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2 years ago

Given x less than y, compare the following expressions and determine which is greater: 2x-y;2y-x. Explain your answer.

1 answer:

8 0

Well in this case, to see which is greater, let's just say that:
x=4 <--- 4 is less than 5
y=5

Now substitute:
2x-y 2y-x
2(4)-5 2(5)-4
8-5 10-4
3 6

Which of these is greater, 3 or 6? 6, obviously. Therefore, we know that 2y-x is greater.
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Precal help if you could could you answer both. Me finishing this helps me graduate.

oee [108]

Exercise 1:

The easiest way to compute powers of complex numbers is to write them in the form

$z = \rho e^{i\theta} = \rho(\cos(\theta)+i\sin(\theta))$

In this form, you have

$z^n = \rho^n e^{in\theta} = \rho^n(\cos(n\theta)+i\sin(n\theta))$

The magnitude of the number is given by

$z=a+bi \implies \rho = \sqrt{a^2+b^2}$

So, we have

$z=-1+\sqrt{3}i \implies \rho = \sqrt{1+3}=2$

As for the angle, we have

$z=a+bi \implies \theta = \text{atan2}\dfrac{b}{a}$

So, we have

$z=-1+\sqrt{3}i \implies \theta = \text{atan2}\left(\dfrac{-\sqrt{3}}{-1}\right) = -\dfrac{2\pi}{3}$

Finally,

$z=-1-\sqrt{3}i = 2\left(\cos\left( -\dfrac{2\pi}{3}\right) + i\sin\left( -\dfrac{2\pi}{3}\right)\right) \implies z^6 = 2^6\left(\cos\left( -4\pi\right) + i\sin\left(-4\pi\right)\right) = 64$

Exercise 2:

You simply have to compute the trigonometric function:

$\cos\left(-\dfrac{\pi}{4}\right) = \dfrac{\sqrt{2}}{2},\quad \sin\left(-\dfrac{\pi}{4}\right) = -\dfrac{\sqrt{2}}{2}$

So, we have

$z = \sqrt{2}\left(\dfrac{\sqrt{2}}{2} - i\dfrac{\sqrt{2}}{2}\right) = 1-i$

7 0

2 years ago

Can someone please explain? I don't understand

Nezavi [6.7K]

A solution for a pair of lines means that they are equal to each other. This occurs when they instersect. Since the lines have the same slope, but are not the same line, they are parallel, so they will never intersect. This means there are zero solutions.
Hope this helps!

6 0

2 years ago

Was doing my work and need help

Arturiano [62]

3/4 divide by 5 is equal to 3/20

4 0

2 years ago

Read 2 more answers

550 tickets were sold for a game for a total of $712.50. If adult tickets sold for $1.50 and children's tickets sold for $1.00,

EastWind [94]

9514 1404 393

Answer:

adult: 325
children's: 225

Step-by-step explanation:

It usually works well to let a variable represent the higher-value item in the mix. Here, we can let 'a' represent the number of adult tickets sold. Then the total revenue is ...

1.50a +1.00(550 -a) = 712.50

0.50a = 162.50 . . . . . . . . . . . . . subtract 550 and collect terms

a = 325

c = 550 -325 = 225

325 adult and 225 children's tickets were sold.

4 0

2 years ago

lori says that 8 is not a factor of 80 because 8 does not end in zero. Does Lori's statement make sense? Explain

77julia77 [94]

You have to know that the zero has no value inless its in a place value .the 8 is a factor of 80 because 80 is 10 times as much as 8

5 0

2 years ago

Read 2 more answers