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ratelena [41]
3 years ago
7

What substitution should be used to rewrite 16(x3 + 1)2 – 22(x3 + 1) – 3 = 0 as a quadratic equation?

Mathematics
2 answers:
Vesna [10]3 years ago
7 0

Answer:

  z = x^3 +1

Step-by-step explanation:

Noting the squared term, it makes sense to substitute for that term:

  z = x^3 +1

gives ...

  16z^2 -22z -3 = 0 . . . . the quadratic you want

_____

<em>Solutions derived from that substitution</em>

Factoring gives ...

  16z^2 -24z +2z -3 = 0

  8z(2z -3) +1(2z -3) = 0

  (8z +1)(2z -3) = 0

  z = -1/8  or  3/2

Then we can find x:

  x^3 +1 = -1/8

  x^3 = -9/8 . . . . . subtract 1

  x = (-1/2)∛9 . . . . . one of the real solutions

__

  x^3 +1 = 3/2

  x^3 = 1/2 = 4/8 . . . . . . subtract 1

  x = (1/2)∛4 . . . . . . the other real solution

The complex solutions will be the two complex cube roots of -9/8 and the two complex cube roots of 1/2.

anastassius [24]3 years ago
5 0

Answer:

x^3 +1

Step-by-step explanation:

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Korvikt [17]

5x + 7 ≤ −8                        or                     3x + 7 > 19

5x  ≤ - 15                            or                          3x > 12

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8 0
3 years ago
A graph is a straight line through the point (0,5). Can the graph represent a proportional relationship?
cupoosta [38]

Answer:

yes because every time x changes y changes the same amount

Step-by-step explanation:

5 0
3 years ago
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Jobisdone [24]

oof

remember some rules

(a/b)(c/d)=(ac)/(bd)

\frac{x^a}{x^b}=x^{a-b}

x^0=1

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x^{-a}=\frac{1}{x^a}


\frac{(7^{-3})(7^{-2})(2^0)}{(7^{-1})(7^{-4})(2^3)}=

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7 0
3 years ago
Tipos de ecuaciones ​
Yanka [14]

Answer:

Ecuaciones algebraicas. De primer grado o lineales. De segundo grado o cuadráticas...

Ecuaciones trascendentes, cuando involucran funciones no polinómicas, como las funciones trigonométricas, exponenciales, logarítmicas, etc.

Ecuaciones diferenciales. Ordinarias...

Ecuaciones integrales.

Ecuaciones funcionales.

Hope this helps! :)

4 0
3 years ago
Are two cubes always similar
Ann [662]
Yes, because similar means same shape same angles different size!!
3 0
3 years ago
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