Find all solutions, if any, to the systems of congruences x ≡ 7 (mod 9), x ≡ 4 ( mod 12) and x ≡ 16 (mod 21).
What are the steps?
I know that you can't directly use the Chinese Remainder Theorem since your modulars aren't prime numbers.

x ≡ 859 (mod 756) is the solution to the system of congruences.

To solve the system of congruences x ≡ 7 (mod 9), x ≡ 4 ( mod 12) and x ≡ 16 (mod 21), we can use the method of simultaneous equations.

Step 1: Start with the first two congruences, x ≡ 7 (mod 9) and x ≡ 4 ( mod 12). We can write these as a system of linear equations:

x = 9a + 7

x = 12b + 4

where a and b are integers. Solving for x, we get:

x = 108c + 67

where c = 4a + 1 = 3b + 1.

Step 2: Substitute x into the third congruence, x ≡ 16 (mod 21), to get:

108c + 67 ≡ 16 (mod 21)

Simplify the congruence:

3c + 2 ≡ 0 (mod 21)

Step 3: Solve the simplified congruence, 3c + 2 ≡ 0 (mod 21), by trial and error or using a modular inverse. In this case, we can see that c ≡ 7 (mod 21) satisfies the congruence.

Step 4: Substitute c = 7 into the expression for x:

x = 108c + 67 = 108(7) + 67 = 859

Therefore, the solutions to the system of congruences are x ≡ 859 (mod lcm(9,12,21)), where lcm(9,12,21) is the least common multiple of 9, 12, and 21, which is 756.

Hence, x ≡ 859 (mod 756) is the solution to the system of congruences.

Learn more about congruences here

https://brainly.com/question/30818154

#SPJ11

Gabby's dad drives a dump truck for a construction company. Last week, he came to Gabby's class for Career Day and talked about how math is used in his job. As an example, he told the class the bed of his truck is shaped like a rectangular prism with a volume of 24 cubic meters. The bed is 4 meters long and 2 meters deep.
How wide is the bed of the truck?


PLEASE HELP!!!!!!!!!!

-2+4x+5-6x=-x+3,2-2x+1​

merhaba adim omer takip edermisiniz​

A bag contains 4 red, 3 green, and 2 yellow marbles. One marble is randomly chosen What is the probability that the marble picked is red?​

what is the factored form of 5(8 + 3x) + 5? ​

which number line shows the graph of x \ 1

If the length of the longest side of the rectangle is 20cm find the shaded area to the nearest hundredth

А
R
29
20
B
21
Find tan(a) in the triangle.

Answer the photo below thanks

Hi!! When we do percents could decimal way be sufficient or will fraction way be?

Tom created a mixed-media mural of a flag to celebrate the 4th of July. He spent $57 on paint and 4 times as much on fabric. How many money did he spend altogether?

PLEASE HELP ASAP!!
In 2015, the cost of bread was $0.40. In 2021, the cost of bread is $2.00. What is the percent of change?
ILL GIVE BRAINLIEST

PLEASE HELP!!
Find AC

3. Find the area of the
shaded region.

A teacher purchased 20 calculators and 10 measuring tapes for her class and paid $495. Later, she realized that she didn't order enough supplies. She placed another order of 8 of the same calculators and 1 more of the same measure tape and paid $178.50.The system represents the situation

`20c+10m=495`

`8c+1m=178.50`

Find the cost of one calculator and the cost of one measure tape using one of our methods of solving systems.

Use the information to answer the question.
There are 2.54 centimeters in 1 inch. There are 100 centimeters in 1 meter.
To the nearest meter, how many meters are in 275 inches? Enter the answer in the box.
meters
0

i'm so confused please hurry

CAN SOMEONE PLEASE HELP ME!!!

Which of the following descriptions is TRUE regarding linear and exponential functions?

There is no difference between a linear function and an exponential function.
Linear functions cross the y-axis above exponential functions.
Linear functions slope down, while exponential functions slope up.
Linear functions have a constant slope, while exponential functions start flat and get steeper.

Select three expressions that are equivalent to 12y + 18 by factoring,
6(2 + 3y)
2(6 + 9)
209 + 6y)
6(3 + 2y)
3(4y + 6)

1. I NEED HELP ASAP!! PLEASE PUT AND ANSWER AND STEP BY STEP EQUATION!! IF YOU DON'T KNOW THE ANSWER DON'T PUT ANYTHING!!
IT'S NOT A.

Write a rule for the linear function shown in the graph.


A. y = -5/2x - 1

B. y = 2/5x + 1

C. y = 3x - 1

D. y = 5/3x + 1

Find the area of a vertical cross section through the centers of the bases of a cylinder with height of 27 inches and a circumference of about 47.1 inches. Use 3.14 for π.

Given f(x)=-3x+7 and g(x)=2x2 - 8, find g(f(x)).

The number 650,000 written in scientific notation would be _____.

A.6.5 × 10 -5
B.6.5 × 10 5
C.65 × 10 4
D.0.65 × 10 -6

?
cuantos es 2X = 8?

What's the answer to -5x+8=-4x+9?

Someone please help me I’ll give out brainliest please don’t answer if you don’t know

18m = 36

Please help me with this for brainliest HURRYYYY

Pleasee helpppp
If you are using indirect measurement, what is true?



A.You must convert dimensions to the same unit of measurement.


B.You do not have to convert dimensions to the same unit of measurement.

which of the following could not be the lengths of the sides of a triangle ​