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2 years ago

Find the greatest common factor of 21 and 33

Mathematics

2 answers:

Stels [109]2 years ago

8 0

Answer:

$GCF=3$

Step-by-step explanation:

1) List the factors of each number.

Factors of 21: $1,3,7,21$

Factors of 33: $1,3,11,33$

2) Find the largest number that is shared by all rows above. This is the GCF.

$GCF=3$

lions [1.4K]2 years ago

5 0

Answer:

As you can see when you list out the factors of each number, 3 is the greatest number that 21 and 33 divides into.

Step-by-step explanation:

As you can see when you list out the factors of each number, 3 is the greatest number that 21 and 33 divides into.

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NARA [144]

Answer:

4 1/4

Step-by-step explanation:

Convert 5 2/3 to an improper fraction. 3 x 5 = 15 + 2=17

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2 years ago

10. George earns $455 per week. He receives a 20% raise. What is George's new weekly salary?

djverab [1.8K]

Answer:

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Step-by-step explanation:

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3 years ago

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Step-by-step explanation:

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1 year ago

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Assume z = x + iy, then find a complex number z satisfying the given equation. d. 2z8 – 2z4 + 1 = 0

kodGreya [7K]

Answer: complex equations has n number of solutions, been n the equation degree. In this case:

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i11,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i101,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i191,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i281,25°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i78,75°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i168,75°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i258,75°}$

$Z=\frac{\sqrt[8]{2} }{\sqrt[4]{2}} e^{i348,75°}$

Step-by-step explanation:

I start with a variable substitution:

$Z^{4} = X$

Then:

$2X^{2}-2X+1=0$

Solving the quadratic equation:

$X_{1} =\frac{2+\sqrt{4-4*2*1} }{2*2} \\X_{2} =\frac{2-\sqrt{4-4*2*1} }{2*2}$

$X=\left \{ {{0,5+0,5i} \atop {0,5-0,5i}} \right.$

Replacing for the original variable:

$Z=\sqrt[4]{0,5+0,5i}$

or $Z=\sqrt[4]{0,5-0,5i}$

Remembering that complex numbers can be written as:

$Z=a+ib=|Z|e^{ic}$

Using this:

$Z=\left \{ {{{\frac{\sqrt{2}}{2} e^{i45°} } \atop {{\frac{\sqrt{2}}{2} e^{i-45°} }} \right.$

Solving for the modulus and the angle:

$Z=\left \{ {{\sqrt[4]{\frac{\sqrt{2}}{2} e^{i45}} = \sqrt[4]{\frac{\sqrt{2}}{2} } \sqrt[4]{e^{i45}} } \atop {\sqrt[4]{\frac{\sqrt{2}}{2} e^{i-45}} = \sqrt[4]{\frac{\sqrt{2}}{2} } \sqrt[4]{e^{i-45}} }} \right.$

The possible angle respond to:

$RAng_{12...n} =\frac{Ang +360*(i-1)}{n}$

Been "RAng" the resultant angle, "Ang" the original angle, "n" the degree of the root and "i" a value between 1 and "n"

In this case n=4 with 2 different angles: Ang = 45º and Ang = 315º

Obtaining 8 different angles, therefore 8 different solutions.

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2 years ago

For any circle, which ratio is equal to the number n? Select all that apply. Plsss help me!!

barxatty [35]

Answer:

Options A-C-F

Step-by-step explanation:

we know that

<em>The circumference of a circle is equal to</em>

$C=\pi D$ or $C=2\pi r$

where

D is the diameter and r is the radius

therefore

$\pi =\frac{C}{D}$ or $\pi =\frac{C}{2r}$

The number pi is the ratio circumference - diameter or is the ratio circumference - 2 times radius

<em>The area of the circle is equal to</em>

$A=\pi r^{2}$

therefore

The number pi is the ratio Area - radius squared

6 0

2 years ago