Put the equation in standard linear form.
Find the integrating factor.
Multiply both sides by 
.
Now the left side the derivative of a product,
Integrate both sides.
On the right side, integrate by parts.
Solve for 
.
Answer:
n squared + 3n + 1
Step-by-step explanation:
5,11,19,29
Firstly look at the difference between each number. The first difference is 6 then 8 then 10 etc. After that you look at your created sequence - 6,8,10 etc. The difference is 2 each time. Then applying rules, you have to do the constant difference divided by 2 to get a coefficient of n squared. So in this case it's n squared because 2/2 = 1 so you don't have to place a 1 in front of the n squared. After you create a sequence from the n squared. That would be 1,4,9 etc. Then you need to see how to get from the sequence: 1,4,9 etc to your original sequence: 5,11,19 etc. So if you calculate it you will get 4,7,10 because firstly 5-1 = 4 then 11-4 = 7 etc. The sequence 4,7,10 is a linear sequence so the constant difference is 3 each time. So to get a nth term of a linear sequence you will start off as 3n then you will substitute 1 then 2 then 3 into the 3n. Therefore that would be 3,6 etc. So if you take the first substituted term, that would be 3 as said before then you will have to see how to get from the 3 to 4 so that is just adding 1. So the nth term of this linear sequence is 3n + 1. Check if it works at the end. So the overall nth term of the quadratic sequence is n squared as said before + 3n + 1.
Answer: The number is 0.75 or 3/4
Step-by-step explanation:
let x = the number.
Now set up an equation: The product of a number (x) and -4 = -4x. So -4x is subtracted from the number - x. x-(-4x)
Then, that equals 3 more than the number (x) = x+3
So the equation is x-(-4x)=x+3.
Then, solve the equation!
x-(-4x)=x+3
x+4x=x+3 (Distribute the negative to the parentheses)
5x=x+3 (Combine like terms)
4x=3 (Get the Xs on one side by subtracting x from both sides)
x=0.75 or 3/4 (divide by the coefficiant, 4, on both sides)
Simplifying
15 + -5(4x + -7) = 50
Reorder the terms:
15 + -5(-7 + 4x) = 50
15 + (-7 * -5 + 4x * -5) = 50
15 + (35 + -20x) = 50
Combine like terms: 15 + 35 = 50
50 + -20x = 50
Add '-50' to each side of the equation.
50 + -50 + -20x = 50 + -50
Combine like terms: 50 + -50 = 0
0 + -20x = 50 + -50
-20x = 50 + -50
Combine like terms: 50 + -50 = 0
-20x = 0
Solving
-20x = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Divide each side by '-20'.
x = 0.0
Simplifying
x = 0.0
Answer:
D
Step-by-step explanation:
Firstly,
≤ or ≥ means closed circle, and
< or > means open circle
Now, let's solve the compound inequality:
x - 1 ≤ 7
x ≤ 8
and
2x ≥ 22
x ≥ 11
This solution means "everything left of 8 (inclusive and closed circle)" and "everything right of 11 (inclusive and closed circle)"
Looking at the choices, D is right.
