5. Which equation is an open sentence?

Mathematics

1 answer:

dimaraw [331]3 years ago

5 0

Answer:

Step-by-step explanation:

there is an unknown thingy which is x

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2 and one half divide by one fourth

solmaris [256]

Hi,

$2 \frac{1}{2} \div \frac{1}{4} \\ 2 \frac{2}{4} \div \frac{1}{4} = 10$

Hope this helps.
r3t40

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3 years ago

What's next in this series: 324, 256, 196, 144?

nydimaria [60]

Next term will be 100

as series is 18²,16²,14²,12² so next will be 10²

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2 years ago

Read 2 more answers

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.