## Philip P.'s Resources 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 Equal ratios:   7/50 = x/75   Solve for x. How do you find the maximum acceleration? First you need to determine the acceleration by taking the second derivative of x(t), a(t) = d²x(t)/dt² Next, take the first derivative of a(t).  Find the extreme points by setting da(t)/dt = 0 and solving for t. To determine if each... P(x) = x4 − 3x3 + 2x2 P(x) = x²(x² - 3x + 2) P(x) = x·x(x-1)(x-2)   Zeros are at x = 0, 0, 1, 2   P(x) is degree 4, so it will have four roots.  You only entered three which is probably why it came up as wrong.  The x² term has a multiplicity of... 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. 5x - 13y = 3x - 8y 2x = 5y (2/5)x = y   < Oops, made a mistake. See comment below for corrected answer. A right angle = 90°.  To trisect means to cut into three equal parts, so 90°/3 = ___° 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... f(x) = 8 − x² y = 8 − x² x = 8 - y² y² = 8-x y = √(8-x) f-1(x) = √(8-x),  x ≤ 8 f(x) = 9 − 7x -5 = 9 - 7x -14 = -7x 2 = x   f-1(-5) = 2 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°. The formula for the gravitational potential energy near the earth's surface is given below.  Be sure all quantities are in the same system of units (SI).   PE = m·g·h PE = gravitational potential energy m = mass in kilograms = 10 kg g = acceleration due to gravity =... As David points out, the problem is difficult to understand as stated.  I think you left some of the problem out.  I think it's "what number multiplied by 8, with 15 subtracted from the product, is equal to 41"?   The number is x   Multiplied by 8 is... Do you have a question or are you merely stating a fact?  Yes, 3 x 3 x 3 x 3 x 3 x 3=36 and 36 is in exponential form, base of 3 exponent of 6. 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... 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,... 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... Let x be the amount of water the bucket can hold when full:   (3/5)x = 21   Solve for x. 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.