Tutor profile: Andrew C.
Solve for x: -76 - 4x + 2(2x-7)^2 = 130
Following PEMDAS is the key here. First, expand the exponential term by using FOIL: -76 - 4x + 2 (4x^2 - 28x +49) = 130 -76 - 4x + 8x^2 - 56x + 98 = 130 Put all the terms on one side (in this case we'll put everything on the left side). 8x^2 - 60x - 108 = 0 Divide all terms by the greatest common factor to make our problem a little simpler. 2x^2 - 15x - 27 = 0 Factor out the trinomial, then solve within each parentheses to find the two answers. (2x+3)(x-9) = 0 2x+3 = 0 2x = -3 x = -3/2 x-9 = 0 x = 9 x = -3/2, 9
Subject: Music Theory
Which triads are shared between E flat major and d minor?
The tonic notes of E flat major and d minor are just a half step apart. First, we would determine what roots are shared between the two keys. E flat major: E flat, F, G, A flat, B flat, C, D d minor: D, E, F, G, A, B flat, C sharp The shared roots are F, G, B flat, and D. However, we must also check the quality of these triads. E flat major: F minor, G minor, B flat major, D diminished d minor: F major, G minor, B flat major, D minor We can see that the ***G minor and the B flat major triads*** are the only ones that are shared between the two keys. the iii and V chords of E flat major correspond respectively to the iv and VI chords of d minor.
Solve for x: 1 / (x+1) - 2 / (x^2+4x+3) = 2
First, multiply the first fraction by (x+3)/(x+3) in order to match the denominator of the next fraction: (x+3) / (x^2+4x+3) - 2 / (x^2+4x+3) = 2 Now that the denominators are the same, subtract the two fractions: (x+3-2) / (x^2+4x+3) = 2 (x+1) / (x^2+4x+3) = 2 The denominator can be factored, and then cancelled out: (x+1) / [ (x+1)(x+3) ] = 2 1 / (x+3) = 2 Now, solve for x by finding the reciprocal of both sides. (x+3) = 1/2 x = -5/2
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