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lara31 [8.8K]
2 years ago
8

What are two consecutive numbers whose cube differs by 271

Mathematics
2 answers:
valentina_108 [34]2 years ago
7 0

Answer:

Two consecutive numbers cubes differ by 271. Let the two consecutive numbers be x and x + 1. The difference of the two consecutive numbers is 271. ( x + 1 ) ^3 - x ^3 = 271. 1 + 3 x ^ 2 + 3 x - 271 = 0.

Step-by-step explanation:

lesya692 [45]2 years ago
4 0

9514 1404 393

Answer:

  9, 10  or  -10, -9

Step-by-step explanation:

Let x represent the smaller of the two numbers. Then x+1 is the larger, and their difference is ...

  (x +1)³ -x³ = 271

  x³ +3x² +3x +1 -x³ = 271

  3x² +3x -270 = 0 . . . . . . simplify

  x² +x -90 = 0 . . . . . . . . divide by 3

  (x +10)(x -9) = 0 . . . . . factor

The two solutions are x = -10, x = 9.

The numbers could be {-10, -9} or {9, 10}.

_____

<em>Additional comment</em>

Solutions to a factored polynomial are the values of the variable that make the factors zero. The product will only be zero if a factor is zero.

The factor (x -a) is zero when x=a.

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Answer:

C : 0

Step-by-step explanation:

First find f(3). That value is 2.

Then g(f(3)) = 0.

3 0
3 years ago
Members of the student concil are conducting a fundraiser by selling school calendars. After selling 80 calendars, they had a lo
Oksana_A [137]

Answer:

a)  y=8x-1000

b) profit=\$8

c) They'd have lost $1000 if they had sold no calendars.

Step-by-step explanation:

a) The equation of the line in Slope-Intercept form is:

y=mx+b

Where "m" is the slope and "b" is the y-intercept.

In this case we know that "y" represents the profit of loss and "x" the number of calendars sold.

Then, according to the exercise, the line passes through these two points:

(80,-360) and (200,600)

Then, we can find the slope of the line with the formula m=\frac{y_2-y_1}{x_2-x_1}

m=\frac{-360-600}{80-200}=8

Now, we can substitute the slope and one of those points into y=mx+b and solve for "b":

600=8(200)+b\\\\b=-1000

Then, subtituting values, we get that the equation that describes the relation between the profit of loss and the number of calendars sold, is:

y=8x-1000

b) The slope of the line is the profit they made from selling each calendar

profit=8

c) The y-intercept is the amount they would have lost if they had sold no calendars:

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They'd have lost $1000 if they had sold no calendars.

6 0
2 years ago
12x +10+3+8x ? What do I have to do ?
Annette [7]

Simplifying

12x + 10 + 3 + 8x = 0

Reorder the terms:

10 + 3 + 12x + 8x = 0

Combine like terms: 10 + 3 = 13

13 + 12x + 8x = 0

Combine like terms: 12x + 8x = 20x

13 + 20x = 0

Solving

13 + 20x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-13' to each side of the equation.

13 + -13 + 20x = 0 + -13

Combine like terms: 13 + -13 = 0

0 + 20x = 0 + -13

20x = 0 + -13

Combine like terms: 0 + -13 = -13

20x = -13

Divide each side by '20'.

x = -0.65

Simplifying

x = -0.65

4 0
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5 0
3 years ago
What is 20.9/9.31?<br> No need to explain. Just need the answer
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