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Inequalities/311021: 0.7< x <0.81
Find a value for x that satisfies the inequality
1 solutions

Answer 222445 by Fombitz(13828) About Me  on 2010-06-03 14:21:04 (Show Source):


Quadratic-relations-and-conic-sections/311025: Which is an equation for the parabola that has vertex (4,2) and passes through the point (-1,-73)?
1 solutions

Answer 222444 by Fombitz(13828) About Me  on 2010-06-03 14:19:52 (Show Source):
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The vertex form of a parabola is,
y=a%28x-h%29%5E2%2Bk
where (h,k) is the vertex.
y=a%28x-4%29%5E2%2B2
Use the point to determine a.
-73=a%28-1-4%29%5E2%2B2
-75=25a
a=-3
.
.
.
highlight_green%28y=-3%28x-4%29%5E2%2B2%29


Linear-equations/311012: Solve the system by elimination method
0.3x-0.2y=4
0.5x+0.3y=71/23
1 solutions

Answer 222442 by Fombitz(13828) About Me  on 2010-06-03 14:11:16 (Show Source):
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Multiply both equations by 10 to eliminate decimals.
1.3x-2y=40
2.5x%2B3y=710%2F23
Mulltiply eq. 1 by 3 and eq. 2 by 2 and add them to eliminate y,
9x-6y%2B10x%2B6y=120%2B1420%2F23
19x=2760%2F23%2B1420%2F23
highlight_green%28+x=4180%2F437%29
Then use either equation to solve for x.
3x-2y=40
12540%2F437-2y=17480%2F437
-2y=4940%2F437
highlight_green%28+y=-2470%2F437%29


Trigonometry-basics/311020: Find the variance and standard deviation of the given set of data to the nearest tenth.
{520, 260, 380, 440, 150, 570, 780}

A. variance = 192.3, standard deviation = 36,991.8
B. variance = 43,157.1, standard deviation = 207.7
C. variance = 36,991.8, standard deviation = 192.3
D. variance = 36,991.8, standard deviation = 18,495.9
I am totally confused on how to solve this.
1 solutions

Answer 222440 by Fombitz(13828) About Me  on 2010-06-03 14:05:31 (Show Source):
You can put this solution on YOUR website!
Mean=442.9 (add the values and divide by 7)
Variance=36991.8 (for each value calculate the difference between the value and the mean, square it, sum for each value, and divide by the number of values)
St.Dev.=192.2 (Take the square root of the variance)
.
.
.
C) is the correct answer.


Linear-equations/311010: Solve the system by elimination method
5x+5y=-13
7x+2y=19 I think I have x solution x=23/15 I can't get y-solution
1 solutions

Answer 222439 by Fombitz(13828) About Me  on 2010-06-03 13:56:12 (Show Source):
You can put this solution on YOUR website!
No, your solution is off somewhere.
Multiply eq.1 by 2 and eq.2 by -5 and add them,
10x%2B10y-35x-10y=-26-95
-25x=-121
highlight%28x=121%2F25%29
Then use either equation to solve for y,
5x%2B5y=-13
121%2F5%2B5y=-13
5y=-65%2F5-121%2F5
5y=-186%2F5
highlight%28y=-186%2F25%29


Polynomials-and-rational-expressions/311017: I need help with this problemz%5E2%2B10z%2B16/z%2B2
1 solutions

Answer 222438 by Fombitz(13828) About Me  on 2010-06-03 13:47:33 (Show Source):
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Factor the numerator,
z%5E2%2B10z%2B16=%28z%2B2%29%28z%2B8%29
Substitute,
%28z%5E2%2B10z%2B16%29%2F%28z%2B2%29=%28%28z%2B2%29%28z%2B8%29%29%2F%28z%2B2%29
%28z%5E2%2B10z%2B16%29%2F%28z%2B2%29=%28cross%28z%2B2%29%28z%2B8%29%29%2Fcross%28z%2B2%29
highlight_green%28%28z%5E2%2B10z%2B16%29%2F%28z%2B2%29=z%2B8%29


Linear-equations/311014: Solve by the elimination method
6x-9y=7.5
7y-3x=-5
1 solutions

Answer 222437 by Fombitz(13828) About Me  on 2010-06-03 13:44:35 (Show Source):
You can put this solution on YOUR website!
Multiply eq.2 by (-3) and add to eq. 1,
6x-9y-21x%2B9y=7.5%2B15
-15x=22.5
x=-1.5
highlight%28x=-3%2F2%29
Then use either equation to solve for y.
6x-9y=7.5
-9-9y=7.5
-9y=33%2F2
highlight%28y=-11%2F6%29


Age_Word_Problems/310882: Next year Peter will be twice as old as his sister will be. She is three years younger than he. How old is each one now?
1 solutions

Answer 222436 by Fombitz(13828) About Me  on 2010-06-03 13:39:37 (Show Source):
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P-Peter's age right now
S-Sister's age right now
Next year, Peter will be P%2B1, Sister will be S%2B1.
1.P%2B1=2%28S%2B1%29
2.S=P-3
Substitute eq. 2 into eq. 1,
P%2B1=2%28P-3%2B1%29
P%2B1=2%28P-2%29
P%2B1=2P-4
-P=-5
highlight%28P=5%29
Then from eq. 2,
S=P-3=5-3
highlight_green%28S=2%29
Peter is 5 years old, his sister is 2 years old.


