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Philip P.'s Resources

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x² - 3x - 28 = 0   This quadratic equation factors.  You want two factors that multiply to give -28 and add to give -3.  The factors are -7 and 4: (-7)(4) = -28 and -7 + 4 = -3   (x-7)(x+4) = 0   x = 7 and -4

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You need to know what the graph of g(x) = 2x looks like.  It's probably in your text book, or you can look it up on the internet.  Changing the 2 to -2 flips (reflects) the graph across the x-axis.  The -1 moves the whole graph down 1 along the y-axis.

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𝑓(𝑥) = 𝑥2 − 7𝑥 + 4 𝑎𝑛𝑑 𝑐 = 2   Evaluate directly:   f(c) = f(2) = 22 - 7·2 + 4 = 4 - 14 + 4 = -6   Evaluate via Synthetic division and the Remainder Theorem.  Divide x2-7x+4 by x-2.  The remainder will equal f(c=2):   2...

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a + b + c = 180° a + a + a + 69° = 180° 3a + 69° = 180°   Solve for a.  Once you have a, b= a and c = a+69°.

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You only gave us part of the problem, but here's the general approach.  First, put the equation into the slope-intercept form (y = mx + b):   6x + 2y = 12 2y = -6x + 12 y = -3x + 6   To find ordered pairs, simply plug in any value for x and...

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The key point here is that velocity is a vector.  Hence it has a horizontal speed (v) and a vertical speed (u) that are independent.  So how long will it take the ball to fall 100 m?   d = (1/2)gt² 100 = (1/2)(9.8)t² 20.41 = t² 4.52 = t   So horizontally,...

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Ignoring air resistance:   h(t) = (1/2)gt² h(t) = distance stone has dropped g = acceleration due to gravity = 9.8 m/s² t = time since stone was dropped (in seconds) = 8.39 sec   h(t) = (1/2)gt² h(t) = (1/2)(9.8)(8.39)²   Use your calculator...

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Spectral classes F, G, K, and M on the main sequence eventually evolve into a white dwarf.  Spectral classes O, B, and A typically supernova and form neutron stars.  So it looks like C is the answer.

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