5. Emmanuel makes 82,000 as a software designer. Use the follow tax chart to find what he will pay in taxes this year.

Step 1:
Solve one of the equations for either x = or y = .
Step 2:
Substitute the solution from step 1 into the other equation.
Step 3:
Solve this new equation.
Step 4:
Solve for the second variable.

Example 1: Solve the following system by substitution
Substitution Method Example
Solution:
Step 1: Solve one of the equations for either x = or y = . We will solve second equation for y.
solution step 1
Step 2: Substitute the solution from step 1 into the second equation.
solution step 2
Step 3: Solve this new equation.
solution step 3
Step 4: Solve for the second variable
solution step 4
The solution is: (x, y) = (10, -5)
Hope this helps!

6 0

3 years ago

(7 + 7i)(2 − 2i)

Ostrovityanka [42]

The complex number -7i into trigonometric form is 7 (cos (90) + sin (90) i) and 3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

<h3>What is a complex number?</h3>

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number shown in the picture:

-7i(3 + 3i)

= -7i

In trigonometric form:

z = 7 (cos (90) + sin (90) i)

= 3 + 3i

z = 4.2426 (cos (45) + sin (45) i)

$\rm 7\:\left(cos\:\left(90\right)\:+\:sin\:\left(90\right)\:i\right)4.2426\:\left(cos\:\left(45\right)\:+\:sin\:\left(45\right)\:i\right)$

$\rm =7\left(\cos \left(\dfrac{\pi }{2}\right)+\sin \left(\dfrac{\pi }{2}\right)i\right)\cdot \:4.2426\left(\cos \left(\dfrac{\pi }{4}\right)+\sin \left(\dfrac{\pi }{4}\right)i\right)$

$\rm 7\cdot \dfrac{21213}{5000}e^{i\dfrac{\pi }{2}}e^{i\dfrac{\pi }{4}}$

$\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}$

=21-21i

After converting into the exponential form:

$\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}$

From part (b) and part (c) both results are the same.

Thus, the complex number -7i into trigonometric form is 7 (cos (90) + sin (90) i) and 3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

Learn more about the complex number here:

brainly.com/question/10251853

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3 0

2 years ago