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Serggg [28]
3 years ago
11

Triangle XYZ has vertices X(-6, 3), Y(4,5), and Z(-2,-1).

Mathematics
1 answer:
Greeley [361]3 years ago
4 0

Answer:

see explanation

Step-by-step explanation:

A translation of 9 units to the right means adding 9 to the x- coordinates of the original points, while the y- coordinate remains unchanged, thus

X(- 6, 3 ) → X'(- 6 + 9, 3 ) → X'(3, 3 )

Y(4, 5 ) → Y'(4 + 9, 5 ) → Y'(13, 5 )

Z(- 2, - 1 ) → Z'(- 2 + 9, - 1 ) → Z'(7, - 1 )

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In a shipment of 56 vials, only 13 do not have hairline cracks. If you randomly select 3 vials from the shipment, in how many wa
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Step-by-step explanation:

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^{13}C_2\cdot ^{43}C_{1}+^{13}C_{1}\cdot ^{43}C_{2}+^{13}C_0\cdot ^{43}C_{3}\\\\=\dfrac{13!}{2!(13-2)!}\cdot\dfrac{43!}{1!(42)!}+\dfrac{13!}{1!(12)!}\cdot\dfrac{43!}{2!(41)!}+\dfrac{13!}{0!(13)!}\cdot\dfrac{43!}{3!(40)!}\\\\=\dfrac{13\times12\times11!}{2\times11!}\cdot (43)+(13)\cdot\dfrac{43\times42\times41!}{2\times41!}+(1)\dfrac{43\times42\times41\times40!}{6\times40!}\\\\=3354+11739+12341=27434

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