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Kitty [74]
3 years ago
7

1/2(7x-8)+2x =2-(10x+4

Mathematics
1 answer:
geniusboy [140]3 years ago
8 0
<span>1/2(7x-8)+2x =2-(10x+4)
Distribute
(7x-8)/2 + 2x = 2 -10x -4
combine like terms
(7x - 8)/2 + 2x = -10x - 2
Multiply both sides by 2
7x - 8 + 4x = -20x -4
Combine like terms
11x - 8 = -20x - 4
add 8 to both sides
11x = -20x + 4
add 20x to both sides
11x + 20x = 4
combine like terms
31x = 4
divide both sides by 31
x = 4/31 or </span><span>0.129.

Hope this helps :)</span>
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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.

3 0
3 years ago
Name the constant(s) in the expression 7x + 9y + 3
mart [117]
The answer is B. 3

It is the only value not attached to a variable, thus remaining constant.
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At the Barclays Center there are 850 seats. Tickets were sold for 816 of the seats. For what percentage of the seats were ticket
snow_tiger [21]
Percent sold=sold/original times 100
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original=850

percent sold=816/850 times 100
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4 0
3 years ago
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Can you evaluate the expressions for the given value. (show steps if you can)
exis [7]

Answer:

Q1. -45

Q2. -10

Q3. 31?

Step-by-step explanation:

Q1 -- you times -8 and 2 which comes out to -16. Since you have -16 + 1 inside of the parentheses you add 1 to -16 which comes out to -15. Then you take -15 times 3 and it comes out to -45.

Q2 -- the m gets replaced by the 5 so now its -2 times 5. Which comes out to -10. Then you take -10 times 2, which is -20. Now take -20 + 10 which gives us the answer of -10.

Q3 -- I'm not completely sure on this one but I think the equation would transfer to this 2*5 + 5*3 + 2*3. So 2*5 is 10, 5*3 is 15, and 2*3 is 6. Add them all together and you get 31.

I hope this was right and it helps you!

6 0
2 years ago
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