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Natali5045456 [20]
3 years ago
6

Find the solution of this system of equations. separate the x and y values. x=2+y -6x-6y=-12

Mathematics
1 answer:
Shkiper50 [21]3 years ago
8 0
{x=2+y
{-6x-6y=-12

-6(2+y) -6y = -12
-12 - 6y - 6y = -12
-12y = -12 + 12
-12y = 0
y = 0

x = 2 + y = 2 + 0 = 2

Answer: x=2, y=0
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At bike shop x it costs $2.75 per hour plus a $3.00 deposit to rent a bike. at bike shop z it costs $1.75 per hour plus a $7.00
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Multiply the rate per hour by the number of hours (n) and add the deposit.

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Using binomial theorem, expand (x+6)^8 <br><br> edit: You could use the help of combinations too.
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x⁸ + 48x⁷ + 1008x⁶ + 12096x⁵ + 90720x⁴ + 435456x³ + 1306368x² + 2239488x + 1679616

<u>Explanation:</u>

We know

(x+y)ⁿ = ∑ ⁿCₐxⁿ⁻ᵃyᵃ

and ⁿCₐ = n! / ( a! ) . ( n-a )!

So,

(x+6)⁸ = ⁸C₀x⁸ + ⁸C₁(x)⁸⁻¹(6)¹ + ⁸C₂(x)⁸⁻²(6)² + ⁸C₃(x)⁸⁻³(6)³ + .......+ ⁸C₈(x)⁸⁻⁸(6)⁸

         = ₓ⁸ + 8x⁷ₓ 6 + 28x⁶ₓ 36 + 56x⁵ₓ 216 + 70x⁴ₓ 1296 + 56x³ₓ 7776 + 28x²ₓ     46656 + 8x . 279936 + 1679616

         = x⁸ + 48x⁷ + 1008x⁶ + 12096x⁵ + 90720x⁴ + 435456x³ + 1306368x² + 2239488x + 1679616

Thus, the expansion of ( x+6)⁸ using binomial theorm is

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