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26 Cards in this Set
- Front
- Back
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Subtract. (14x3y2 - 5xy + 14y) - (7x3y2 - 8xy + 10y)
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Distribute the negative sign
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Multiply. (4x - 7xy)(2y + 3x)
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4x • 2y = 8xy First4x • 3x = 12x2 Outer−7xy • 2y = −14xy2 Inner−7xy • 3x = −21x2y Last
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Multiply. (9b - ab)(5a2b + 7ab - b) |
Distribute and then combine LIKE terms. |
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A quadratic equation in x is an equation that can be written in the standard form |
ax2+bx+c=0 |
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Solve (x-2)2+8=0 . Find real solutions only! |
(x-2)2=-8 (x-2)=+-sqrt-8 x=+-(2i)(sqrt2)+2 x=(2i)(sqrt2)+2 there are no REAL solutions |
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ax2 + bx + c = 0 |
{-b \pm \sqrt{ b^2 -4( a)(c)} }{2(a)}\ |
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When solving inequalities, if you multiply or divide through by a negative, you must |
flip the inequality sign. |
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Solve 10 < 3x + 4 < 19. |
This is what is called a "compound inequality". It works just like regular inequalities, except that it has three "sides". So, for instance, when I go to subtract the 4, I will have to subtract it from all three "sides".10 < 3x + 4 < 19 6 < 3x < 15 2 < x < 5 |
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The velocity of an object fired directly upward is given by V = 80 - 32t, where t is in seconds. When will the velocity be between 32 and 64 feet per second? |
32 < 80 - 32t < 64 32 - 80 < 80 - 80 - 32t < 64 - 80 -48 < -32t < -16 -48 / -32 > -32t / -32 > -16 / -32 1.5 > t > 0.5 |
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The graph of a first degree polynomial is always a |
straight line. |
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The graph of a second degree polynomial is a |
a parabola |
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logb(mn) = logb(m) + logb(n) |
) logb(m/n) = logb(m) - logb(n) |
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logb(mn) = n · logb(m) |
the above rules work only if the bases are the same. |
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Expand log3(2x) |
log3(2) + log3(x) |
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Expand log5(x3) |
log5(x3) = 3 · log5(x) = 3log5(x) |
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Change-of-Base formula |
Logb x = Loga x/Loga b |
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Evaluate log3(6) |
ln(6)/ln(3)=1.63 |
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log(e)= |
1 |
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since 2^0 = 1, then |
log2(1) = 0 |
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since 2^1 = 2, |
then log2(2) = 1 |
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sin(x) = 1 |
x = 90° |
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The distance between the points and is |
distance=√(x2−x1)2+(y2−y1)2 |
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The Midpoint Formula |
( ( xA+xB)/2 , (yA+yB)/2 ) |
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Standard Form of the Equation of a Circle |
(x-h)2 + (y-k)2 = r2The standard form of the equation of a circle with center at and radius is |
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To divide a polynomial by a monomial, divide each term of the polynomial by the monomial. |
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To divide a polynomial by a binomial, we use a method similar to that used to dividewhole numbers |
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