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Answer:
20. The sum of a number and ten is three times the number
21. The sum of the product of two and a number and the product of four and another number is twenty
22. Four times the sum of a and b is the product of nine times a
23. The product of six and a number subtracted from eight is the sum of four and two times a number
24. The difference of the square of s and the square of n is equal to the product of two and b.
25. d
26. f
27. c
28. b
29. a
30. e
31. Real, Irrational
32. Real, Rational, Integer
33. Real, Rational
34. -
35.-
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Answer:
Step-by-step explanation:
Let
Subbing in:
a = 9, b = -2, c = -7
The product of a and c is the aboslute value of -63, so a*c = 63. We need 2 factors of 63 that will add to give us -2. The factors of 63 are {1, 63}, (3, 21}, {7, 9}. It looks like the combination of -9 and +7 will work because -9 + 7 = -2. Plug in accordingly:
Group together in groups of 2:
Now factor out what's common within each set of parenthesis:
We know this combination "works" because the terms inside the parenthesis are identical. We can now factor those out and what's left goes together in another set of parenthesis:
Remember that
so we sub back in and continue to factor. This was originally a fourth degree polynomial; that means we have 4 solutions.
The first two solutions are found withing the first set of parenthesis and the second two are found in other set of parenthesis. Factoring gives us that x = 1 and -1. The other set is a bit more tricky. If
then
and
You cannot take the square root of a negative number without allowing for the imaginary component, i, so we do that:
±
which will simplify down to
±
Those are the 4 solutions to the quartic equation.