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3 years ago

Which expression is the product of (x + 4i)(x − 4i)(x + 4)?

2 answers:

7 0

Answer= x³+4x²+16x+64

Expand the following:(x + 4 i) (x - 4 i) (x + 4)
(x - 4 i) (x + 4) = (x) (x) + (x) (4) + (-4 i) (x) + (-4 i) (4) = x^2 + 4 x - 4 i x - 16 i = -16 i + (4 - 4 i) x + x^2:
-16 i + (-4 i + 4) x + x^2 (4 i + x)
| | | | x | + | 4 i
| | x^2 | + | (4 - 4 i) x | - | 16 i
| | | | (-16 i) x | + | 64
| | (4 - 4 i) x^2 | + | (16 + 16 i) x | + | 0
x^3 | + | (4 i) x^2 | + | 0 | + | 0
x^3 | + | 4 x^2 | + | 16 x | + | 64:
Answer: x^3 + 4 x^2 + 16 x + 64

RUDIKE [14]3 years ago

6 0

First multiply first 2 elements, so:
(x+4i)*(x-4i) =x^2-16i^2

Now: (x^2-16i^2)*(x+4)=x^3 + 4x^2 - 16xi^2 - 64i^2

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How do you write (243)^ 3/5 in radical form? THEN simplified?! *PLEASE HELP

SOVA2 [1]

Answer:

Step-by-step explanation:

If you have an exponent that is a fraction, you need to make a radical with the index from the denominator and an exponent of the radicand from the numerator.

(243)^3/5=( $\sqrt[5]{243}^3$ )

This would come out as $\sqrt[5]{14348907^}$ . this further simplifies down to the final answer of 27

6 0

3 years ago

Write the equation of the line that passes through the given points. (0,4) (-2,-5)

valentina_108 [34]

Answer:

y=-9/2x plus 4

Step-by-step explanation:

y=ax plus b

Use points from the task.

4=0x plus b

so b=4

-5=-2a plus 4

-2a = -9

a = -9/2

y=-9/2x plus 4

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3 years ago

A group of friends were working on a student film. They spent $481 on costumes, which was 37% of their total budget. What was th

iogann1982 [59]

The total budget for the student film was $1300 and $481 was spent on costumes

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the total budget for the student film.

The student spent $481 on costumes, which was 37% of their total budget, hence:

37% of x = 481

0.37x = 481

x = $1300

The total budget for the student film was $1300 and $481 was spent on costumes

Find out more on equation at: brainly.com/question/2972832

#SPJ1

6 0

2 years ago

Fill in the table with the cost to swim the given number of days. Each amount should be the total cost to swim that number of da

Lesechka [4]

Answer:

y = 0x + 70

y = 4x + 15

y = 6x + 0

Step-by-step explanation:

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3 years ago

Which line is perpendicular to a line that has a slope of -5/6?

Anni [7]

Answer:

Line LM

Step-by-step explanation:

First, we need to know what the slope is of a line that would be perpendicular to a line with a slope of -5/6. To find this, we take the reciprocal and multiply it by -1. Therefore, the line we are looking for needs to have a slope of 6/5.

Based on the fact that the slope is positive, we can eliminate lines PQ and JK as they have a negative slope. This leaves us with lines LM and NO.

To find out whether or not it is between LM and NO, you could eyeball it by looking at the graph and simply counting which might be faster if you understand how to do that (rise/run), or you can use the pair of coordinates given to you on each line to calculate for slope.

Line LM - $\frac{-3-3}{-5-0}=\frac{-6}{-5}=\frac{6}{5}$

Line NO - $\frac{-5-0}{-6-0}=\frac{-5}{-6}=\frac{5}{6}$

Based on this, we know that line LM is perpendicular to a line that has a slope of -5/6.

<em>If you need help on calculating slope from two points, I'd suggest watching this video: </em><u>https://www.brightstorm.com/math/algebra/linear-equations-and-their-graphs/finding-the-slope-of-a-line-from-2-points-problem-1/#:~:text=Use%20the%20slope%20formula%20to,second%20points%20are%20x2%2C%20y2.</u>

7 0

1 year ago