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checkley77 answered: 12560 problems
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Rectangles/277730: Solve the problem.
Find the length of a rectangular lot with a perimeter of 72 m if the length is 8 m more than the width
1 solutions

Answer 202268 by checkley77(12569) About Me  on 2010-03-06 18:48:37 (Show Source):
You can put this solution on YOUR website!
L=W+8
2L+2W=72
2(W+8)+2W=72
2W+16+2W=72
4W=72-16
4W=56
W=56/4
W=14 ANS. FOR THE WIDTH.
L=14+8=22 ANS. FOR THE LENGTH.
PROOF:
2*22+2*14=72
44+28=72
72=72


Travel_Word_Problems/277732: Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 160 miles in the same time that Dana travels 145 miles. If Chuck's rate of travel is 3 mph more than Dana's, and they travel the same length of time, at what speed does Chuck travel?
1 solutions

Answer 202266 by checkley77(12569) About Me  on 2010-03-06 18:44:32 (Show Source):
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D=RT
160=(R+3)T
T=160/(R+3)
145=RT
T=145/R
SEEING AS THE TIMES ARE THE SAME:
160/(R+3)=145/R CROSS MULTIPLY.
160R=145(R+3)
160R=145R+435
160R-145R=435
15R=435
R=435/15
R=29 MPH FOR DANA'S RATE.
29+3=32 MPH FOR CHUCK'S RATE.
PROOF:
160/32=145/29
5=5


absolute-value/277733: Solve the problem.
The difference between two positive integers is 52. One integer is three times as great as the other. Find the integers
1 solutions

Answer 202264 by checkley77(12569) About Me  on 2010-03-06 18:37:30 (Show Source):
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x-y=52
x=3y
3y-y=52
2y=52
y=52/2
y=26 ans.
x-26=52
x=52+26
x=78 ans.
Proof:
3*26=78
78=78


Percentage-and-ratio-word-problems/277735: Suzanne buys bagels for $6.60 per dozen. She spends $16.50 for the bagels and then sells all of them for $23.70 . What is her average profit per bagel?
A.$0.24 B.$0.30 C.$0.36 D.$0.40 E.$0.42
1 solutions

Answer 202262 by checkley77(12569) About Me  on 2010-03-06 18:35:02 (Show Source):
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16.50/6.60=2.5 dozen bought
2.5doz=2.5*12=30 bagels.
16.50/30=$.55 cost per bagel.
23.70/30=$.79 selling price per bagel
.79-.55=$.24 profit per bagel.
Answer A).


Linear-equations/277739: graphical method and solve
y=x+3
y=-x-1
1 solutions

Answer 202259 by checkley77(12569) About Me  on 2010-03-06 18:31:01 (Show Source):
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y=x+3 (red line)
y=-x-1 (green line)
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+x+%2B3%2C+-x+-1%29+ (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions x +3 and -x -1).
Solution (-2,1).


Pythagorean-theorem/277747: If the length of two sides of a right triangle are 8 cm and 15 cm, the length of the third side can be x cm or y cm. Rounded to the nearest tenth centimeter, the sum x + y equals
A.24 B. 25.4 C29.7 D.30 E.35.7

1 solutions

Answer 202258 by checkley77(12569) About Me  on 2010-03-06 18:28:04 (Show Source):
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8^2+15^2=x^2
64+225=x^2
289=x^2
x=sqrt289
x=17 cm.
8^2+y^2=15^2
64+y^2=225
y^2=225-63
y^2=161
y=sqrt161
y=12.7
17+12.7=29.7 ans C) for the sum of x+y.


Radicals/277763: using the equation P = 1000 sqrt(t) +2750 how many years it would take to reach 7000 given t=0
1 solutions

Answer 202255 by checkley77(12569) About Me  on 2010-03-06 18:22:08 (Show Source):
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7,000=1000sqrt(t)+2,750
1,000sqrt(t)=7,000-2,750
1,000sqrt(t)=4,250
sqrt(t)=4,250/1,000
sqrt(t)=4.25
t=sqrt4.25
t=2.06 years ans.


Parallelograms/277769: The area of a right triangle is 120 sq. in. The longer leg is 4 more than twice the shorter leg. Find the length of each leg. Show all work to receive credit.

