He draws the triangle on a coordinate plane and finds that it has vertices at 2, 13, 4 and 1, 4. Find the area of the triangle. Mixed Problem Solving For mixed problem-solving practice, see page

You can put this solution on YOUR website! Vertical asymptotes occur for x values that make the denominator of the simplified fraction zero.

So we start by factoring the numerator and denominator: This is all the factoring that can be done. And, as we can see, there are no common factors to cancel. So we now determine what values for x will make the denominator zero. Having the denominator factored helps in this. The only way can be zero is if one or more of the factors is zero.

So or With some thought we should be able to realize that can never be zero! But the square of no real numbers would be negative. Therefore the only x value that makes the denoimnator zero is zero itself.

We have one vertical asymptote: Horizontal and Oblique Asymptotes. To find them we need to be able to analyze the function for these large values of x.

So we will use some Algebra on the function to transform it into a form which we can better determine what happens for large values of x. The steps of this transformation are these: If the degree of the numerator is equal to or greater than the degree of the denominator, then use long division to divide the fraction.

At this point, the only fraction with x in the denominator that remains should have a numerator whose degree is less than the degree of the denominator. Let's try this on your function. Divide if the degree of the numerator is greater than or equal to the degree of the denominator.

The degrees of your numerator and denominator are 4 and 3 respectively. So we need to divide, using long division: Multiply the numerator and denominator of the fraction by the reciprocal of the largest power of x in the fraction.

The largest power of x in this fraction is so we'll multiply by " Now we have a form we can analyze to see what happens when x becomes a very large number.

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Look at all the "little" fractions within the big fraction. As x becomes a very large number, these "little" fractions become very small. The larger x gets the smaller these "little" fractions get. In fact these "little" fractions will become very close to zero in value.However, we can write the length in terms of the width as [latex]L=W+3[/latex].

Substitute the perimeter value and the expression for length into the formula. It is often helpful to make a .

A 4 x x Aligning common factors can help you find the greatest common factor of two or more terms. 4x 2 = 2 2 x x Find the GCF. 3x = 3 x 4x(x) - 3 (x) x (4x - 3) Check x(4x - 3) 4x x x The GCF of 4 x 2 and 3x .

Factor out the GCF. 2. Identify the number of terms. 4 terms: Factor by grouping either 2 terms with 2 terms or 3 terms with 1 term. Write an expression in terms of x that represents the area Perfect square trinomial: 9x2 ϩ 6x ϩ 1 ϭ (3x ϩ 1)2 3 terms: If the trinomial is a perfect square trinomial, 2x2 ϩ 11x ϩ 5 (2x ϩ 5)(x ϩ.

Factor out the GCF from the first pair of terms. factor out the greatest common factor. 2x 5x 3y 6y 4 13 For Exercises 1–2. 1. Factor out the GCF or its opposite from the second pair of terms.

6x2 7. May 03, · The formula for the area of a trapezoid is A = (1/2)h(b 1 + b 2).Express b 1 in terms of A, h, and b The area of a trapezoid is 60 square feet, its height is 6 ft, and one base is 12 ft.

Find the number of feet in the other base. So with your denominator,, we need to multiply by its conjugate,, to get a denominator made up of perfect square terms.

And, of course, we will have to multiply the numerator by the same thing: And, of course, we will have to multiply the numerator by the same thing.

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