The answer is 171.25.
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Answer: Lenayah's presentation was 12 minutes long.
Step-by-step explanation:
- Set up a proportion. 2/3 = 8/x.
- Cross multiply. 2x = 24
- Divide both sides by 2. x =12
2x + 5y = 26....multiply by 3
3x + 4y = 26...multiply by -2
------------------
6x + 15y = 78 (result of multiplying by 3)
-6x - 8y = - 52 (result of multiplying by -2)
-----------------add
7y = 26
y = 26/7 (or 3 5/7)
2x + 5y = 26
2x + 5(26/7) = 26
2x + 130/7 = 26
2x = 26 - 130/7
2x = 182/7 - 130/7
2x = 52/7
x = 52/7 * 1/2
x = 52/14 which reduces to 26/7 (or 1 5/7)
solution is : (26/7, 26/7)
(a) The inverse of 1234 (mod 4321) is x such that 1234*x ≡ 1 (mod 4321). Apply Euclid's algorithm:
4321 = 1234 * 3 + 619
1234 = 619 * 1 + 615
619 = 615 * 1 + 4
615 = 4 * 153 + 3
4 = 3 * 1 + 1
Now write 1 as a linear combination of 4321 and 1234:
1 = 4 - 3
1 = 4 - (615 - 4 * 153) = 4 * 154 - 615
1 = 619 * 154 - 155 * (1234 - 619) = 619 * 309 - 155 * 1234
1 = (4321 - 1234 * 3) * 309 - 155 * 1234 = 4321 * 309 - 1082 * 1234
Reducing this leaves us with
1 ≡ -1082 * 1234 (mod 4321)
and so the inverse is
-1082 ≡ 3239 (mod 4321)
(b) Both 24140 and 40902 are even, so there GCD can't possibly be 1 and there is no inverse.
