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# a parabola has an axis of symmetry at x=-7, a maximum height of 4 and also passes through the point (-6,0). Write the equation of the parabola in vertex form. (answer)

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; definitively,...

# how do you factor polynomials this problem (answer)

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 our trinomial factors...

# Factor The expression completely (answer)

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 + y(y + 12))    Now, expand the expression inside the parenthesis: y4u3(36...

# 19-8d=d-17 how do i solve this? (answer)

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 necessary, I use it as a mean...

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 in feet/microsecond...

OK. Let's try again.  8/(x-2) + 8/(x+2) = 3  On the left side, the LCD is (x-2)(x+2): (8(x+2) + 8(x-2))/(x-2)(x+2) = 3     Also: (x-2)(x+2) = x2 - 4: (8x + 16 + 8x - 16)/(x2 - 4) = 3       Simplify the numerator and multiply both sides by the denominator: 16x = 3(x2 - 4)  or  16x...

# - 2/3x < 6 (answer)

If your inequality is: (-2/3)x < 6, then you just need to multiply both sides by the reciprocal of -2/3.  Since you're multiplying by a negative number, you need to flip the inequality sign: (-3/2)(-2/3)x > 6(-3/2) Now, simplify:   x > -9 Finally, you may need to graph the solution...

# I am struggling with a problem. I need to graph 6x + 3y > 18 on a typical 10 number graph. Can you help me? (answer)

I-   Solve for y:        3y > -6x + 18                                y > -2x + 6 II -  Draw the boundary line:  y = -2x + 6        (Since y is greater than, and not equal to, -2x + 6, this is a dotted line) III - Test any point away of the line to determine the shaded region.  For...