D + 3n = 1 Subtract d from both sides
3n = 1 - d Divide both sides by 3
n =
3n = 1 - d Divide both sides by 3
n =
N(17+x)=34x−r I need to solve for x
2 answers:
Answer:
The value of x is,
Explanation:
Given:
Distributive Property states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately.
If
Now, using distributive property on left hand side of the given expression as:
or
Addition Property of equality state that we add the same number from both sides of an equation.
Add r to both sides of an equation:
Simplify:
Subtraction Property of equality state that we subtract the same number from both sides of an equation.
Subtract Nx from both sides of an equation;
Simplify:
or
Division Property of equality states that we divide the same number from both sides of an equation.
Divide by (34-N) to both sides of an equation;
On Simplify:
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The solution to this system is (x, y) = (8, -22).
The y-values get closer together by 2 units for each 2-unit increase in x. The difference at x=2 is 6, so we expect the difference in y-values to be zero when we increase x by 6 (from 2 to 8).
You can extend each table after the same pattern.
In table 1, x-values increase by 2 and y-values decrease by 8.
In table 2, x-values increase by 2 and y-values decrease by 6.
The attachment shows the tables extended to x=10. We note that the y-values are the same (-22) for x=8 (as we predicted above). That means the solution is ...
... (x, y) = (8, -22)
The summation indicates the sum from n = 1 to n = 3 of the expression 2(n+5).
2 (n+5) = 2n + 10
2n + 10 denotes an Arithmetic Series, with a common difference of two and first term as 12.
For n =1, it equals 12
For n = 2, it equals 14
For n = 3, it equals 16
So the sum from n=1 to n=3 will be 12 + 14 + 16 = 42
Sum of an Arithmetic Series can also be written as:
Using the value of a₁ and d, we can simplify the expression as:
This expression is equivalent to the given expression and will yield the same result.
For n=3, we get the sum as:
S₃ = 3(11+3) = 42
2 (n+5) = 2n + 10
2n + 10 denotes an Arithmetic Series, with a common difference of two and first term as 12.
For n =1, it equals 12
For n = 2, it equals 14
For n = 3, it equals 16
So the sum from n=1 to n=3 will be 12 + 14 + 16 = 42
Sum of an Arithmetic Series can also be written as:
Using the value of a₁ and d, we can simplify the expression as:
This expression is equivalent to the given expression and will yield the same result.
For n=3, we get the sum as:
S₃ = 3(11+3) = 42