Solve the equation on the attached picture.

Rewrite

27

as

3^2⋅3

Pull terms out from under the radical.

3(3√3)

Multiply 3 by 3

9√3

The result can be shown in multiple forms.

Exact Form:

9√3

Decimal Form:

15.58845726

…

3

Step-by-step explanation:

To find x, we first look at the other the side of the equation that tells us how to figure it out, which, in this case, is by finding the cubed root of 27.

The cubed root of 27 is found through multiplying a certain number by itself three times to give 27, which is commonly known to be 3- which is our x value.

We can check this by multiplying 3 by 3 by 3, mentally or arithmetically.

3 by 3 is 9, and 9 by the final 3 is 27, therefore, 3 is for sure the answer, as cubing 3 gives us 27.

An alternative method we could also use is trial and error. We'd figure it out by trialling each number from one to see if it could present us with 27.

E.g: trialling 2 cubed.

2 by 2 is 4, and 4 by 2 is 8 therefore, it cannot be two as the value is much lesser than 27.

We would then move on to the next number, this being three, we'd trial 3 cubed.

step-by-step explanation:

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°