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3 years ago

In the complex number system, which of the following is equal to

Mathematics

2 answers:

jeka943 years ago

8 0

Step-by-step explanation:

(14+2i)(7+12i)=14×7+14×12i+2i×7+2i×12i

=98+168i+14i−24

=74+182i

pogonyaev3 years ago

3 0

Answer:

C) $122+154i$

Step-by-step explanation:

$(14-2i)(7+12i)\\\\(14)(7)+(14)(12i)+(-2i)(7)+(-2i)(12i)\\\\98+168i-14i-24i^2\\\\98+154i-24(-1)\\\\98+154i+24\\\\122+154i$

Therefore, C is correct. Recall that $i^2=-1$

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DENIUS [597]

Answer:

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Step-by-step explanation:

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3 years ago

What is the value of x in the equation 7(4x+1)-3x=5x-13

skelet666 [1.2K]

Answer:

in this equation, x = -1

Step-by-step explanation:

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5 0

4 years ago

Read 2 more answers

Let’s pretend that we want to give our employees in total a28% raise in the next two years, but we want to spread out aconsisten

Roman55 [17]

Solution

- The solution steps are given below:

$\begin{gathered} \text{ Let the original amount be X} \\ \\ \text{ If we want a 28\% raise over the next two years, then it means that the amount will be:} \\ X+\frac{28}{100}X=1.28X \\ \\ \text{ If we want to give them a consistent raise each year, we can compute the scenario as follows:} \\ \text{ Let the percentage be }y \\ \\ X+y\%\text{ of }X=\text{ Salary after first year} \\ \\ (X+y\%\text{ of }X)+y\%\text{ of }(X+y\%\text{ of }X)\text{ = Salary after second year.} \\ \\ \text{ But we already know that the salary after second year is }1.28X \\ \text{ Thus, we can say:} \\ (X+y\%\text{ of }X)+y\%\text{ of }(X+y\%\text{ of }X)=1.28X \\ \\ \text{ Simplifying, we have:} \\ X+\frac{yX}{100}+\frac{y}{100}(X+\frac{yX}{100})=1.28X \\ \\ \text{ Divide through by }X \\ 1+\frac{y}{100}+\frac{y}{100}(1+\frac{y}{100})=1.28 \\ \\ \text{ Subtract 1 from both sides and expand the brackets} \\ \frac{y}{100}+\frac{y}{100}+(\frac{y}{100})^2=1.28-1=0.28 \\ \\ \frac{2y}{100}+(\frac{y}{100})^2=0.28 \\ \\ \text{ Multiply both sides by }100^2 \\ 200y+y^2=2800 \\ \\ \text{ Rewrite, we have:} \\ y^2+200y-2800=0 \\ \\ Solving\text{ the equation using the Quadratic formula, we have that:} \\ y=\frac{-200\pm\sqrt{200^2-4(-2800)}(1)}{2(1)} \\ \\ y=-213.137\text{ or }13.137 \\ \\ \text{ Since the change in salary is an increase, thus, the rate }y\text{ has to be positive.} \\ \text{ Thus, } \\ y=13.137\approx13.14\% \\ \\ \end{gathered}$

Final Answer

y = 13.14%

The screenshots of the solution are:

5 0

1 year ago

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AveGali [126]

Answer:

Step-by-step explanation:

84 - (15+13)/4

84 - 28/4

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3 0

3 years ago

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A caterer will provide the meal for the football banquet. The caterer charges a base fee of $400 plus $6 per plate.

Anuta_ua [19.1K]

Answer: y = 6x + 400

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y-intercept = total cost

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3 years ago