1 solutions

Answer 202254 by checkley77(12569) About Me  on 2010-03-06 18:17:37 (Show Source):
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Area=bh/2
b=2h+4
120=(2h+4)h/2
120=h^2+2h/2
120=h^2+2h
h^2+2h-120=0
(h-10)(h+12)
h-10=0
h=10 ans.
b=2*10+4
h=20+4
h=24 ans.
Proof:
120=10*24/2
120=240/2
120=120


Radicals/277791: Rewrite with rational exponents
〖(√(5mn))〗^3
1 solutions

Answer 202252 by checkley77(12569) About Me  on 2010-03-06 18:11:10 (Show Source):
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〖(√(5mn))〗^3
(SQRT(5MN))^3
(5MN)SQRT(5MN)


Travel_Word_Problems/277794: driving at a rate of 50 mph for 4 hours find the distance traveled
1 solutions

Answer 202250 by checkley77(12569) About Me  on 2010-03-06 18:06:14 (Show Source):
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D=RT
D=50*4=200 MILES ANS.


Surface-area/277796: A circular flower garden with a diameter 30 meters has a walkway around it. If the width of this walkway is 3 meters, what is the area?
1 solutions

Answer 202249 by checkley77(12569) About Me  on 2010-03-06 18:05:09 (Show Source):
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Area=pir^2
Area=3.14(30/2)^2
Area=3.14*15^2
Area=3.14*225
Area=706.5 m^2 is the area of the flower garden.
Area=3.14(33/2)^2
Area=3.14*16.5
Area=3.14*272.25
Area=854.865 m^2 is the area of the flower garden plus the walkway.
The diference in area is the area of the walkway.
854.865-706.5=148.365 m^2 is the area of the walkway.


Coordinate-system/277797: Graph the equation and identify the y-intercept. y=5x-3. I am lost on this problem.
1 solutions

Answer 202246 by checkley77(12569) About Me  on 2010-03-06 17:58:21 (Show Source):
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y=5x-3
The standard line equation is:
Y=mX+b where m=slope & b=Y intercept.
In this equation the Y intercept=-3.
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+5x+-3%29+ (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, 5x -3).


Linear-systems/277798: A cellular phone company offers a contract for which the cost C in dollars,of t minutes if telephoning is given by C=0.25(t-300)+59.95, where it is assumed that t>300 minutes. What times will keep costs between $107.70 and $125.70?
1 solutions

Answer 202245 by checkley77(12569) About Me  on 2010-03-06 17:55:21 (Show Source):
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107.70<0.25(t-300)+59.95<125.70
107.70<.25T-75+59.95<125.70
107.70<.25T-15.05<125.70
107.70+15.05<.25T<125.70+15.05
122.75<.25T<140.75
122.75/.25 491


Money_Word_Problems/277800: How much of $1000 was invested at 4% and 3%, if the 1 year interest earned was $38?
1 solutions

Answer 202243 by checkley77(12569) About Me  on 2010-03-06 17:33:57 (Show Source):
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.04X+.03(1,000-X)=38
.04X+30-.03X=38
.01X=38-30
.01X=8
X=8/.01
X=800 INVESTED @ 4%.
1,000-800=200 INVESTED $ 3%.
PROOF:
.04*800+.03*200=38
32+6=38
38=38


Numbers_Word_Problems/277801: I need help with this problem
The larger of two numbers is 8 more than four times the smaller. If the larger is increased by four times the smaller, the result is 40. Find the two numbers.
1 solutions

Answer 202242 by checkley77(12569) About Me  on 2010-03-06 17:30:27 (Show Source):
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Y=4X+8 OR
Y-4X=8
Y+4X=40 ADD.
--------------
2Y=48
Y=48/2
Y=24 ANS.
24=4X+8
4X=24-8
4X=16
X=16/4
X=4 ANS.
PROOF:
24+4*4=40
24+16=40
40=40


Linear-systems/277802: For The Equation y=2(x)+15,and y=4x+7. Find an x-value that gives the same y-value for both equations
1 solutions

Answer 202241 by checkley77(12569) About Me  on 2010-03-06 17:27:05 (Show Source):
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y=2x+15
y=4x+7 SUBTRACT.
-----------------
0=-2X+8
2X=8
X=8/2
X=4 ANS.
PROOF:
Y=2*4+15
Y=8+15
Y=23
Y=4*4+7
Y=16+7
Y=23


Age_Word_Problems/277803: Sammy takes 5 hours longer to complet 300 lines of code than Martin. Together Sammy and Martin can complete the code in 6 hours.
How long it takes each programmer to complete the code if they program on their own. (hint: Quadratic equaiton )and 2) at what speed they are programming lines per hour.

