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3 years ago

PLEASE HELP THESE ARE URGENT

Mathematics

1 answer:

Evgen [1.6K]3 years ago

6 0

Q1: vertical shift of down 4: Indicated by the subtraction of 4 at the end of the function, and a horizontal shift of 2 unit left as indicated by the addition of 2 to the independent variable "x"

Q2: To stretch a function, you can just multiply it by the desired factor. Thus, the function g(x)= $2(2) (3)^{x+1} +4$

Q3: g(x) = $3^{x-2} -1$ Note that the initial point (2,0) has shifted down 1 and to the right 2. Subtracting 2 from x takes care of the horizontal shift of 2 to the right, and subtracting 1 at the end of the function produces a vertical shift of down 1.

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3 years ago

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Sergeu [11.5K]

Answer:

43-7i

Step-by-step explanation:

We are given the expression:

$\displaystyle \large{(3 - 4i)(6i + 7) - (2 - 3i)}$

First, expand 3-4i in 6i+7. To expand binomial with binomial, first we expand 3 in 6i+7 then expand -4i in 6i+7.

$\displaystyle \large{[(3 \cdot 6i) + (3 \cdot 7) + ( - 4i \cdot 6i) + ( - 4i \cdot 7)]- (2 - 3i)} \\ \displaystyle \large{[18i + 21 - 24 {i}^{2} - 28i]- (2 - 3i)}$

Now combine like terms.

$\displaystyle \large{[ - 10i+ 21 - 24 {i}^{2} ]- (2 - 3i)}$

Imaginary Unit

$\displaystyle \large{i = \sqrt{ - 1} } \\ \displaystyle \large{ {i}^{2} = - 1 }$

Therefore:-

$\displaystyle \large{[ - 10i+ 21 - 24 ( - 1) ]- (2 - 3i)} \\ \displaystyle \large{[ - 10i+ 21 + 24]- (2 - 3i)} \\ \displaystyle \large{[ - 10i+ 45]- (2 - 3i)}$

Then expand negative sign in 2-3i; remember that negative times negative is positive and negative times positive is negative.

$\displaystyle \large{- 10i+ 45 - (2 - 3i)} \\ \displaystyle \large{- 10i+ 45 - 2 + 3i}$

Combine like terms.

$\displaystyle \large{43 - 7i}$

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3 years ago