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nasty-shy [4]
4 years ago
15

Simplify

alt=" \frac{4}{2 + i} " align="absmiddle" class="latex-formula">

Mathematics
1 answer:
skad [1K]4 years ago
6 0
Hey! Apologies that I can’t make this look nice because I’m on mobile.

To simplify this, we can multiply the denominator by its conjugate. For a imaginary function (a+bi), its conjugate would be (a-bi), so we can apply that here to multiply both sides by (2-i)/(2-i). This works because it simplifies to one. Then, we have our fraction as 4*(2-i)/((2-i)(2+i))=(8-4i)/(4-i^2)=(8-4i)/5

Feel free to ask further questions, and have a great rest of your day!
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A rectangle has width w and its length is 2 units shorter that 3 times the width
topjm [15]
2(3w-2+w)
=2(4w-2)
=8w-4

the formula for solving perimeters is 2(WL). so L=3w-2, because the question said the length is 2 units shorter than 3 times the width, and the width is w. so the final equation is <span>2(3w-2+w), and then you just have to simplify that </span>
8 0
3 years ago
Write an explicit formula for an, the nth term of the sequence 19,24,29
o-na [289]

Answer:

explicit formula for an, the nth term of the sequence 19,24,29

a_1=19 ; \ a_n=a_{n-1}+5

Step-by-step explanation:

We need to Write an explicit formula for an, the nth term of the sequence 19,24,29

In the sequence the First term a₁= 19

Common Difference d= 5

The Formula used for explicit formula is: a_1=First \ term ; \ a_n=a_{n-1}+d

Where d is common difference and n is nth term of sequence.

So, explicit formula for an, the nth term of the sequence 19,24,29

a_1=19 ; \ a_n=a_{n-1}+5

3 0
3 years ago
haru rides his bike from his home for 30 minutes at a fast pace. He stops to rest for 20 minutes, and then continues riding in t
Bezzdna [24]

Using the given information and what we know about linear equations, we will find the sketch below.

<h3>How to sketch a graph?</h3>

Here we need to analyze each part separately.

In a coordinate axis where the y-axis represents distance and the x-axis represents time, we will have that:

First, we know that he rides for 30 minutes at a given speed, this will be represented with an increasing linear function.

Then he stops for 20 minutes, this is represented with a horizontal line.

Finally, he returns the motion, but slower than before, so the slope of this line will be smaller than the first one.

So for 0 to 30 we have an increasing linear equation, then for 30 to 50 we have a constant horizontal line, then for 50 to 80 we have another increasing linear equation

The sketch can be seen below.

If you want to learn more about linear equations, you can read:

brainly.com/question/4074386

6 0
3 years ago
Simplify . (1/c + 1/h)/(1/(c ^ 2) - 1/(r ^ 2))
Marrrta [24]

Answer:

\frac{\left(h+c\right)cr^2}{h\left(r^2-c^2\right)}

Step-by-step explanation:

\frac{\frac{1}{c}+\frac{1}{h}}{\frac{1}{c^2}-\frac{1}{r^2}}

Combine \frac{1}{c} + \frac{1}{h}

\frac{\frac{h+c}{ch}}{\frac{1}{c^2}-\frac{1}{r^2}}

Combine the bottom, too.

=\frac{\frac{h+c}{ch}}{\frac{r^2-c^2}{c^2r^2}}

Apply the fraction rule

=\frac{\left(h+c\right)c^2r^2}{ch\left(r^2-c^2\right)}

Cancel

=\frac{\left(h+c\right)cr^2}{h\left(r^2-c^2\right)}

Therefore, \frac{\left(\frac{1}{c}+\frac{1}{h}\right)}{\left(\frac{1}{\left(c^2\right)}-\frac{1}{\left(r^2\right)}\right)}:\quad \frac{\left(h+c\right)cr^2}{h\left(r^2-c^2\right)}

5 0
3 years ago
Which of the following ordered pairs could represent the x-intercept of a function?
Murrr4er [49]

Answer:

b

Step-by-step explanation:

4 0
3 years ago
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