To simplify 4/(2+7i), we multiply it by a fraction equal to one that removes the i value in the denominator. The best value to do this is the complex conjugate divided by itself, so we have 4(2-7i)/((2+7i)(2-7i)). Simplifying, we have (8-28i)/(4-(-49))=(8-28i)/53, which is a completely simplified fraction since 8 and 53 are relatively prime (or coprime), and there are no radicals in the denominator.
m3 = 110°
Step-by-step explanation:
m1 = 180° - m4 ( sum of angles in a straight angle )
m1 = 180° - 150° = 30°
m3 = 180° - (m2 + m1) ← sum of angles in a triangle
m3 = 180° - (40 + 30 )° = 180° - 70° = 110°
Every confidence interval has associated z value. As confidence interval increases so do the z value associated with it.
The confidence interval can be calculated using following formula:

Where

is the mean value, z is the associated z value, s is the standard deviation and n is the number of samples.
We know that standard deviation is simply a square root of variance:

The confidence interval of 95% has associated z value of <span>1.960.
</span>Now we can calculate the confidence interval for our income:
<em>In order to increase the area of a rectangular garden that measures 12 feet by 14 feet by 50% Jake must increase each dimension by equal lengths, x:</em>

<h2>
Explanation:</h2><h2 />
First of all, let's calculate the area of the original rectangular garden:

Jake wants to increase the area by 50%, so the new area would be:

He wants to increase the area by 50% and plans to increase each dimension by equal lengths, x, so this is represented by the figure below, therefore:

Finally:
<em>In order to increase the area of a rectangular garden that measures 12 feet by 14 feet by 50% Jake must increase each dimension by equal lengths, x:</em>

<h2>Learn more:</h2>
Dilation: brainly.com/question/10945890
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I... don’t know? How many hours is he working a year? How many days is he working?