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3 years ago

Suppose y is a positive integer. If x-(-y) = z, will z be greater than, or less than x?

Mathematics

2 answers:

labwork [276]3 years ago

7 0

Answer

Z would be greater than x

Step-by-step explanation:

Suppose x=5, -y = -8

Our problem would be:

5 - (-8) = ?

5 - (-8) = 13

5 < 13

Brilliant_brown [7]3 years ago

7 0

Answer:

It would be greater

Step-by-step explanation:

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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

Rent-Me Rent-A-Car charges $25.00 per day plus $0.14 per mile to rent an economy car. Better Deal Rental Car charges $23.00 per

zalisa [80]

Answer:

The number of miles at which a car rented from either company cost the same amount is 50 miles.

Step-by-step explanation:

Let x represents the number of miles at which a car rented from either company cost the same amount. Therefore, we can have the following equation:

RC = 25 + 0.14x ....................... (1)

BC = 23 + 0.18x ...................... (2)

Where;

RC = Total cost of Rent-Me Rent-A-Car

BC = Total cost of Better Deal Rental Car

The the cost of the two companies equal where RC = BC. Therefore, we equate equations (1) and (2) and solve for x as follows:

25 + 0.14x = 23 + 0.18x

25 - 23 = 0.18x - 0.14x

2 = 0.04x

x = 2 / 0.04

x = 50

Therefore, the number of miles at which a car rented from either company cost the same amount is 50 miles.

Note:

This can be confirmed for equations (1) and (2) individually by substituting for x = 50 as follows:

For equation (1):

RC = 25 + 0.14(50)

RC = 25 + 7

RC = 32

For equation (2):

BC = 23 + 0.18(50)

BC = 23 + 9

BC = 32

Therefore, RC = BC = 32 confirms the answer.

3 0

3 years ago

What is X for? x+20=35-4x

Helen [10]

X+4x=35-20. 5x=35-20. 5x=15. X=3

4 0

3 years ago

Read 2 more answers

A 3. A card is pulled from a standard deck of cards.

dexar [7]

<h3>Answer: 4/13</h3>

Explanation:

There are 13 hearts, including the queen of hearts. Then there are 3 more queens to get us to 13+3 = 16 cards we're after.

There are 16 cards we want out of 52 total, so the probability is 16/52 = (4*4)/(4*13) = 4/13

3 0

2 years ago

Function f is shown below f(-3) f(4) find x when f(x) = 5 find x when f(x)= -3

hjlf

Answer:

See below ~

Step-by-step explanation:

Based on the graph,

f(-3)

f(-3) = 0

2. f(4)

f(4) = -3

3. x when f(x) = 5

f(x) = 5
x = 0

4. x when f(x) = -3

f(x) = -3
x = ±4

4 0

2 years ago