Answer:
a19 = -71.74
Step-by-step explanation:
The general term of an arithmetic sequence with first term a1 and common difference d is ...
an = a1 +d(n -1)
The given 5th and 15th terms tell us ...
-3.7 = a1 +d(5 -1)
-52.3 = a1 +d(15 -1)
Subtracting the first of these equations from the second, we find ...
10d = -48.6
d = -4.86 . . . . . . divide by 10
The 19th term will be ...
a19 = a1 +d(19 -1)
Subtracting the 15th term from this, we find ...
a19 -a15 = 4d
a19 = 4d +a15 = 4(-4.86) +(-52.3)
a19 = -71.74
Answer:
video game: $29.50
DVD: $10
Step-by-step explanation:
Let d = price of one DVD, and let v = price of 1 video game.
"A bundle of two video games and three DVDS can be purchased for $89.00."
2v + 3d = 89
"A bundle of one video game and two DVDS can be purchased for $49.50."
v + 2d = 49.5
We have two equations in two unknowns, so we can solve them as a system of 2 equations.
2v + 3d = 89
v + 2d = 49.5
Rewrite the first equation.
Multiply both sides of the second equation by -2 and write it below the first equation.
Add the equations.
2v + 3d = 89
(+) -2v - 4d = -99
---------------------------
-d = -10
d = 10
Now we substitute 10 for d in the second original equation and solve for v.
v + 2d = 49.5
v + 2(10) = 49.5
v + 20 = 49.5
v = 29.5
Answer: video game: $29.50; DVD: $10
Remember the distributive property? It goes like x(a+b)=xa+xb... For example 3(6+7)=(3*6)+(3*7)=39
Same here
5(3x-6)-8(3x-7)
do the thing
(15x-30)-(24x-56)
Take parentheses off.
15x-30-24x+56
//WHY PLUS 56 NOT MINUS?
//because there was a minus sign outside the original parentheses, so the signs inside have to be flipped when the parentheses is taken off
//Let's simplify now
15x-24x-30+56
-9x+26
^^The answer!
Answer:
Step-by-step explanation:
Let x ft be the length of the fence and y ft be the width of the fence.
1. The length of the habitat should be at least 80 feet, then
2. The perimeter of the habitat should be no more than 300 feet. The perimeter of the fences 2x+2y ft, then
3. The system of inequalities that represent the model is
The graph of these inequalities is attached.
Two possible solutions are
1. x=100 ft, y=20 ft (100≥80 and 2·100+2·20=240≤300);
2. x=110 ft, y=30 ft (110≥80 and 2·110+2·30=280≤300).
Answer:
9 feet
Step-by-step explanation:
