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Christy, a segment that goes from a vertex of a triangle and is perpendicular to its opposite side is called...?  Yes!  The height. So, if segment CD is the height of ΔABC, and D lies on line AB, then Line CD is perpendicular to side AB.  Then the fence that you intend...

Perhaps this function should be written: p(x)=(-4x-1)/(x-5) If this is the case, then, what is the vertical asymptote (VA)?   Remember... the denominator can not be equal to 0.  So... what value of x will make x-5=0?  That vertical line will be your VA: x=? Now,...

This is the deal:   Since the axis of symmetry is a vertical line, x = -7 and the parabola has a maximum height of 4 units above the x axis; we can safely conclude that it opens down and its vertex is at (-7, 4). Besides, it passes through the point (-6, 0), which is below the vertex;...

Organize your polynomial in 2 groups: (3p^3 - 21p^2) - (p - 7) Now, factor the first group by GCF: 3p^2(p - 7) - (p - 7) Notice that (p - 7) is a common factor, then factor again by GCF: (p - 7)(3p^2 - 1) Finally, rearrange your answer: (3p^2 - 1)(p - 7)

b2 + 5b + 6 = 0 This trinomial may be factored as the product of two binomials if we find two numbers such that: - Their product is equal to 6, and - Their sum is equal to 5 These two numbers indeed exist: they are 3 and 2: (3)(2) = 6; and (3)+(2) = 5 Then...

36y4(y + 12)3 + y5(y + 12)4 Let (y + 12) = u   Now rewrite the expression: 36y4u3 + y5u4     GCF: y4u3   y4u3(36 + yu)   Now, for the sake of simplicity, revert u=(y+12) inside the parenthesis only: y4u3(36...

19-8d = d-17   I advise my students to start with the unknown (d).  If you eliminate the smaller one, you will deal with positive values.  So, let's eliminate -8d; how? add 8d on both sides of the equal sign: 19-8d+(8d) = d-17+(8d)   The parenthesis are not...

Assuming the Transverse axis is horizontal and the center of the hyperbole is the origin, the foci are: A(250, 0) and B(-250, 0) ; thus c = 250 Now, let's figure out how far appart is P from A and B.  This is the fun part.  Ready?  OK. Since the speed of the signal is given...