Remaining water in the tank is (19/2-19/3) gallons = 57-38/6=19/6 =3 1/6 gallons
If you're multiplying by 10, you're moving the decimal point to the right, the same with any multiplication in the 10's, so 100, 1,000, etc. This is because you are making the number 10 times larger, so if you had 3.4, the 4 is in the 1/10 column so multiplying by 10 would put it in the units column, making the number 34.
On the other hand, dividing by the 10's makes the decimal point move to the left because you are making the number 10 times smaller, so if the units column is worth 1, then 10 times less than that is 1/10, which is the first decimal place.
I hope this helps! I tried to explain it well but let me know if you still don't understand or if I've confused you in any way :)
When n = 1, 2(1) + 1 = 3
When n = 2, 2(2) + 1 = 5
When n = 3, 2(3) + 1 = 7
When n = 4, 2(4) + 1 = 9
When n = 5, 2(5) + 1 = 11
Sum = 3 + 5 + 7 + 9 + 11 = 35
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Answer: 35
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1.
the x value of the vertex in form
ax^2+bx+c=y
is
-b/2a
so
-2x^2+8x-18
x value of vertex is
-8/(2*-2)=-8/-4=2
plug it in to get y value
-2(2)^2+8(2)-18
-2(4)+16-18
-8-2
-10
vertex is at (2,-10)
or you could complete the square to get into y=a(x-h)^2+k, where the vertex is (h,k)
so as follows
y=(-2x^2+8x)-18
y=-2(x^2-4x)-18
y=-2(x^2-4x+4-4)-18
y=-2((x-2)^2-4)-18
y=-2(x-2)^2+8-18
y=-2(x-2)^2-10
vertex is (2,-10)
5.
vertex is the time where the speed is the highest
at about t=10, the speed is at its max
Let the steaks = X and the salmon = y.
Set up two equations:
15x + 18y = 559.81
19x + 9y = 583.66
Now using the elimination method:
Multiply the second equation by -2, then add the equations together.
(15x+18y=559.81)
−2(19x+9y=583.66)
Becomes:
15x+18y=559.81
−38x−18y=−1167.32
Add these equations to eliminate y:
−23x=−607.51
Divide both sides by -23 to solve for x:
x= -607.51 = -23 = 26.413478
Now you have the cost for a steak.
To solve for the cost of the salmon, replace x with the value in the first equation and solve for y.
15(26.413478) + 18y = 559.91
396.202174 + 18y = 559.81
Subtract 396.202174 from both sides:
18y = 163.607826
Divide both sides by 18:
y = 163.607826 / 18
y = 9.089324
Round both x and Y to the nearest cent:
X (Steaks) =$26.41
Y (Salmon) = $9.09
