Complete the puzzle by clicking on the puzzle piece that contains equivalent expression.

Mathematics

1 answer:

Liono4ka [1.6K]1 year ago

8 0

Answer:

-5 when ...

Step-by-step explanation:

The rules of exponents can help you simplify the given product.

<h3>Rules</h3>

(a/b)^c = (a^c)/(b^c)

(ab)^c = (a^c)(b^c)

(a^b)(a^c) = a^(b+c)

(a^b)/(a^c) = a^(b-c)

<h3>Application</h3>

$\left(\dfrac{x}{y}\right)^2(-x^2y)^3=\\\\\dfrac{x^2(-1)^3(x^2)^3y^3}{y^2}=-x^{2+2\cdot3}y^{3-2}=-x^8y$

This expression does not match any of those offered.

When x=-1 and y=5, this becomes ...

$-(-1)^8(5)=\boxed{-5}$

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Which inequality is equivalent to x-6/x+5≥x+7/x+3?

yawa3891 [41]

To find equivalent inequalities you have to work the inequality given.

The first step is transpose on of sides to have an expression in one side and zero in the other side:

x - 6        x + 7
--------- ≥ --------
x + 5       x + 3

=>

x - 6          x + 7
--------- - --------   ≥ 0
x + 5       x + 3

=>

(x - 6) (x + 3) - (x + 7) (x + 5)
--------------------------------------- ≥ 0
(x + 5) (x + 3)

=>

x^2 - 3x - 18 - x^2 - 12x - 35
--------------------------------------- ≥ 0
         (x + 5) (x + 3)

           15x + 53
-     ------------------- ≥ 0
       (x + 5) (x + 3)

That is an equivalent inequality. Sure you can arrange it to find many other equivalent inequalities. That is why you should include the list of choices. Anyway from this point it should be pretty straigth to arrange the terms until making the equivalent as per the options.

4 0

3 years ago

Read 2 more answers

For f(x) =4x+1 g(x)=x²-5, find (f•g)(x)

Marta_Voda [28]

Step-by-step explanation:

The composite function (f o g)(x)

= f(x² - 5)

= 4(x² - 5) + 1

= 4x² - 19.

5 0

3 years ago