Subject: Spanish

¿Qué son algunos países hispanos en el Caribe?

Algunos países hispanos en el Caribe son Cuba, la República Dominicana, y Puerto Rico.

### Subject: Geometry

Find the dimensions of the rectangle that has a length 3 meters more than its width and a perimeter equal in value to its area.

First, give the "length" and "width" of the rectangle variable to make it easier to set up an equation. For the purpose of this problem, we will let a = length and b = width. From the question, we see that a = b +3. Because a rectangle is a quadrilateral with two sets of equal sides, the equation for the perimeter can be set up as 2a + 2b = p. There are two different variable in this equation however, so to simplify, we know that the length, a, is equal to the width, b, + 3. 2a + 2b = 2(b+3) +2b. To find the area of this rectangle, the length and the width are multiplied, (a)(b). Similar to what was done for finding the perimeter, substitute the expression that represents length, b + 3, in for a. The result is (b+3)(b). The resulting expressions for perimeter and area, respectively, when simplified, are 4b + 6 and (b^2) + 3b. The area and perimeter are equal in value according to the question, so these two expressions should be set equal to each other. The result should be a quadratic equation, 0 = (b^2) - b + 6, with roots at b = 3 and b = -2. Distance cannot have a negative value, so the value of the width must equal 3, and the value of the length must equal 6 (3 + 3).

### Subject: Algebra

Find all the rational zeros of P(x) = x^3 - 7x + 6

First, identify the leading coefficient and the constant, and determine the factors of both. Leading coefficient = 1; Factors = 1, -1 Constant = 6; Factors = 1, -1, 2, -2, 3, -3, 6, -6 These factors are the POSSIBLE rational zeros of this equation. To determine the actual rational zeros, each factor must be substituted into the above equation, and the result of the substitution must equal zero. For this particular example, the rational zeros are: x = 1, x = 2, and x = -3.

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