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Mars2501 [29]
3 years ago
15

What is the solution to the system of equations y= -3x+6 and y =9

Mathematics
1 answer:
Lilit [14]3 years ago
7 0
Plug the value of 9 in for y
9=-3x+6

Subtract 6 from both sides
3=-3x

Divide both sides by -3
-1=x

Final answer: x=–1
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5 0
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8 0
3 years ago
PLEASE HELP!<br>Calculate $40^{13} \pmod{85}.$
SVEN [57.7K]
In this type of calculations, we decompose 13 by checking the lowest powers of the base, that is 40. for example we check 40^2, or 40^3 and compare it to 85

Notice

40*40*40=64,000

so we check how many time does 85 fit into 64,000:

64,000/85=752.94

85*753=64,005;       64000-64,005=-5

this means that 

40^{3} =-5\pmod{85}

thus

40^{13} =40^{3*4+1}={(40^{3})}^{4}*40=(-5)^{4}*40 \pmod{85}=\\\\625*40\pmod{85}=(7*85+30)*40\pmod{85}=30*40\pmod{85}\\\\=1200\pmod{85}=(14*85+10)\pmod{85}=10\pmod{85}


Answer: 10 (mod85)

Remark, the set of all solutions is:

{......-75, 10, 95, .....}, that is 85k +10
7 0
3 years ago
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