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marin [14]
3 years ago
15

Plot the complex number 5i and find its absolute value

Mathematics
1 answer:
cupoosta [38]3 years ago
4 0
Check the picture below.

\bf 5i\implies \stackrel{a}{0}~~\stackrel{b}{+5}i\implies \stackrel{\stackrel{absolute~value}{modulus}}{r=\sqrt{a^2+b^2}}\implies r=\sqrt{0^2+5^2}\implies r=5

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Which statement explains the property of integer exponents shown in this equation? aman = am + n
harkovskaia [24]

Answer:

D

Step-by-step explanation:

The rule of exponents

a^{m} × a^{n} = a^{(m+n)}

Shows that when 2 powers with the same base are being multiplied then the exponents are added.

4 0
2 years ago
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Determine the solution to 8x = 32 that makes the equation true.
ratelena [41]

Answer:

4

Step-by-step explanation:

8x=32

x = 4

6 0
3 years ago
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Solve the equation x+3/x-4 = x-5/x+4
Serga [27]

Answer:

\large\boxed{x=\dfrac{1}{2}}

Step-by-step explanation:

\dfrac{x+3}{x-4}=\dfrac{x-5}{x+4}\\\\\text{Domain:}\ x-4\neq0\ \wedge\ x+4\neq0\\\\x\neq4\ \wedge\ x\neq-4\\\\D:x\in\mathbb{R}-\{-4,\ 4\}

\dfrac{x+3}{x-4}=\dfrac{x-5}{x+4}\qquad\text{cross multiply}\\\\(x+3)(x+4)=(x-4)(x-5)\qquad\text{use FOIL}\ (a+b)(c+d)=ac+ad+bc+bd\\\\(x)(x)+(x)(4)+(3)(x)+(3)(4)=(x)(x)+(x)(-5)+(-4)(x)+(-4)(-5)\\\\x^2+4x+3x+12=x^2-5x-4x+20\qquad\text{combine like terms}\\\\x^2+(4x+3x)+12=x^2+(-5x-4x)+20\\\\x^2+7x+12=x^2-9x+20\qquad\text{subtract}\ x^2\ \text{from both sides}\\\\7x+12=-9x+20\qquad\text{subtract 12 from both sides}\\\\7x=-9x+8\qquad\text{add}\ 9x\ \text{to both sides}\\\\16x=8\qquad\text{divide both sides by 16}\\\\x=\dfrac{8}{16}\\\\x=\dfrac{8:8}{16:8}\\\\x=\dfrac{1}{2}\in D

7 0
3 years ago
Are the lines below parallel, perpendicular, or neither?
levacccp [35]

Answer:

<h2>Neither </h2><h2></h2>

2y = 3x - 4

y = 2/3x - 3

Step-by-step explanation:

Parallel means the lines never cross. These two lines cross. Perpendicular means they cross and form a 90° angle.

5 0
3 years ago
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Determine the value of each unknown angles.<br><br> HELP PLEASE DO ANY! I’ll give you brilliance
zlopas [31]

For D:

A triangle always has 180 degrees total. No more, no less. Seeing as though all the sides and angles are the same length, we can just divide 180 by 3, giving us 60. x = 60 degrees.

For E:

We can see there is a 90 degree symbol that surmises both angles. We know the lower angle is 30 degrees, so m must equal 60 degrees.

For G:

Same concept as D, except we gotta do a bit of math. A triangle always has 180 degrees, So we add 50 and 55 together and get 105. Subtract 105 from 180 and we get 75. Therefore, your angle is 75 degrees.

For H:

The 75 degree angle and m are parallel, with the same line passing through it, meaning that m is identical to the other angle. m = 75.

7 0
2 years ago
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