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iogann1982 [59]
2 years ago
7

Katherine has a points card for a movie theater.

Mathematics
1 answer:
mario62 [17]2 years ago
7 0

Answer:

s >= 45/13.5

4

Step-by-step explanation:

First you take 120 and subtract the 75 reward points. That gets you 45 more points you need to get. The inequality would be s is greater than or equal to  45/13.5. The minimum number of visits would be 4.

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On a shelf at a gaming store, there are five Sony Playstations and three Nintendo Wii consoles left. If one gaming system is sel
Tpy6a [65]

Step-by-step explanation:

a probability is always desired cases over total possible cases.

so, we have actually 8 systems (5 + 3) we can pick from.

therefore, the total possible cases are 8.

the desired case is in this question to pick one of the 3 Wii consoles.

the probability to pick a Wii is therefore

3/8 = 0.375

5 0
2 years ago
Read 2 more answers
Math 2 Of high school
Daniel [21]

Answer:

  • B. BC = 18 so ∆ABC ~ ∆DEF by SAS

Step-by-step explanation:

\bf \cfrac{AB}{DE}  =  \cfrac{BC}{EF}

  • \bf \cfrac{15}{10}  =  \cfrac{BC}{12}
  • \bf  \cfrac{3}{2}  =  \cfrac{BC}{12}
  • \bf BC =  \cfrac{3}{2}  \times 12
  • \bf 3 \times 6
  • \bf BC = 18
  • \bf \angle B = \angle \: E

So, ∆ABC ~ ∆DEF by SAS.

<h3><u>------------------------------------</u></h3>
7 0
2 years ago
(x + 5)2 + (y - 7)2 = 36, its radius is
sashaice [31]
6 because the 36 is r² where r is the radius, r² = 36; we have to isolate the r so it's by its self, so square root both sides, r = 6 
5 0
2 years ago
Any body wana play imvu.........​
Igoryamba
Dfkcghkbftff is that
7 0
2 years ago
Read 2 more answers
What is (2-2i√3)4 equivalent to?
maxonik [38]

a. (2 - 2i√3)⁴ in polar form is 256(cos(-4π/3) + isin(-4π/3)) = 256cis(-4π/3)

b. (2 - 2i√3)⁴ in rectangular form is -128 + 128√3

To answer the question, we need to know what complex numbers are

<h3>What are complex numbers?</h3>

Complex numbers are numbers of the form z = x + iy

<h3>a. Complex numbers in polar form</h3>

Complex numbers in polar form z = r(cosθ + isinθ) where

  • r = √(x² + y²) and
  • θ = tan⁻¹(y/x)

Given that z = (2 - 2i√3)⁴ =

So,

  • x = 2 and
  • y = -2√3

So, converting to polar form

r = √(x² + y²)

= √[2² + (-2√3)²]

= √[4 + 4(3)]

= √[4 + 12]

= √16

= 4

θ = tan⁻¹(y/x)

θ = tan⁻¹(-2√3/2)

θ = tan⁻¹(-√3)

θ = -π/3

So, z = r(cosθ + isinθ)

= 4(cos(-π/3) + isin(-π/3))

<h3>Powers of complex numbers</h3>

A complex number z raised to power n is zⁿ = rⁿ(cosnθ + isin(nθ)]

z⁴ = (2 - 2i√3)⁴

= r⁴(cos4θ + isin4θ)

= 4⁴(cos(4 × -π/3) + isin(4 × -π/3))

= 256(cos(-4π/3) + isin(-4π/3))

= 256cis(-4π/3)

(2 - 2i√3)⁴ in polar form is 256(cos(-4π/3) + isin(-4π/3)) = 256cis(-4π/3)

<h3>b. Complex numbers in rectangular form</h3>

The complex number z =  r(cosθ + isinθ) in rectangular form is z = x + iy where

  • x =  rcosθ and
  • y =  rsinθ

Given that z⁴ = 256(cos(-4π/3) + isin(-4π/3)) in rectangular form,

x = rcosθ

= 256(cos(-4π/3)

= 256cos(-4 × 60°)

= 256cos(-240)

= 256cos(240)

= 256 × -1/2

= -128

y =  rsinθ

= 256sin(-4π/3)

= 256sin(-4 × 60°)

= 256sin(-240)

= -256sin240

= -256 × -√3/2

= 128√3

So, z⁴ = x + iy

= -128 + 128√3

So, (2 - 2i√3)⁴ in rectangular form is -128 + 128√3

Learn more about complex numbers in polar form here:

brainly.com/question/9678010

#SPJ1

7 0
1 year ago
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