1 solutions

Answer 202240 by checkley77(12569) About Me  on 2010-03-06 17:23:36 (Show Source):
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1/X+1/(X+5)=1/6
(X+5+X)/X(X+5)=1/6
(2X+5)/(X^2+5X)=1/6 CROSS MULTIPLY
X^2+5X=6(2X+5)
X^2+5X=12X+30
X^2+5X-12X-30=0
X^2-7X-30=0
(X-10)(X+3)=0
X-10=0
X=10 HOURS FOR MARTIN CODING ALONE.
10+5=15 HOURS FOR SAMMY CODING ALONE.
Proof:
1/10+1/15=1/6
(15+10)/150=1/6
25/150=1/6
1/6=1/6
300/10=30 LINES OF CODE PER HOUR FOR MARTIN.
300/15=20 LINES OF CODE PER HOUR FOR SAMMY.


Rational-functions/277804: how do you solve this rational expression?????
21x^2-23x+6
-----------
21x^2+x-10
1 solutions

Answer 202237 by checkley77(12569) About Me  on 2010-03-06 17:10:26 (Show Source):
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21x^2-23x+6
----------- FACTOR BOTH NUMERATOR & DENOMINATOR.
21x^2+x-10
********************
(7X-3)(3X-2)
------------ CANCEL OUT THE (3X-2) TERMS.
(7X+5)(3X-2)
*********************
(7X-3)
------ ANS.
(7X+5)


Numbers_Word_Problems/277806: two less than a product of two numbers
1 solutions

Answer 202236 by checkley77(12569) About Me  on 2010-03-06 17:04:21 (Show Source):


Matrices-and-determiminant/277817: A truck carrying
3600 cubic feet of cargo consisting of washing machines and refrigerators was hijacked. The washing machines are worth $300 each and are shipped in 36-cubic-foot cartons.
The refrigerators are worth $900 each and are shipped in
45-cubic-foot cartons. If the total value of the cargo was
$51,000, then how many of each was there on the truck?

1 solutions

Answer 202235 by checkley77(12569) About Me  on 2010-03-06 17:01:52 (Show Source):
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3,600=36x+45y multiply this equation by -20 & add.
51,000=300x+900y
-72,000=-720x-900y
-----------------------
-21,000=-420x
x=-21,000/-420
x=50 washing machines were on the truck.
3,600=36*50+45y
45y=3,600-1,800
45y=1.800
y=1,800/45
y=40 refrigerators wer eon the truck.
Proof:
51,000=300*50+900*40
51,000=15,000+36,000
51,000=51,000


Graphs/277820: y=(3/4)x+1
y=-(1/2)x-4
1 solutions

Answer 202234 by checkley77(12569) About Me  on 2010-03-06 16:53:53 (Show Source):
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y=(3/4)x+1 (red line)
y=-(1/2)x-4 (green line)
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+3x%2F4+%2B1%2C+-x%2F2+-4%29+ (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions 3x/4 +1 and -x/2 -4).
Intersection (-4,-2).


Rational-functions/277832: g(x)=4x^2-3x+1 slove it please
1 solutions

Answer 202233 by checkley77(12569) About Me  on 2010-03-06 16:47:24 (Show Source):
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g(x)=4x^2-3x+1
g(x)=(4x+1)(x-1)
4x+1=0
4x=-1
x=-1/4 ans.
x-1=0
x=1 ans.


Expressions-with-variables/277833: 1. Solve for x. 3/10 = 5/x where / means a fraction bar.

2. Divide and simplify: The fraction (x^2-4)/(x) divided by the fraction
(4x - 8) / (x)

3. Add and simplify: The fraction 4/(a^2 -1) + the fraction (1)/(2a + 2)
4. Using the LCD, solve: 3 + the fraction (1)/(x - 2) = the fraction
(2x - 3) / (x - 2)
Show use of the LCD.

1 solutions

Answer 202231 by checkley77(12569) About Me  on 2010-03-06 16:45:05 (Show Source):
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1. Solve for x. 3/10 = 5/x
cross multiply
3x=5*10
3x=50
x=50/3
x=16 2/3 ans

2. Divide and simplify: The fraction (x^2-4)/(x) divided (4x-8)/(x)
Invert the denominator & multiply.
(x^2-4)/x*x/(4x-8) cross multiply
(x^2-4)/4(x-2)
(x+2)(x-2)/(x-2) cancel out the (x-2 terms.
x+2 ans.

