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nata0808 [166]
3 years ago
6

What is a simpler form of the radical expression?

Mathematics
1 answer:
adoni [48]3 years ago
5 0
∛125x^21y^24

Split them up:
∛125 * ∛x^21 * ∛y^24

∛125 = 5
∛x^21 = x^7           21/3 = 7
∛y^24 = y^8           24/3 = 8

The simpler form of the radical expression: ∛25x^21y^24 is: <span>D. 5x^7y^8</span>
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IgorLugansk [536]
Now, we know that he's charging $12 per session to each of his students, and he has 14 students currently, so his revenue is just 14 * 12 or 168 bucks.

now, let's take a peek as the session price goes up in jumps of 2, from 12, to 14, 16, 18 and so on, as each jumps happen, the students drop by 1, from 14, to 13, to 12 and so on.

\bf \begin{array}{ccccllll}&#10;\stackrel{increase}{x}&\stackrel{new}{price}&students&\stackrel{revenue}{y}\\&#10;------&------&------&------\\&#10;0&12&14&168\\&#10;1&14&13&182\\&#10;2&16&12&192\\&#10;3&18&11&198\\&#10;\boxed{4}&20&10&\boxed{200}\\&#10;5&22&9&198\\&#10;6&24&8&192\\&#10;7&26&7&182\\&#10;8&28&6&168\\&#10;..&..&..&..&#10;\end{array}

notice, the revenue starts off at 168, goes up up, reaches 200 bucks and then starts to drop back down.

thus, that means the U-turn or vertex of that revenue function is at 4,200, namely h = 4, and k = 200

\bf \qquad \textit{parabola vertex form}\\\\&#10;\begin{array}{llll}&#10;\boxed{y=a(x-{{ h}})^2+{{ k}}}\\\\&#10;x=a(y-{{ k}})^2+{{ h}}&#10;\end{array} \qquad\qquad  vertex\ ({{ h}},{{ k}})\\\\&#10;-------------------------------\\\\&#10;\stackrel{c(x)}{y}=a(x-\stackrel{h}{4})\stackrel{k}{+200}&#10;\\\\\\&#10;\textit{now, we also know that }&#10;\begin{cases}&#10;x=2\\&#10;y=192&#10;\end{cases}\implies 192=a(2-4)^2+200&#10;\\\\\\&#10;-8=a(-2)^2\implies -8=4a\implies \cfrac{-8}{4}=a\implies -2=a&#10;\\\\\\&#10;

\bf therefore\qquad \stackrel{ c(x)}{y}=-2(x-4)^2+200\impliedby \textit{let's expand that}&#10;\\\\\\&#10;y=-2(x^2-8x+16)+200\implies y=-2x^2+16x-32+200&#10;\\\\\\&#10;\stackrel{y}{c(x)}=-2x^2+16x+168
3 0
3 years ago
Read 2 more answers
Libby, Mike and Kyle share £44 in the ratio 2 : 3:6
anastassius [24]

Answer:

libby: £8

Mike: £12

Kyle: £24

Step-by-step explanation:

hope I helped

3 0
3 years ago
Round each decimal to the nearest hundredth.<br> A. .596<br> B. .367<br> C .24<br> D. 13.578
Gennadij [26K]
A .600

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D I'm not quite sure
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3 years ago
What is the value of x ? (Make sure you give the value of x !!!!)
DochEvi [55]

Answer:

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Step-by-step explanation:

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2(x) = 40

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A) 20 degrees

6 0
2 years ago
Are 2/7 and 6/21 equivalent ratios
ra1l [238]
6 / 2 = 3
21 / 7 = 3

Yes, 2/7 and 6/21 are equivalent ratios.  The second number is simply the first number tripled.  
5 0
3 years ago
Read 2 more answers
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