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Simora [160]
2 years ago
12

Rob buys a rocking chair priced at 27$. if the sales tax is 10%, what will be the total cost including tax?

Mathematics
1 answer:
seraphim [82]2 years ago
8 0

Answer:

$29.7

Step-by-step explanation:

10 percent of 27 is 2.7 then you add 27 and 2.7 and you get 29.7

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Solve (x + 5)^(3/2)= (x - 1)^3
IRINA_888 [86]

Answer:

  x = 4

Step-by-step explanation:

For an equation of this sort, my first step is to rewrite it so the solutions are the x-intercepts of the graph:

  (x +5)^(3/2) -(x +1)^3 = 0

The graph is attached. The one real solution is x=4.

__

The solution method for something like this is necessarily ad hoc. Here, it appears that progress can be made by raising both sides of the equation to the 2/3 power:

  ((x +5)^(3/2))^(2/3) = ((x -1)^3)^(2/3)

  x +5 = (x -1)^2

Now, you have an ordinary quadratic that can be solved using any of the usual methods.

  x^2 -2x +1 = x +5 . . . . swap sides, expand the square

  x^2 -3x -4 = 0 . . . . . . put in standard form

  (x -4)(x +1) = 0 . . . . . . factor

The solutions to this are ...

  x = 4, x = -1 . . . . . . . values of x that make the factors zero

__

To see if either of these solutions is extraneous, we can check them:

  (4 +5)^(3/2) = (4 -1)^3 . . . . . substitute 4 for x

  9^(3/2) = 3^3 . . . . . . . . . true

  (-1 +5)^(3/2) = (-1 -1)^3 . . . . . substitute -1 for x

  4^(3/2) = (-2)^3

  8 = -8 . . . . . . . . . . . false; x = -1 is extraneous

The solution is x = 4.

_____

<em>Additional comment</em>

You can eliminate the x=-1 "solution" by considering the domains of the left- and right-side expressions. The 3/2 power is equivalent to the square root of the cube. That will generally only be defined for non-negative values (x ≥ -5). The cube on the right will only be positive for x > 1, so the practical domain of this equation is x ≥ 1.

5 0
2 years ago
Composing functions is a way to "link" them together.<br> A. True<br><br> B. False
Sati [7]

This statement is true.

8 0
3 years ago
15x - 24 &gt; 3(4x - 10)
serious [3.7K]
24 / 15 =1.6
12x-10=83.33
7 0
3 years ago
PLS HELP ME
erastovalidia [21]

Answer:

part 1 its telling you to measure people

part two is telling you to put it into a graph and find the rate of change. more than likely there won't be a rate of change for you

part three:

y = 0.860x + 3.302

y = 0.860(17) + 3.302

0.860(17) = 14.62

14.62 + 3.302 = 17.922

y = 17.922

sorry this is as far as i had gotten

7 0
3 years ago
7 Alex grew 1 foot over the past year. He is now 6 feet tall. Lesson 13
pav-90 [236]

Answer:

7 Alex grew 1 foot over the past year. He is now 6 feet tall. Lesson 13

Part A

Draw a bar model to compare Alex's previous height to the amount he grew over

Step-by-step explanation:

raw a bar model to compare Alex's previous height to the amount he grew over

the past y

3 0
3 years ago
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