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Ronch [10]
2 years ago
3

Translate and solve: 64 less than y is no less than −128.

Mathematics
2 answers:
Ymorist [56]2 years ago
8 0

For this case we must write the following expression algebraically:

"64 less than" y "is no less than −128"

So:

64 less than y is represented as: y-64

no less than −128 means that the expression y-64 must be greater than or equal to -128.

Then, rewriting the expression we have:

y-64 \geq-128

We solve:

y \geq-128 + 64\\y \geq-64

ANswer:

y\geq-64

Varvara68 [4.7K]2 years ago
5 0

Answer:

y - 64 ≥ -128

y ≥ -64

Step-by-step explanation:

Translation:

y - 64 ≥ -128

Solving:

y - 64 + 64 ≥ -128 + 64

y ≥ -64

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A multiplicative inverse of an integer a is an integer x such that the product ax is congruent to 1 with respect to the modulus m.  

1. Z_{11}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10}\}.

Check:

  • 5\cdot 0=\overline{0};
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  • 5\cdot 3=15=\overline{4};
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  • 5\cdot 6=30=\overline{8};
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  • 5\cdot 8=40=\overline{7};
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  • 5\cdot 10=50=\overline{6}.

The multiplicative inverse of 5 in Z_{11} is 9.

2.   Z_{12}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10},\overline{11}\}.

Check:

  • 5\cdot 0=\overline{0};
  • 5\cdot 1=\overline{5};
  • 5\cdot 2=\overline{10};
  • 5\cdot 3=15=\overline{3};
  • 5\cdot 4=20=\overline{8};
  • 5\cdot 5=25=\overline{1};
  • 5\cdot 6=30=\overline{6};
  • 5\cdot 7=35=\overline{11};
  • 5\cdot 8=40=\overline{4};
  • 5\cdot 9=45=\overline{9};
  • 5\cdot 10=50=\overline{2};
  • 5\cdot 11=55=\overline{7}.

The multiplicative inverse of 5 in Z_{12} is 5.

3.  Z_{13}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10},\overline{11},\overline{12}\}.

Check:

  • 5\cdot 0=\overline{0};
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  • 5\cdot 9=45=\overline{6};
  • 5\cdot 10=50=\overline{11};
  • 5\cdot 11=55=\overline{3};
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The multiplicative inverse of 5 in Z_{13} is 8.

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