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ch4aika [34]
3 years ago
10

What is the value of (–7 + 3i) – (2 – 6i)?

Mathematics
2 answers:
const2013 [10]3 years ago
7 0
The answer is correct. If you have a graphing calculator, there is an "i" button, so the calculator does all your work for you and is a good way to check your answers.
GrogVix [38]3 years ago
6 0
-9+9i is in fact correct so A is right
:)
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NikAS [45]

Answer:

\Large\boxed{\text{Perpendicular Equation:} \ y = -\frac{2}{7}x + \frac{22}{7}}

\Large\boxed{\text{Parallel Equation:} \ y = \frac{7}{2}x -12}

Step-by-step explanation:

In order to find the equations that are parallel/perpendicular to the line y = \frac{7}{2}x - 4, we need to note a couple things about the relationships between lines and their parallel/perpendicular lines.

  • A) If a line is perpendicular to another, the slopes will be opposite reciprocals (for instance -2 and \frac{1}{2} - multiplied, they equal -1.)
  • B) If a line is parallel to another, they will have the exact same slope.

<h2>Perpendicular:</h2>

We know that the slope of a perpendicular line will be the the opposite reciprocal of the line we're comparing it to.

Since the slope of our base line is \frac{7}{2}, we can find the reciprocal, then the opposite of that.

  • Reciprocal of \frac{7}{2} = \frac{2}{7}
  • Opposite of \frac{2}{7} = -\frac{2}{7}

So the slope of this line will be -\frac{2}{7}, making our equation y = -\frac{2}{7}x+ b

However, y-intercepts will not stay the same. In order to find this, we can substitute the point (4, 2) into our equation to solve for b.

  • 2 = -\frac{2}{7} \cdot 4 + b
  • 2 = -\frac{8}{7} + b
  • b = 2+\frac{8}{7}
  • b = 2 \frac{8}{7}
  • b=\frac{22}{7}

Now we know the y-intercept of this equation is \frac{22}{7}. We can now finish off our equation of the line by substituting that in to what we already have,  y = -\frac{2}{7}x+ b.

y = -\frac{2}{7}x+ \frac{22}{7}

<h2>Parallel:</h2>

As mentioned earlier, parallel lines will have the exact same slope but not the same y-intercept. Since the slope of our original equation is \frac{7}{2}, the slope for this one will also be \frac{7}{2}.

So we now know the equation looks something like y = \frac{7}{2}x + b.

In order to solve for b, we apply the same logic we did in the perpendicular line and substitute in the point (4, 2) into the equation.

  • 2 = \frac{7}{2} \cdot 4 + b
  • 2 = \frac{28}{2}+b
  • 2 = 14+b
  • b = 2-14
  • b =-12

Now that we know the slope and the y-intercept, we can finish off our equation as y = \frac{7}{2}x -12.

Hope this helped!

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3 years ago
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2 years ago
Read 2 more answers
Please help me with question 2 thank you !!
ipn [44]
A is the correct answer. Both diagonals would be the same length as it is a rectangle and when you substitute 7 for X in the equations, the answer is 26 for both.
6 0
2 years ago
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