Use inverse operations to find the inverse of y = 27x?
The inverse of y = 27x3 is y =

  y = (∛x)/3

Step-by-step explanation:

To undo the multiplication by 27, you multiply by its inverse:

  (1/27)y = (1/27)(27x^3)

  y/27 = x^3 . . . . . . . . . . . simplify

To undo the cube, you take the cube root:

  (∛y)/(∛27) = ∛(x^3)

  (∛y)/3 = x

Apparently, you want the inverse function, so you swap the variables:

  y = (∛x)/3

You can swap the variables at the beginning or end. It doesn't matter. If you do it at the beginning, you have ...

  x = 27y^3

and you're solving for y. You use the same inverse operations that we used above.

$4

step-by-step explanation:

$30×5=$150

$150 minus $130=$20

$20÷5=$4.

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m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°