All categories

2 years ago

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]2 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

_____

Solutions derived from that substitution

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]2 years ago

5 0

Answer:

x^3 +1

Step-by-step explanation:

You might be interested in

Estimate the value of 50.75 x 0.18 Estimate the value of 196 divided by 0.499

DIA [1.3K]

This question is a simple one. To answer this question, you need to understand the description in the question and determine to multiply or divide the number.

The first problem would be:
50.75 x 0.18= 9.135
If you need to estimate, 50.75 is near 50; 0.18 is near 0.2 or 1/5 so it would be: 50/0.2= 10

The second problem would be:
196 / 0.499: 392.785
If you need to estimate, 0.499 is near 0.5 then 196/0.5 would be 392

3 0

2 years ago

Read 2 more answers

Hallie can use the equation p = 4l + 4w + 4h to determine the sum of the lengths of the edges of a rectangular prism. She begins

alexira [117]

Answer: the answer will be the letter A

( l + w )

9 0

2 years ago

Read 2 more answers

Two triangles are similar with a scale factor of 3. The preimage triangle has a base of 7 inches and a height of 10 inches. What

vaieri [72.5K]

Answer:

The area of the larger triangle is 315 inches²

Step-by-step explanation:

1. Let's review all the information provided for answering the questions properly:

Pre-image triangle has a base of 7 inches and a height of 10 inches

Scale used : Factor of 3

2. What is the area of the larger triangle??

For calculating the area of the larger triangle, we use the scale this way:

Base = 7 inches * 3

21 inches

Height = 10 inches * 3

30 inches

Area of the larger triangle = 1/2 (Base * Height)

Area of the larger triangle = 1/2 (21 * 30)

Area of the larger triangle = 630/2 = 315 inches²

6 0

2 years ago

John took all his money from his savings account. He spent $110 on a radio and 4/11 of what was left on presents for his friend

svp [43]

Answer:

$1210

Step-by-step explanation:

Let x be total amount

First John spent $110 on a radio and 4/11 of what was left on presents for his friends so he was left with

$\frac{7}{11}(x-110)=\frac{7}{11}x-70$

Then he put 2/5 of his remaining money into a checking account

$\frac{3}{5}\left(\frac{7}{11}x-70\right)$

Rest he donated to charity

$420=\frac{3}{5}\left(\frac{7}{11}x-70\right)\\\Rightarrow \left(\frac{7}{11}x-70\right)=\frac{2100}{3}\\\Rightarrow \frac{7}{11}x-70=700\\\Rightarrow \frac{7}{11}x=770\\\Rightarrow x=1210$

Hence total amount of money John originally had was $1210

8 0

2 years ago

Jabari is thinking of three numbers. The greatest number is twice as large as the least number. The middle number is three more

Likurg_2 [28]

Answer:

18, 21, 36

Step-by-step explanation:

Let L represent the least number. Then the greatest is 2L and the middle number is (L+3). Their sum is ...

L +(2L) +(L+3) = 75

4L = 72 . . . . . . . . . subtract 2, collect terms

L = 18 . . . . . . . . . . . divide by 4

L+3 = 21

2L = 36

The numbers are 18, 21, and 36.

5 0

2 years ago