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Verdich [7]
3 years ago
15

Find the Unit Rate. The Johnson family traveled 840 miles in 15 hours.

Mathematics
1 answer:
sesenic [268]3 years ago
4 0

Heya!

Here's your answer!!

speed = 56 miles per hour

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Solve the following simultaneous linear congruences.
Anastaziya [24]

a. The moduli are coprime, so you can apply the Chinese remainder theorem directly. Let

x=4\cdot5+3\cdot5+3\cdot4

  • Taken mod 3, the last two terms vanish, and 20\equiv2\pmod3 so we need to multiply by the inverse of 2 modulo 3 to end up with a remainder of 1. Since 2\cdot2\equiv4\equiv1\pmod3, we multiply the first term by 2.

x=4\cdot5\cdot2+3\cdot5+3\cdot4

  • Taken mod 4, the first and last terms vanish, and 15\equiv3\pmod4. Multiply by the inverse of 3 modulo 4 (which is 3 because 3\cdot3\equiv9\equiv1\pmod4), then by 2 to ensure the proper remainder is left.

x=4\cdot5\cdot2+3\cdot5\cdot3\cdot2+3\cdot4

  • Taken mod 5, the first two terms vanish, and 12\equiv2\pmod5. Multiply by the inverse of 2 modulo 5 (3, since 3\cdot2\equiv6\equiv1\pmod5) and again by 3.

x=4\cdot5\cdot2+3\cdot5\cdot3\cdot2+3\cdot4\cdot3\cdot3

\implies x=238

By the CRT, we have

x\equiv238\pmod{3\cdot4\cdot5}\implies x\equiv-2\pmod{60}\implies\boxed{x\equiv58\pmod{60}}

i.e. any number 58+60n (where n is an integer) satisifes the system.

b. The moduli are not coprime, so we need to check for possible contradictions. If x\equiv a\pmod m and x\equiv b\pmod n, then we need to have a\equiv b\pmod{\mathrm{gcd}(m,n)}. This basically amounts to checking that if x\equiv a\pmod m, then we should also have x\equiv a\pmod{\text{any divisor of }m}.

x\equiv4\pmod{10}\implies\begin{cases}x\equiv4\equiv0\pmod2\\x\equiv4\pmod5\end{cases}

x\equiv8\pmod{12}\implies\begin{cases}x\equiv0\pmod2\\x\equiv2\pmod3\end{cases}

x\equiv6\pmod{18}\implies\begin{cases}x\equiv0\pmod2\\x\equiv0\pmod3\end{cases}

The last congruence conflicts with the previous one modulo 3, so there is no solution to this system.

5 0
3 years ago
I WILL AWARD BRAINLIEST FOR CORRECT ANSWER :)
Colt1911 [192]

Answer:

The first one is correct

The second one is 20years

The third one is £8820

Step-by-step explanation:

5 0
3 years ago
What are the solutions to the equation y² + 16 = 212?
Levart [38]
Y² + 16 = 212 
<span>y</span>² <span>= 196 </span>
<span>y = -14 and 14</span>
6 0
3 years ago
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Suppose you invest $63 a month in an annuity that earns a 3.3% APR
lisov135 [29]

Answer: $3227.93 APEX

4 0
3 years ago
Explain how you can use strategy guess check and revise to solve problems that involve a given area when the relationship betwee
Aleksandr-060686 [28]
You can try finding numbers that are close to what you think you can use for exaple lets say we want to find the answer to 54x34 you could multiply 50x30 to get an estimated answer
3 0
2 years ago
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