<span><span>an</span>=<span>1<span>a−</span></span></span><span>4a10b</span>n hope i helped
It will be A bc youre multiplying the total amount of the car by how much it is worth. If it is decreasing by 10% each year then it is worth 90% of its value, hence 0.9
So I think maybe the example for the first problem created some confusion, and you may want to have your child take another look.
If we numbered the top half 1 to 9 going from left to right, numbers 1, 2, 6, 7 and 8 are right. They worked because the top number (numerator) perfectly fit into the bottom number (denominator). This is not true for the rest.
The key is to find the largest number that you can think of that will go into BOTH the top and the bottom evenly.
So for number 3: 18/24; 18 does not fit evenly into 24. The highest number that will fit into both is 6, so you divide both top and bottom by 6 and your answer is 3/4.
Number 4: 45/54; the highest number that goes into both is 9, so you divide both top and bottom by 9 and your answer is 5/6.
Number 5: 55/66; the highest number that can go into both is 11, so the answer is 5/6.
Is this making sense?
The bottom, numbering 1 to 9 from left to right. The correct ones are 1, 6 and 9.
For 2: 14/41 is about 15/40. Both can be divided by 5, so the answer is 3/8.
For 3: 20/81 is about 20/80, and 2/8 is close, but can still be divided by 2, so the answer is 1/4.
For 4: 24/49 is closer to 25/50 than 20/50. 25/50 can be divided by 25, so the answer is 1/2.
For 5: it was all correct, but the answer can be further reduced from 2/8 to 1/4.
For 7: 23/72 is about 25/75, and 25 goes into both, so it reduces to 1/3.
For 8: 13/21 is about 15/20, and 5 goes into both, so the answer is 3/4.
As your child continues to learn this, remember that if he or she gets an answer like 2/6 or 6/12, they should ask themselves if they can further reduce the fractions- 2/6 reduces to 1/3, and 6/12reduces to 1/2. I know it's confusing, but they do get the hang of it with practice
Answer:
length of the pretty side and length of the side oppositte to the pretty side = 37.91 ft
length of the other two sides = 27.52 ft
Step-by-step explanation:
The mathematical problem is:
Max A = b1*h
subject to: 35*b1 + 18*(2*h + b2) <= 3000
Where
A: area of the garden
b1: length of the pretty side
b2: length of the side oppositte to the pretty side
h: length of the other two sides
Replacing with b1 = b2 and taking only the equality sign in the restriction (in the maximum all the money will be spent), we get:
35*b1 + 18*(2*h + b1) = 3000
35*b1 + 36*h + 18*b1 = 3000
53*b1 + 36*h = 3000
b1 = 3000/53 - (36/53)*h
Substituing in Area's formula
A = (3000/53 - (36/53)*h)*h
A = (3000/53)*h - (36/53)*h^2
In the maximum, the derivative of A is equal to zero
dA/dh = 3000/53 - 2*(36/53)*h =
3000/53 - 72/35*h = 0
h = (3000/53)*(35/72)
h = 27.52 ft
then,
b1 = 3000/53 - (36/53)*27.52
b1 = 37.91 ft =b2
