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Kisachek [45]
3 years ago
12

I'll give brainliest and five stars if you help me!

Mathematics
1 answer:
andrezito [222]3 years ago
6 0
A.)))))))))))


- Harvard university professor
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What substitution should be used to rewrite 16(x3 + 1)2 – 22(x3 + 1) – 3 = 0 as a quadratic equation?
Vesna [10]

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.

7 0
3 years ago
Read 2 more answers
Elena went on a 6-mile walk. She completed the first half of the walk 1 mi/h faster than usual and the second half of the walk 2
xxTIMURxx [149]

Answer:

Her usual rate is 0.8333 miles per hour.

Step-by-step explanation:

The velocity formula is given by:

v = \frac{d}{t}

In which d is the distance and t is the time.

She completed the first half of the walk 1 mi/h faster than usual

Her usual rate is v. 1mph faster is v + 1.

The second half of the walk 2 mi/h slower than the first half.

The first half is v + 1.

2mph slower is v + 1 - 2 = v - 1. Then

Total rate:

7.2 hours, and 6 miles. So

One half is v+1 and the other is v - 1. This is why each is multiplied by 0.5.

0.5(v + 1) + 0.5(v - 1) = \frac{6}{7.2}

0.5v + 0.5 + 0.5v - 0.5 = 0.8333

v = 0.8333

Her usual rate is 0.8333 miles per hour.

8 0
3 years ago
Mindy can a drive a total of 375 miles on a full tank of gas, which is 25 gallons. Based on this information, what is the consta
stepan [7]

Answer:

15

Step-by-step explanation:

\frac{25}{375} = \frac{1}{x}

Cross multiply to get 25x = 375

Divide each side by 25 to get x = 15

5 0
2 years ago
Please help me! Please!
user100 [1]

Answer:

C) -3 is the answer

6 0
3 years ago
Simplify the expression below. (x5)(x2)
sp2606 [1]
Mutiply straight across 10x
8 0
4 years ago
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