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3 years ago

What is the simplest form of i^16 plus i^6 minus 2i^5 plus i^13?

1 answer:

6 0

$\bf \textit{recall that}\qquad i^4=1\qquad i^3=-i\qquad i^2=-1\\\\
-------------------------------\\\\
i^{16}+i^6-2i^5+i^{13}\implies i^{4\cdot 4}~+~i^{4+2}~-~2i^{3+2}~+~i^{4+4+4+1}
\\\\\\
(i^4)^4~+~i^4\cdot i^2~-~2\cdot i^3\cdot i^2~+~i^4\cdot i^4\cdot i^4\cdot i^1
\\\\\\
(1)^4+[1\cdot -1]-[2(-i)(-1)]+[(1)(1)(1)(i)]
\\\\\\
1-1-2i+i\implies -i$

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Solve |2x - 5| = 4. {x | x = -4.5 or x = 4.5} {x | x = 0.5 or x = 4.5} {x | 0.5 < x < 4.5}

kotykmax [81]

Answer:

{x | x = 0.5 or x = 4.5}

Explanation:

Before we begin, remember that:

The modulus gives the positive value of what's inside it.

This means that:

|a| = |-a| = a

Now, for the given, we have:

|2x-5| = 4

From the above rule, we can deduce that:

either:

2x - 5 = 4

2x = 4 + 5 = 9

x = 4.5 ............> first solution

Or:

2x - 5 = -4

2x = 5-4 = 1

x = 0.5 ..........> second solution

Now, we check:

at x = 4.5: |2(4.5)-5| = |9-5| = |4| = 4 ..........> first solution verified

at x = 0.5: |2(0.5)-5| = |1-5| = |-4| = 4 .........> second solution verified

Hope this helps :)

6 0

3 years ago

What is the value of x in the figure below?

Mrac [35]

Answer:

x = 125°

Step-by-step explanation:

180° - 55° = 125°

125°

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

4 0

3 years ago

3. Factor.

sleet_krkn [62]

It seems that some the work is already here, but I'd be glad to!! So for #3 which is 9x^2+15x, we can factor out both a 3 and an x (3x) so we know that 3x * 3x =9x^2 and 3x * 5 = 15x so once we take the 3x out of the equation, we are left with 3x(3x+5) and that's as far as you can factor.
For #4, we see that the common factor is 10m because 10m * 2n = 20mn and 10m * 3 = 30m so once we take 10m out of the original, it becomes 10m(2n-3)
For #5, this one the common factor is 4xy because 4xy * 2xy=8x^2y^2 and 4xy*x= 4x^2y and 4xy*3=12xy so once we take the 4xy out of the equation, it becomes 4xy(2xy-x-3)
Hope this helps!

5 0

3 years ago

What is the percent of increase from 106 miles to 122 miles?

Elis [28]

Answer:

15.094 %

Step-by-step explanation:

[(122 - 106) /106] 100

(16/106) 100

(0.15094)x100

15.094

8 0

3 years ago

-25+t=-44 solve. Use the addition principle to find solution. T=

Taya2010 [7]

To find T, you add 25 to both sides, isolating the varible. This gives you T=-19

Hope this helped!

4 0

3 years ago