I need some help I totally suck @ word problems! PLEASE!!?

Question

I need some help I totally suck @ word problems!
1.The length of a rectangle is 6 cm less than twice its width. Find the dimensions of the rectangle if its area is 108 cm2. Which equation can be used to solve this problem?
a.w(2w + 6w) = 108
b.w(2w - 6w) = 108
c.w(2w - 6) = 108
d.w(2w + 6) = 108

2.The difference of two positive numbers is 5 and the sum of their squares is 233. Which pair of numbers is the solution to this word problem?
A. The two numbers are 8 and 13.
B. The two numbers are 7 and 12.
C. The two numbers are 6 and 11.
D. The two numbers are 9 and 14.

3.Mitch tossed an apple to Kathy, who was on a balcony 40 ft above him. The initial speed of the toss was 56 ft/s. Kathy missed the apple on its way up, but she caught it on its way down. Which of the times represents how long the apple was in the air?
A. The apple was in the air for 2.1 s.
B. The apple was in the air for 2.5 s.
C. The apple was in the air for 2.4 s.
D. The apple was in the air for 2.0

Answer 1

1.The length of a rectangle is 6 cm less than twice its width. Find the dimensions of the rectangle if its area is 108 cm2. Which equation can be used to solve this problem?
l=2w-6
A=lw=(2w-6)w
c.w(2w - 6) = 108 is correct

a.w(2w + 6w) = 108
b.w(2w - 6w) = 108
c.w(2w - 6) = 108
d.w(2w + 6) = 108

2.The difference of two positive numbers is 5 and the sum of their squares is 233. Which pair of numbers is the solution to this word problem?
x-y=5
x=y+5
x^2+y^2=233
(y+5)^2+y^2=233
y^2+10y+25+y^2=233
2y^2+10y-208=0
y^2+5y-104=0
(y+13)(y-8)=0
y=-13, 8
since it was specifiet that y>0
y=8
x=5+y=5+8=13
A. The two numbers are 8 and 13. is correct

A. The two numbers are 8 and 13.
B. The two numbers are 7 and 12.
C. The two numbers are 6 and 11.
D. The two numbers are 9 and 14.

3.Mitch tossed an apple to Kathy, who was on a balcony 40 ft above him. The initial speed of the toss was 56 ft/s. Kathy missed the apple on its way up, but she caught it on its way down. Which of the times represents how long the apple was in the air?
height h=56t-16t^2=40
-16t^2+56t-40=0 divide by -8
2t^2-7t+5=0
(2t-5)(t-1)=0
2t-5=0
t=5/2 dec
t-1=0
t=1 sec
5/2 sec is the time on the way down
B. The apple was in the air for 2.5 s. is correct

A. The apple was in the air for 2.1 s.
B. The apple was in the air for 2.5 s.
C. The apple was in the air for 2.4 s.
D. The apple was in the air for 2.0

Answer 2

Area = Length x Width

w(2w - 6) = 108

The answer is c

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Problem 2

x - y = 5- - - - - - - -Equation 1
x² + y² = 233- - - - -Equation 2
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Substitute method equation 1

x - y = 5

x - y + y = 5 + y

x = 5 + y

The answer is x = 5 + y

Insert the x value into equation 2

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x² + y² = 233

(5 + y)² +y² = 233

25 + 10x + y² + y² = 233

25 + 10x + 2y² = 233

- 233 + 25 + 10x + 2y² = 233 - 233

- 208 + 10x + 2y² = 0

- 104 + 5x + y² = 0

- 104 - 8y + 13y + y² = 0

-8 (13 + y) + y ( 13 + y) = 0

(- 8 + y)(13 + y) = 0

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roots

- 8 + y = 0

- 8 + y + 8 = 0 + 8

y = 8

The answer is y = 8

Insert the y value into equation 2

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Roots

13 + y = 0

13 + y - 13 = 0 - 13

y = - 13. . .<=. .not used

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x² + y² = 233

x² + (8)² = 233

x² + 64 = 233

x² + 64 - 64 = 233 - 64

x² = 169

x² = √169

x = 13

The answer is x = 13

Insert the x value into equation 2

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Check for equation 2

x² + y² = 233

(13)² + (8)² = 233

169 + 64 = 233

233 = 233

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Check for equation 1

x - y = 5

13 - 8 = 5

5 = 5

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The solution set is { 13., 8 }

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Answer 3

number 1. c.

number 2. a.

number 3. this is a gravity question, and how would gravity, at 9.8m per second per second would pull on the apple, and slow it down, then you would have to figure how far up, past Kathy the apple went, to determine how far back down it went to Kathy. It's a little too difficult for working it out in my head. but I'd say about 2.1 seconds.

Answer 4

Forget the fact that they are word problems and substitute each of the answers into an equation you already know like A=WL and until you find the one that gives you a true answer.

Answer 5

1c

2)A

solve
x^2+5x-104=0
x1=8
x2=13

Answer 6

u seem to know your words ok,its your maths that you lack,or maybe your time,i've seen the answers and some are correct,i think u better off as a quiz master

Answer 7

1)c
2)a---->x-y=5 x2+y2=233
3)c