Answer:
S₁₅ = 645
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
= 
[ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Using the nth term formula 
= 5n + 3 , then
a₁ = 5(1) + 3 = 5 + 3 = 8
a₂ = 5(2) + 3 = 10 + 3 = 13 , then
d = a₂ - a₁ = 13 - 8 = 5
Thus
S₁₅ = 
[ (2 × 8) + (14 × 5) ]
= 7.5( 16 + 70)
= 7.5 × 86
= 645
Answer:
Step-by-step explanation:
2x = 3y + 1/2
standard : Ax + By = C
2x = 3y + 1/2....multiply everything by 2 to get rid of the fractions
4x = 6y + 1 ....subtract 6y from both sides
4x - 6y = 1 <==
slope intercept : y = mx + b
2x = 3y + 1/2....subtract 1/2 from both sides
2x - 1/2 = 3y....divide everything by 3
2/3x - 1/6 = y...rearrange
y = 2/3x - 1/6 <===
Answer:
Step-by-step explanation:
7) 2ab + 4ac = 2*a*b + 2 *2 *a*c
= 2a(b + 2c)
8) ac - a²c² = c( a - a²c)
bc - abc = c(b - ab)
9) b²+ 4b - 5 = b² + 5b - 1b - 5
= b(b + 5) - 1(b + 5)
= (b +5)(b - 1)
b² + 8b + 15 = b² + 5b + 3b + 15
= b(b + 5) + 3(b + 5)
= (b + 5 )(b + 3)
• So we know that.....
x represent bags of snack and y is bottles of water.
This equations shows the total amount and the cost of each water bottle and snack:
20.00 = 2.50x + 1.00y
Total: $20.00
Snack: $2.50
Water Bottle: $1.00
And this question shows the total items:
11 = x + y
Which there will be some snack + some water bottle = 11 items
—————————————————————
• Now I’m going to first solve for x, which is the amount of bags of snack.
I will use the equation, 11 = x + y.
(First, we’ll subtract y from both side, since we’re solving for x [UNDO])
11 = x + y
-y = - y
_______
11 - y = x —> so x is equal to 11 minus y.
—————————————————————
• Now we’re going to plug the 11 - y as x in the equation: 20.00 = 2.50x + 1.00y to solve for y.
20.00 = 2.50 (11 - y) + 1.00y
20.00 = 27.5 - 2.50y + 1.00y (Distributed)
20.00 = 27.5 - 1.50y (Combine like terms)
20.00 = 27.5 - 1.50y
-27.5 = -27.5 (Subtract -27.5 both side)
——————————
-7.5 = - 1.50y
-7.5 = -1.50y
—— ——— (Divide both side by -1.50)
- 1.50 = -1.50
5 = y
y is equals to 5, which means that there are 5 water bottles.
Now we know there are 11 items total and because there are 5 water bottles, there will be 6 bags of snacks. 11-5=6
—————————————————————
ANSWER:
They bought 6 bags of snacks! :)
