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Trigonometry-basics/158705: I re-submitted this question. I had missing data, sorry!
An A-frame lake house is 21 feet wide.If the roof of the home makes a 45 degree angle with the base of the home,what is the length of the house from ground level to the peak of the roof?
Larson, R., Hostetler, R. P., & Edwards, B. H. (2005). Trigonometry a graphing approach (4th ed.). Boston: Houghton Mifflin.
1 solutions
Answer 116973 by checkley77(12569)   on 2008-09-24 21:06:23 (Show Source):
You can put this solution on YOUR website!(180-45)/2=135/2=67.5 is the angle to the peak.
tan67.5=2.414
2.414(21/2)=25.34 is the height of the A-frame
10.5^2+25.34^2=c^2
110.25+642.12=c^2
752.366=c^2
c=sqrt752.366
c=27.43 ft. is the distance from the ground to the peak.
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Rational-functions/158815: I was looking for a 4th root chart but I can't find one and when I do type in the 4th root of 48 it gives me a decimal and I can't use a decimal...can you help me please??
1 solutions
Answer 116967 by checkley77(12569) on 2008-09-24 20:32:13 (Show Source):
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Proportions/158820: A giraffe can run 32 miles per hour. What is this speed in feet per second? Round to the neareast 10th. I said it was 1020 feet per second. Am I right?
1 solutions
Answer 116966 by checkley77(12569) on 2008-09-24 20:29:30 (Show Source):
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Numbers_Word_Problems/158814: The sum of the squares of three consecutive even integers is 116. Find the integers...
This is what I have tried...
x + (x + 2)+ (x + 4)= 116
3x + 6 = 116
-6 - 6
3x = 110
3x/3 110/3
x = 36.6666
This doesnt make sense. What am i doing wrong?
1 solutions
Answer 116964 by checkley77(12569) on 2008-09-24 20:21:12 (Show Source):
You can put this solution on YOUR website!You are asked for the sum of the [squares]
You need to pay more attention to what is given & asked for.
x + (x + 2)+ (x + 4)= 116 [x^2+(x+2)^2+(x+4)^2=116]
3x + 6 = 116 [x^2+x^2+4x+4+x^2+8x+16=116]
-6 - 6 [3x^2+12x+20-116=0]
[3x^2 +12x-96=0]
3x = 110 [3(x^2+4x-32)=0]
3x/3 110/3 3(x+8)(x-4)=0]
x = 36.6666 [x-4=0]
[x=4]
Proof:
4^2+6^2+8^2=116
16+36+64=116
116=116
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Geometric_formulas/158809: Hi,
My question is about finding a measure in simplest form. I have to use the distance formula. The coordinates are (-5,3) and (3,4. The answer I got for that question was 65. Now I have to simplify the answer and I'm not sure what to do.
Thank You
1 solutions
Answer 116963 by checkley77(12569) on 2008-09-24 20:13:47 (Show Source):
You can put this solution on YOUR website!The x distance=3+5=8
The y distance=4-3=1
using the pythagorean theorem a^2+b^2=c^2 we get the distance (c)
8^2+1^2=c^2
64+1=c^2
c^2=65
c=sqrt65
c=8.06226 is the distance from (-5,3) to (3,4)
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Money_Word_Problems/158808: This question is from textbook
Henry paid $.80 for each bag of peanuts. He sold all but 20 of them for $1.50 and made a profit of $54. how many bags did he buy?
1 solutions
Answer 116962 by checkley77(12569) on 2008-09-24 20:03:37 (Show Source):
You can put this solution on YOUR website!.80x=(x-20)1.50-54
.80x=1.5x-30-54
.8x-1.5x=-84
-.7x=-84
x=-84/-.7
x=120 bags were bought.
Proof:
.80*120=(120-20)1.5-54
96=100*1.50-54
96=150-54
96=96
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Linear-equations/158802: hi,can anyone help me on this one:
(-4,2) perpendicular to 2x+3y=-6
i know i have to change 2x+3y=-6 to slope:y=mx+b
yeah.
