19 and 42 are coprime, so we can use the CRT right away. Start with
![x=19+42](https://tex.z-dn.net/?f=x%3D19%2B42)
Taken mod 42, we're left with a remainder of 19. Notice that
![19\cdot3\equiv57\equiv15\pmod{42}](https://tex.z-dn.net/?f=19%5Ccdot3%5Cequiv57%5Cequiv15%5Cpmod%7B42%7D)
so we need to multiply the first term by 3 to get the remainder we want.
![x=19\cdot3+42](https://tex.z-dn.net/?f=x%3D19%5Ccdot3%2B42)
Next, taken mod 19, we're left with a remainder of 4. Notice that
![42\cdot6\equiv252\equiv5\pmod{19}](https://tex.z-dn.net/?f=42%5Ccdot6%5Cequiv252%5Cequiv5%5Cpmod%7B19%7D)
so we need to multiply the second term by 6.
Then by the CRT, we have
![x\equiv19\cdot3+42\cdot6\equiv309\pmod{42\cdot19}\implies x\equiv309\pmod{798}](https://tex.z-dn.net/?f=x%5Cequiv19%5Ccdot3%2B42%5Ccdot6%5Cequiv309%5Cpmod%7B42%5Ccdot19%7D%5Cimplies%20x%5Cequiv309%5Cpmod%7B798%7D)
so that any solution of the form
is a solution to this system.
Answer:
see below
Step-by-step explanation:
2/3 ÷ 4
We use copy dot flip
The flip means make a reciprocal of the second number
2/3 * 1/4
Multiply the numerators
2*1 = 2
Multiply the denominators
3*4 =12
Put the numerator over the denominator
2/12
Simplify
1/6
Answer:
B
Step-by-step explanation:
Soemthing is a function if it can pass the vertical line test
the vertical line test is when you draw a vertical line and it only touches the graph once
Another way of thinking about this is no function can have two of the same values on the x axis
I'm not too sure what's happening with the third response but the answer is B
Answer:
135 to nearest whole number.
Step-by-step explanation:
∑ 5(4/3)^(k-1) from k = 1 to k = 8.
First term = 5 , second term = 5*4/3
This is a Geometric series with first term a1 = 5 and common ratio r = 4/3.
The sum of n terms = a1(r^n - 1) / (r - 1).
The sum of 8 terms is given by 5 * (4/3)^8 - 1) / ( 4/3 - 1)
= 135 to the nearest whole number.