SOLUTION: I would like to know if you can help me with this portion also? Number 1-5 I definitely have a clear understanding of and I need help with the additional problems 6, 7, and 8. I a

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I would like to know if you can help me with this portion also? Number 1-5 I definitely have a clear understanding of and I need help with the additional problems 6, 7, and 8. I a      Log On


   

Question 622104: I would like to know if you can help me with this portion also? Number 1-5 I definitely have a clear understanding of and I need help with the additional problems 6, 7, and 8. I also need help with Part B 1-3. Thanks in advance.
1. Gina wants to begin by figuring out how long the corn bed will be. She knows that in her previous two gardens, she was able to plant 2 rows in a 5 foot long space and 5 rows in an 11 foot l ong space. Find a linear equation for the length of the bed (y) in which she can fit x rows of corn. Hint: Use the two pairs of values from her previous two gardens to write two ordered pairs of the form (x,y), then use these pairs to write an equation of the form y = mx + b.
2. If Gina wants the corn bed to be12 feet in width, write an expression for the area of the corn bed (assuming she is going to plant x rows of corn). Simplify your answer.
3. Next, Gina plans to plant a square bed of peas. If the length of each side of the pea bed is 3 feet less than the length of the corn bed (from #1), what is the length of each side of the pea bed? Simplify your answer.
4. Find an expression for the area of the pea bed. Simplify your answer.
5. In order to know how much topsoil the beds will need altogether, Gina needs to know the total square footage of both of the beds. Write an expression for the combined area of the two beds. Simplify your answer by combining like terms.
6. How many rows of corn can Gina plant if she wants to make the total area of the two beds 400 square feet? If you solve your equation correctly, you will get two solutions. Only one makes sense in terms of this problem – which solution doesn’t make sense and why?
7. Based on the number of corn rows found in #7, what are the dimensions of each of Gina Greena’s beds? (Give length and width of each bed as integers). 8. The last thing Gina needs to do is buy the wood to encase the beds. How many feet of lumber does Gina need to surround both of the beds? 6. How many rows of corn can Gina plant if she wants to make the total area of the two beds 400 square feet? If you solve your equation correctly, you will get two solutions. Only one makes sense in terms of this problem – which solution doesn’t make sense and why? 7. Based on the number of corn rows found in #7, what are the dimensions of each of Gina Greena’s beds? (Give length and width of each bed as integers).
8. The last thing Gina needs to do is buy the wood to encase the beds. How many feet of lumber does Gina need to surround both of the beds?
PART B After retiring in 2006, Gina Greena decided to buy 2,000,000 shares in Seed Som’ore seed company at $.17 per share PROBLEM SHOW YOUR SOLUTIONS HERE
1. How much did Gina Greena spend in 2006 when she bought stock in Seed Som’ore? (give your answer in scientific notation)
2. Last year, in 2011, Gina Greena sold her shares for $421,000. Write this number in scientific notation.
3. Calculate the percent increase in the value of Gina’s shares by following these steps: • Find the increase in value from 2006 to 2011 • Find what percent increase that is of the 2006 value [Round your answer to the nearest tenth of a percent]
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
1. y=2x%2B1
2. For the corn, the area (in square feet) is
A=12%2A%282x%2B1%29=24x%2B12
3. length=2x%2B1-3=2x-2=2%28x-1%29
4. For the pea bed, the area (in square feet) is
A=%282%2A%28x-1%29%29%5E2=4%28x%5E2-2x%2B1%29=4x%5E2-8x%2B4
5. The total garden area (in square feet) is
A=4x%5E2-8x%2B4%2B24x%2B12=4x%5E2%2B16x%2B16=4%28x%5E2%2B4x%2B4%29
6. How many rows of corn can Gina plant if she wants to make the total area of the two beds 400 square feet?
4%28x%5E2%2B4x%2B4%29=400 --> x%5E2%2B4x%2B4=100 --> x%5E2%2B4x-96=0
Factoring,
x%5E2%2B4x-96=0 --> %28x%2B8%29%28x-12%29=0 --> x=12 or x=-8
Of course, -8 rows of corn does not make sense, so
highlight%28x=12%29 rows of corn.
7. For the corn y=2-12%2B1=highlight%2825%29 feet is the space needed for 12 rows, and the corn portion of the garden was to be 12 feet long (according to part 2 of the problem). So the corn area is 25 feet by 12 feet.
The pea garden is 3 feet less in length that the 25 feet from part 1 (with the x=12 from part 7). That is
35-3=highlight%2822%29 feet, and it is square. It measure 22 feet by 22 feet.
8. Assuming that the wood has to fully encase each section of the garden (no adjoining sections and skipping the fence in between), we need to encase a 25 foot by 12 foot rectangle and a 22 foot by 22 foor square. The perimeters are
P=25%2A2%2B12%2A2=74 feet for the corn and
P=4%2A22=88 feet for the peas.
The total length is 74%2B88=highlight%28162%29 feet.
PART B
1. $0.17%2A2000000=$340000=$3.4%2A100000=$3.4%2A10%5E5
2. $421000=$4.21%2A100000=$4.21%2A10%5E5
3. The increase is
$4.21%2A10%5E5-$3.4%2A10%5E5=$%284.21-3.4%29%2A10%5E5=$0.81%2A10%5E5
As a fraction of $3.4%2A10%5E5 , That amounts to
0.81%2A10%5E5%2F%283.4%2A10%5E5%29=0.81%2F3.4=0.238 (rounded)
That fraction (0.238 as decimal) is 23.8/100=23.8% as a percentage