1 solutions
Answer 116958 by checkley77(12569) on 2008-09-24 19:46:31 (Show Source):
You can put this solution on YOUR website!2x+3y=-6
First we need to put this equation in the line equation form Y=mX+b where m=slope & b=the y intercept.
3y=-2x-6
y=-2x/3-6/3
y=-2x/3-2 here we have a slope(m)=-2/3.
Any line perpendicular to this line has a slope=3/2 (the negative reciprical of the original slope).
Now replace the x&y terms with the values(-4,2) & the new slope & solve for b.
2=3/2*-4+b
2=-12/2+b
2=-6+b
b=2=6
b=8 for the y intercept (0,8).
y=3x/2+8 (green line) is this perpendicular line to y=-2x/3-2 (red line) & passes through (-4,2).
 (graph 300x300 pixels, x from -10 to 10, y from -10 to 10, of TWO functions -2x/3 -2 and 3x/2 +8).
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Linear-equations/158803: hi again,i was hoping someone can help on this one.
(-4,2) perpendicular to 2x+3y=-6,
all i know is that u change 2x+3y=-6 to y=mx+b and perpendicular is recipical to its self. after u find what it is u have to grap it out. my teacher really doesnt explain this one that well.
1 solutions
Answer 116957 by checkley77(12569) on 2008-09-24 19:43:17 (Show Source):
You can put this solution on YOUR website!2x+3y=-6
First we need to put this equation in the line equation form Y=mX+b where m=slope & b=the y intercept.
3y=-2x-6
y=-2x/3-6/3
y=-2x/3-2 here we have a slope(m)=-2/3.
Any line perpendicular to this line has a slope=3/2 (the negative reciprical of the original slope).
Now replace the x&y terms with the values(-4,2) & the new slope & solve for b.
2=3/2*-4+b
2=-12/2+b
2=-6+b
b=2=6
b=8 for the y intercept (0,8).
y=3x/2+8 (green line) is this perpendicular line to y=-2x/3-2 (red line) & passes through (-4,2).
 (graph 300x300 pixels, x from -10 to 10, y from -10 to 10, of TWO functions -2x/3 -2 and 3x/2 +8).
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Matrices-and-determiminant/158796: This question is from textbook Advanced Mathematical Concepts
The perimeter of a triangle is 83 inches. The longest side is three times the length of the shortest side and 17 inches more than one-half the sum of the other two sides. Use a system of equations to find the length of each side. I don't really understand this and I asked some people to help, but they couldn't get it either. Please help me... Thanks!
1 solutions
Answer 116955 by checkley77(12569) on 2008-09-24 19:32:16 (Show Source):
You can put this solution on YOUR website!Longest side=3*shortest side.
Longest side=17+(shortest side + other side)/2
3ss=17+(ss+os)/2
os/2=3ss-17-ss/2
0s/2=2.5ss-17
os=5ss-34
3ss+ss+5ss-34=83
9ss=83+34
9ss=117
ss=117/9
ss=13 inches for the short side.
ls=3*13=39 inches for the long side.
os=5*13-34=31 inches for the other side.
Proof
13+39+31=83
83=83
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Rational-functions/158797: KATHY IS STACKING ENCYCLOPEDIA VOLUMES ON A LIBRARY BOOKSHELF. EACH VOLUME IS 2.5 INCHES WIDE. THE SELF IS 48 INCHES WIDE.
2.5x < 48
2.5x > 48
48x < 2.5
48x > 2.5
1 solutions
Answer 116954 by checkley77(12569) on 2008-09-24 19:19:34 (Show Source):
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Mixture_Word_Problems/158793: 1)How many liters of pure acid must be added to 40 L of a 20% acid solution to make a solution which is 36% acid?
2)A laboratory technician has a solution that is 25% acid. He wishes to increase the concentration to 40% by adding pure acid. If he has 800 mL of solution to begin with, how much acid must be added to make the desired concentration?
