Answer:\frac{s-a}{n-1}
Step-by-step explanation:
formula, s=a+(n-1)d
1. get rid of the a on d's side by subtracting it from both sides.
s=a+(n-1)d becomes s-a=(n-1)d
2. get rid of (n-1) by dividing it from both sides. s-a=(n-1)d becomes
\frac{s-a}{n-1} =d
Answer:
26
Step-by-step explanation:
Let x be the first even integer
x+2 is the second even integer
x+4 is the third even integer
The sum of three consecutive even integers is 84
x+ (x+2) + (x+4) =84
Combine like terms
3x +6 = 84
Subtract 6 from each side
3x+6-6 =84-6
3x =78
Divide each side by 3
3x/3 = 78/3
x =26
The three integers are 26, 28,30
The smallest is 26
First, we simplify 6x+2y=36 into 3x+y=18 by dividing by 2. This means that y=-3x+18.
The sum

can be written as:

,
<span>
from the binomial expansion formula: </span>

.
<span>
Thus, substituting </span>y=-3x+18 and simplifying we have<span>
</span>



.
This is a parabola which opens upwards (the coefficient of x^2 is positive), so its minimum is at the vertex. To find x, we apply the formula -b/2a. Substituting b=-108, a=10, we find that x is 108/20=5.4.
At x=5.4, the expression

, which is equivalent to

, takes it smallest value.
Substituting, we would find

=32.4 This is the smallest value of the expression.
For x=5.4, y=-3x+18=-3(5.4)+18=1.8.
Answer: (5.4, 1.8)
Answer:

Step-by-step explanation:
<u>System of Equations</u>
Let's call:
x = number of nickels in the student's pocket
y = number of dimes in the student's pocket
Each nickel has a value of $0.05, so x nickels have a value of 0.05x
Each dime has a value of $0.10, so y dimes have a value of 0.10y
The student has a total of 10 coins, thus:

The total value of the coins is $0.85, thus

The system of linear equations that represents this scenario is:

24 miles is 1 gallon so 360 miles is 15 gallons + 24 is 384 miles so they are not equivalent!