Answer:
The smallest positive integer solution to the given system of congruences is 30.
Step-by-step explanation:
The given system of congruences is
where, m and n are positive integers.
It means, if the number divided by 5, then remainder is 0 and if the same number is divided by 11, then the remainder is 8. It can be defined as
Now, we can say that m>n because m and n are positive integers.
For n=1,
19 is not divisible by 5 so m is not an integer for n=1.
For n=2,
The value of m is 6 and the value of n is 2. So the smallest positive integer solution to the given system of congruences is
Therefore the smallest positive integer solution to the given system of congruences is 30.
Answer: a) y=-29x-20 b) y=3/5x-18
Step-by-step explanation:
a) m = (-49-38)/(1 - (-2)) = -87/3 = -29
y=-29x+b --> Substitute (1,-49) as a point
(-49)=-29(1)+b
-49=-29+b
-b=-29+49
b=-20
Therefore, the equation of the line is y=-29x-20
b) m = (-18-(-9)/(0-15)) = -9/-15 = 3/5
The y-intercept is (0,-18) as it's where the line intersects the y-axis and x equals 0
Therefore, the equation of the line is y=3/5x-18
Answer:Feudalism helped protect communities from the violence and warfare that broke out after the fall of Rome and the collapse of strong central government in Western Europe. Feudalism secured Western Europe's society and kept out powerful invaders. Feudalism helped restore trade. Lords repaired bridges and roads.
Step-by-step explanation:
Part A: Describe the two factors in this expression. (4 points) The factors are (1) the constant coefficient 9 and (2) the binomial (7+2x).
Part B: How many terms are in each factor of this expression? (4 points) The first factor (multiplicand), 9, has one term. The second factor (multiplicand), (7+2x), has two terms (and is thus called a binomial).
Part C: What is the coefficient of the variable term? (2 points) The only such coefficient is 2.
Sum means add, a number means x, and four means, uh, 4...
x+4. is what you're looking for
