On 3 algebra questions ! ***19. write the domain of the function in interval notation. f(x)=root 3√x-12 a. (– ∞, ∞) b. (– ∞, 12) c. (12, ∞) d. (–12, ∞)17. convert the expression to radical notation. (18 y2)1/7 10. what's the definition of the number i? a. i = (–1) 2 b. i = –1 c. i = √ –1 d. i = – √ 1

19) The domain is (12 , ∞) ⇒ answer C

17) The radical notation is

10) The definition of number i is √(-1) ⇒ answer C

Step-by-step explanation:

19)

* Lets explain the meaning of the domain of the function

- The domain of any function is the values of x which makes the

  function defined

- Examples:

# In the fraction the denominator con not be zero, then if the function

  is a rational fraction then the domain is all the values of x except

  the values whose make the denominator = 0

# In the even roots we can not put negative numbers under the radical

  because there is no even roots for the negative number belonges to

  the real numbers, then the domain is all the values of x except the

  values whose make the quantity under the radical negative

* Now lets solve the question

∵ f(x) = 3 √(x - 12)

- To find the domain let (x - 12) greater than zero because there is

 no square root for negative value

∵ x - 12 > 0 ⇒ add 12 to both sides

∴ x ≥ 12

∴ The domain is all values of x greater than 12

* The domain is (12 , ∞)

17)

* Lets talk about the radical notation

- The radical notation for the fraction power is:

  the denominator of the power will be the radical and the numerator

  of the power will be the power of the base

- Ex:

* Lets solve the problem

∵ (18 y²)^(1/7)

- The power 1/7 will be the radical over (18 y²)

∴

* The radical notation is

10)

* Lets talk about the imaginary number

- Because there is no even root for negative number, the imaginary

 numbers founded to solve this problem

- It is a complex number that can be written as a real number multiplied

  by the imaginary unit i, which is defined by i = √(-1) or i² = -1

- Ex: √(-5) = √[-1 × 5] = i√5

* The definition of number i is √(-1)

b

step-by-step explanation:

ez

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .