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Reil [10]
3 years ago
7

I need help with 5 and 14 pls

Mathematics
1 answer:
Julli [10]3 years ago
4 0

Answer:

5

(3a²b³c)³(2a⁴b²c²)³

= (3a⁶b⁹c³)(8a¹²b⁶c⁶)

= 24a¹⁸b¹⁵c⁹

14

⁴√(81a¹⁶b¹²c⁹)

= (⁴√81)(⁴√a¹⁶)(⁴√b¹²)(⁴√c⁹)

= 3 (a^{\frac{16}{4} }) (b^{\frac{12}{4} } ) (c^{\frac{9}{4} } )

= 3a^{4} b^{3} c^{\frac{9}{4} }

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Choose the graphic representation of the quadratic function f(x) = x2 – 8x + 24.
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Refer the attached figure for the graphic representation of the given quadratic equation.

<u>Step-by-step explanation:</u>

Given expression:

    f(x)=x^{2}-8 x+24

To find:

  The graphic representation of the given quadratic function

For solution, plot the graph to the given quadratic equation.

The standard form of the equation is

  y=a x^{2}+b x+c

When comparing with given quadratic equation,

a = 1, b = - 8, c = 24

Axis of symmetry is x=\frac{-b}{2 a}

By applying the values, the axis of symmetry of given equation is

     x=\frac{-(-8)}{2(1)}=4

The vertex form of quadratic equation is f(x)=a(x-h)^{2}+k

Where, (h,k) are the vertex.

Convert the quadratic equation into vertex form.

By completing the square,

f(x)=x^{2}-8 x+24

f(x)=\left(x^{2}-2(4) x+4^{2}\right)-4^{2}+24

f(x)=(x-4)^{2}+8

On comparison,

(h , k) = (4 , 8)

Now, plot the equation with vertex (4,8) [refer attached figure].

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