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Mars2501 [29]
3 years ago
6

What is the simplified form of 15 x to the eighth power over 24 y to the fifth power divided by 4 x to the fourth power over 8 s

quared
A) 4 y cubed over 5 x to the fourth power
B) 4 y to the fourth power over 5 x cubed
C) 5 x to the fourth power over 4 y cubed
D) 5 x cubed over 4 y to the fourth power
Mathematics
1 answer:
IRISSAK [1]3 years ago
3 0
The exponent symbol when typing is ^. so I so rewrite this for you.
(15x^8 / 24y^5) / (4x^4 / 8y^2)

I assumed you meant 8y squared because you said 8 squared.

now when we divide by a fraction, we can actually multiply by it's reciprocal and get the same thing. The word reciprocal really just means flip it over. so:

(15x^8 / 24y^5) * (8y^2 / 4x^4)

let's reduce the coefficients ( the numbers in front of the x and y) to make it easier.

We have 15/24 which can be reduced to 5/8
and 8/4 which is 2/1

so:
(5x^8 / 8y^5) * (2y^2 / x^4)

multiply numerator and denominator
(10x^8y^2) / (8x^4y^5)

now reduce coeffient. 10/8 is 5/4
reduce x: x^8/x^4 is x^4
reduce y: y^2/y^5 is 1/y^3

now put together
5x^4 / 4y^3

so C
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The function h(x) = x2 + 14x + 41 represents a parabola.
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Part A:

h(x)= x^{2} +14x+41

The first step of completing the square is writing the expression x^{2} +14x as (x+7)^{2} which expands to x^{2} +14x+49.

We have the first two terms exactly the same with the function we start with: x^{2} and 14x but we need to add/subtract from the last term, 49, to obtain 41. 

So the second step is to subtract -8 from the expression x^{2} +14x+49

The function in completing the square form is
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Part B:

The vertex is obtained by equating the expression in the bracket from part A to zero

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A quadratic function a x^{2} +bx+c can either make U-shape or ∩-shape depends on the value of the constant a that goes with x^{2}. When a is (+), the curve is U-shape. When a (-), the curve is ∩-shape

Part C:

The symmetry line of the curve will pass through the vertex, hence the symmetry line is x=-7

This function is shown in the diagram below




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I did a manual computation per company: My computation is entirely based on trial and error.

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Hr 1                    72                                      222   => 150 + 72
Hr 2                    72                                      294  =>  222 + 72
Hr 3                    72                                      366  => 294  + 72
Hr 4                    72                                      438  => 366 + 72
Hr 5                    72                                      510  => 438 + 72

I'll do the same process with Blue Bus Co.

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Hr 1                54                                      294 => 240 + 54
Hr 2                54                                       348 => 294 + 54
Hr 3                54                                      402 => 348 + 54
Hr 4                54                                      456 => 402 + 54
Hr 5                54                                      510 => 456 + 54



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