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2 years ago

Find the midpoint between 1 + 9i and 5 — 3i

Mathematics

1 answer:

stellarik [79]2 years ago

3 0

Answer:

3+3i

Step-by-step explanation:

The mid point formula in a complex plane is for points a+bi and s+ti is

$Midpoint = \frac{a+s}{2} +\frac{(b+t)i}{2} \\$

For points 1 + 9i and 5 — 3i

$Midpoint = \frac{1+5}{2} + \frac{(9-3)i}{2}$

$Midpoint = \frac{6}{2} + \frac{6i}{2}$

Midpoint = 3 + 3i

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Which if the following summation notations represent this series?

kati45 [8]

Answer:

Step-by-step explanation:

Let's look at the sequence:

$3,8,13,\cdots$

The sequence has a common difference. We say it has a common difference because 8-3 has the same value as 13-8.

The common difference is what these differences are equal which is 5.

The sequence is therefore linear or arithmetic (same thing).

So it has form $y=mx+b$ where the slope/common difference is 5.

$y=5x+b$

We need to find the $y-$ intercept $b$ .

The list of points is related to the above sequence:

$(x,y)$

$(1,3)$

$(2,8)$

$(3,13)$

I only need one of these points to find $b$ .

Let's use the first one since it has smallest numbers and I don't wish to use the calculator unless I really have to.

$y=5x+b$ with $(x,y)=(1,3)$ :

$3=5(1)+b$

$3=5+b$

Subtract 5 on both sides:

$3-5=b$

$-2=b$

So the equation for the set of points is:

$y=5x-2$

Now they are using $i$ instead of x[/tex]:

$a_i=5i-2$

Since all summations begin at $i=1$ , then the choices are done to either choice C and choice E.

I need to find how many terms are in the given series. The last number is 33. So what term number is associated with the value 33.

$a_i=5i-2$

$33=5i-2$

Add 2 on both sides:

$35=5i$

Divide both sides by 5:

$\frac{35}{5}=i$

$7=i$

So there are 7 terms and the 7th term is 33.

So the answer is choice E.

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4 years ago

Suppose a store has 100 light bulbs in stock. Assume 40 light bulbs are from Distributor A and the remainder of the light bulbs

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3 years ago

Distributive property to write an equivalent expression 9(9m+3t)

Klio2033 [76]

Answer:

Step-by-step explanation:

9(9m+3t) = 9 *9m + 9*3t

= 81m + 27t

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4 years ago

e 400 trials in which the assistant maintained a neutral expression, the driver stopped in 229 out of the 400 trials. Find a 95%

Fittoniya [83]

Answer:

Step-by-step explanation:

n = 400

Proportion p = 229/400= 0.5725

For 95% confidence interval we use Z value as 1.96

Std error = 0.025

margin of error = 1.96*0.025

Confidence interval 95% = 0.5725±Margin of error

= (0.524, 0.621)

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p = 0.6925

Std error = 0.023

Margin of error= 1.96*0.023

Confidence interval = (0.647, 0.738)

Smiling increases the chances of stopping since mean and conidence interval bounds are showing increasing trend.

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3 years ago

Y=4x+7 x-intercept: y-intercept:

MAXImum [283]

X=-7/4,0
y=(0,7)
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4 years ago

Find the midpoint between 1 + 9i and 5 — 3i​

Find the midpoint between 1 + 9i and 5 — 3i