1 solutions
Answer 116953 by checkley77(12569) on 2008-09-24 19:17:21 (Show Source):
You can put this solution on YOUR website!x+.2*40=.36(40+x)
x+8=14.4+.36x
x-.36x=14.4-8
.64x=6.4
x=6.4/.64
x=10 liters of pur acid is needed.
Proof:
10+.2*40=.36(40+10)
10+8=.36*50
18=18
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.25*800+x=.4(800+x)
200+x=320+.4x
x-.4x=320-200
.6x=120
x=120/.6
x=200 ml of pure acid is needed.
Proof:
.25*800+200=.4(800+200)
200+200=.4(1,000)
400=400
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Equations/158787: Two angles are complementary if thier sum is90 degrees. If the measure of the firt angle isxdegrees and the measure of the second angle is (3x-2)degrees, find the measure of each angle
1 solutions
Answer 116943 by checkley77(12569) on 2008-09-24 18:45:01 (Show Source):
You can put this solution on YOUR website!x+(3x-2)=90
x+3x-2=90
4x=90+2
4x=92
x=92/4
x=23 for the smaller angle.
3*23-2=69-2=67 for the other angle.
Proof:
23+67=90
90=90
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Equations/158788: It took Sara's mother 5 hours round trip to drive to the University and bring Sara back home for spring break. If the university is 137 1/2 miles from home, find her mothers average speed.
1 solutions
Answer 116939 by checkley77(12569) on 2008-09-24 18:40:09 (Show Source):
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Systems-of-equations/158769: (20b^3+17b^2+22b+48)(divided by)(4b+5)the answer I got was 5b^2-2b+8+8/4b+5
1 solutions
Answer 116935 by checkley77(12569) on 2008-09-24 17:10:25 (Show Source):
You can put this solution on YOUR website!(20b^3+17b^2+22b+48)(divided by)(4b+5)
```````````5b^2-2b+8 r8/(4b+5)
`````____________________
4b+5)20b^3+17b^2+22b+48
`````20b^3+25b^2
`````--------------
```````````-8b^2+22b
```````````-8b^2-10b
```````````-------------
````````````````32b+48
````````````````32b+40
````````````````-------
`````````````````````8/(4b+5)
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Polynomials-and-rational-expressions/158716: can someone please help me with this problem:
What is the result of x^4 + 4x^3 + 6x^2 + 4x + 1 divided by x + 1?
1 solutions
Answer 116934 by checkley77(12569) on 2008-09-24 17:03:02 (Show Source):
You can put this solution on YOUR website!x^4 + 4x^3 + 6x^2 + 4x + 1 divided by x + 1?
`````````x^3+3x^2+3x+1 answer.
````_________________
x+1)x^4+4x^3+6x^2+4x+1
````x^4+x^3
````--------
````````3x^3+6x^2
````````3x^3+3x^2
````````----------
`````````````3x^2+4x
`````````````3x^2+3x
`````````````---------
```````````````````x+1
```````````````````x+1
```````````````````---
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Money_Word_Problems/158733: Of the $50,000 that Natasha pocketed
on her last real estate deal, $20,000 went to charity. She
invested part of the remainder in Dreyfus New Leaders Fund
with an annual yield of 16% and the rest in Templeton
Growth Fund with an annual yield of 25%. If she made
$6060 on these investments in 1 year, then how much did she
invest in each fund?
1 solutions
Answer 116931 by checkley77(12569) on 2008-09-24 16:45:00 (Show Source):
You can put this solution on YOUR website!.25x+.16(30,000-x)=6,060
.25x+4,800-.16x=6,060
.09x=6,060-4,800
.09x=1,260
x=1,260/.09
x=14,000 is the amount invested @ 25%.
30,000-14,000=16,000 invested @ 16%.
Proof:
.25*14,000+.16*16,000=6,060
3,500+2,560=6,060
6,060=6,060
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