3. Add and simplify: The fraction 4/(a^2-1)+(1)/(2a+2)
Find the LCD (a^2-1)(2a+2)
[4(2a+2)+(a^2-1)]/(a^2-1)(2a+2)
[4*2(a+1)+(a+1)(a-1)]/(a+1)(a-1)*2(a+1)
[(8+1)(a+1)(a-1)]/3(a+1)(a-1)
[8(a+1)(a-1)]/3(a+1)(a-1) cancel out 3(a+1) & (a-1)
5(a+1) ans.
4. Using the LCD, solve: 3+(1)/(x-2)=(2x-3)/(x-2)
LCD=(x-2)
3(x-2)+1/(x-2)=(2x-3)/x-2)
[3x-6+1]/(x-2)=(2x-3)/(x-2) cancel out the denominators.
3x-5=2x-3
3x-2x=-3+5
x=2 ans.
Proof is not valid because (2-2)=0 & you cannot divide by 0.
Show use of the LCD.


Quadratic_Equations/277834: Quadratic functions
I'm confused on how to set up and solve this problem. Among all pairs of numbers with a sum of 205, find the pair whose product is maximum.
1 solutions

Answer 202219 by checkley77(12569) About Me  on 2010-03-06 16:02:07 (Show Source):
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Normally it would be (205/2)^2
But 205/2=102.5^2=10,506.25 ans.
Unless you're looking for awhole number, then:
103*102=10,506 ans.


Numbers_Word_Problems/277433: Find two consecutive even integers such that twice the smaller exceeds the larger by 18. Thank you.
1 solutions

Answer 202010 by checkley77(12569) About Me  on 2010-03-05 08:58:52 (Show Source):
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Let x & x+2 be the 2 consecutive even integers.
2x=(x+2)+18
2x=x+20
2x-x=20
x=20 ans. for the smallest integer.
20+2=22 ans. for the larger integer.
Proof:
2*20=22+18
40=40


Polynomials-and-rational-expressions/277435: I can't seem to figure out how to work this problem:
Find the volume of a cylinder, do not approximate pi.
r = (y-3)cm
h = 7ycm
I've tried:
y^2-6*7= 7y^2-42
and
ended up with y^2-3y-9

1 solutions

Answer 202009 by checkley77(12569) About Me  on 2010-03-05 08:54:42 (Show Source):
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r = (y-3)cm
h = 7ycm
V=pir^2h
V=22/7*(y-3)^2*7y
V=22/7(y^2-6y+9)7y
V=22/7*7y(y^2-6y+9)
V=22y(y^2-6y+9) ans.


Numbers_Word_Problems/277437: The first of three numbers exceeds twice the second number by 4, while the third number is twice the first. If the sum of the three numbers is 54, find the numbers. Thank You
1 solutions

Answer 202008 by checkley77(12569) About Me  on 2010-03-05 08:44:37 (Show Source):
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x+y+z=54
x=2y+4 or 2y=x-4 or y=(x-4)/2
z=2x
x+(x-4)/2+2x=54
(2x+x-4+2*2x)/2=54
(2x+x-4+4x)/2=54
(7x-4)/2=54
7x-4=54*2
7x-4=108
7x=108+4
7x=112
x=112/7
x=16 ans.
y=(16-4)/2=12/2=6 ans.
z=2*16=32 ans.
Proof:
16+6+32=54


absolute-value/277465: Solve the inequality. 2x+8<36. Here is how I solved the inequality. 2x+8-8<36-8
2x>28 x<14. Is this correct? Was I suppose to flip the sign? Thanks.
1 solutions

Answer 202007 by checkley77(12569) About Me  on 2010-03-05 08:30:40 (Show Source):
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2x+8<36
2x<36-8
2x<28
x<28/2
x<14 ans.
Proof:
Let x=13.9
2*13.9+8<36
27.8+8<36
35.8<36


Rational-functions/277471: i could please use some help. i must simplify 3square root of 250. im not sure about the 3 its small and just outside the square root sign. help please?
1 solutions

Answer 202006 by checkley77(12569) About Me  on 2010-03-05 08:26:46 (Show Source):
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cubert(250)=6,2996
OR
3sqrt(250)=3sqrt(25*10)
3*5sqrt(10)=15sqrt(10) ans.



Square-cubic-other-roots/277472: i am asked to simplify the suare root of a^2/b^5. im not sure how to go about it thanks.
1 solutions

Answer 202005 by checkley77(12569) About Me  on 2010-03-05 08:22:25 (Show Source):
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sqrt(a^2/b^5)
(a/b^2)sqrt(1/b) ans.


Miscellaneous_Word_Problems/277479: John’s computer has a 20 gigabyte hard drive. Bill’s computer has a hard drive that is 2/5 bigger than John’s. How many gigabytes does the hard drive on Bill’s computer have?
1 solutions

Answer 202004 by checkley77(12569) About Me  on 2010-03-05 08:18:39 (Show Source):
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20*1.4=28 gigabyte ans.