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fiasKO [112]
3 years ago
8

Help!!!!!! Will give Brainlist answer!!!! 3 parts pls thank you so much

Mathematics
1 answer:
wariber [46]3 years ago
6 0
Part A
The small red arcs indicate that angles PQS and RQS are congruent.

13x - 1 = 2(6x + 4)

13x - 1 = 12x + 8

x = 9

m<PQR = 13x - 1 = 116

m<RQS = 6x + 4 = 6(9) + 4 = 58

m<PQS = 116 - 58 = 58

Part B

12^2 + (OH)^2 = 13^2

144 + (OH)^2 = 169

(OH)^2 = 25

OH = 5

r = OH = 5

Part C

WZ/ZY = WX/XY

24/12 = 30/XY

2 = 30/XY

2(XY) = 30

XY = 15
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Simplify the following expression as much as you can use exponential properties. (6^-2)(3^-3)(3*6)^4
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Answer:

Simplifying the expression (6^{-2})(3^{-3})(3*6)^4 we get \mathbf{108}

Step-by-step explanation:

We need to simplify the expression (6^{-2})(3^{-3})(3*6)^4

Solving:

(6^{-2})(3^{-3})(3*6)^4

Applying exponent rule: a^{-m}=\frac{1}{a^m}

=\frac{1}{(6^{2})}\frac{1}{(3^{3})}(18)^4\\=\frac{(18)^4}{6^{2}\:.\:3^{3}} \\

Factors of 18=2\times 3\times 3=2\times3^2

Factors of 6=2\times 3

Replacing terms with factors

=\frac{(2\times3^2)^4}{(2\times 3)^{2}\:.\:3^{3}} \\=\frac{(2)^4\times(3^2)^4}{(2)^2\times (3)^{2}\:.\:3^{3}} \\

Using exponent rule: (a^m)^n=a^{m\times n}

=\frac{(2)^4\times(3)^8}{(2)^2\times (3)^{2}\:.\:3^{3}} \\=\frac{2^4\times 3^8}{2^2\times 3^{2}\:.\:3^{3}}

Using exponent rule: a^m.a^n=a^{m+n}

=\frac{2^4\times 3^8}{2^2\times 3^{2+3}}\\=\frac{2^4\times 3^8}{2^2\times 3^{5}}

Now using exponent rule: \frac{a^m}{a^n}=a^{m-n}

=2^{4-2}\times 3^{8-5}\\=2^{2}\times 3^{3}\\=4\times 27\\=108

So, simplifying the expression (6^{-2})(3^{-3})(3*6)^4 we get \mathbf{108}

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