Linear_Equations_And_Systems_Word_Problems/310903: Sky diving. According to this formula= t = (sqrt)h/16, how long would it take a sky diver to reach the earth when jumping from 17,000 feet? (A sky diver can actually get about twice as much falling time by spreading out and using the air to slow the fall.)
1 solutions

Answer 222435 by Fombitz(13828) About Me  on 2010-06-03 13:36:47 (Show Source):


Linear_Equations_And_Systems_Word_Problems/311006: Rationalize the denominator.
ab
1 solutions

Answer 222434 by Fombitz(13828) About Me  on 2010-06-03 13:35:15 (Show Source):
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I don't see a denominator, just the expression ab.
Please re-post.


Linear-equations/311002: Solve and graph the solution set to the inequality -8x-1<-17
1 solutions

Answer 222433 by Fombitz(13828) About Me  on 2010-06-03 13:34:39 (Show Source):


Linear_Equations_And_Systems_Word_Problems/311003: Use a calculator to approximate the square roots. Round to three decimal places 567788. I got an answer of 753.517 please correct me if I am wrong.
1 solutions

Answer 222432 by Fombitz(13828) About Me  on 2010-06-03 13:25:03 (Show Source):
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Yes, you are correct.


Mixture_Word_Problems/311004: How much pure hydrocloric acid must be added to 40 milliliters of a 50% solution to obtain a 75% acid solution?

1 solutions

Answer 222431 by Fombitz(13828) About Me  on 2010-06-03 13:24:25 (Show Source):
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Let X be the ml of 100% acid added.
50%2840%29%2B100%28X%29=75%2840%2BX%29
2000%2B100X=3000%2B75X
25X=1000
highlight%28X=40%29
40 ml of 100% acid need to be added.


Numbers_Word_Problems/310900: 7x=152 round answer to nearest thousandth
1 solutions

Answer 222430 by Fombitz(13828) About Me  on 2010-06-03 13:22:55 (Show Source):
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7x=152
x=152%2F7
x=21.7142857
To the nearest thousandth, x=21.714


Rectangles/310895: how do you find the dimensions of a rectangle with the smallest perimeter and an area of 120000 inches?
1 solutions

Answer 222429 by Fombitz(13828) About Me  on 2010-06-03 13:21:29 (Show Source):
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The area of a rectangle is,
A=L%2AW=120000
L=120000%2FW
The perimeter of a rectangle is,
P=2%2A%28L%2BW%29
Substituting,
P=2%2A%28120000%2FW%2BW%29
Now P is a function of W only.
To minimize P, find the derivative wrt W and set it equal to zero.
dP%2FdW=2%2A%28-120000%2FW%5E2%2B1%29=0
120000%2FW%5E2=1
W%5E2=120000
W=sqrt%28120000%29
From the area equation above,
L=120000%2FW=120000%2Fsqrt%28120000%29=sqrt%28120000%29
The rectangle with the smallest perimeter and area of 120000 sq. in. is a square with sides of sqrt%28120000%29 in.


Exponential-and-logarithmic-functions/310891: If exclusive, find P(S or T); P(S)=20% P(T)=22%
1 solutions

Answer 222428 by Fombitz(13828) About Me  on 2010-06-03 13:17:15 (Show Source):
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Since it's exclusive, then
P(S or T)=P(S)+P(T)=0.2+0.22=0.42 or 42%


Geometry_Word_Problems/310892: A circular window of radius 12 inches is to be laminated with a sunblock coating that costs $0.65 per square inch to apply. What is the total cost of coating the window, to the nearest cent? (Use п = 3.14. Hint: Area of Circle: A = пr2)
1 solutions

Answer 222427 by Fombitz(13828) About Me  on 2010-06-03 13:16:27 (Show Source):
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Find the area of the window.
Multiply by the cost/area of coating to get the total cost.
C=0.65%2A%28pi%2AR%5E2%29=0.65%2A%283.14%2A12%5E2%29=293.90
It would cost $293.90 to coat this window.


Equations/310889: How do I solve this method?
4/9(w2) + 1 = 5/3(w)
1 solutions

Answer 222426 by Fombitz(13828) About Me  on 2010-06-03 13:14:17 (Show Source):
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Is this your equation?
%284%2F9%29w%5E2+%2B+1+=+%285%2F3%29w
Multiply by 9 to remove all denominators,
4w%5E2+%2B+9+=+15w
4w%5E2-15w%2B9=0
Factor the quadratic
%284w-3%29%28w-3%29=0
Two solutions:
4w-3=0
4w=3
highlight_green%28+w=3%2F4%29
.
.
.
w-3=0
highlight_green%28+w=3+%29


Rectangles/310958: Find the perimeter of a rectangle if its length measures 13 centimeters and its width measures 12 centimeters. Include the correct units.
1 solutions

Answer 222425 by Fombitz(13828) About Me  on 2010-06-03 13:08:19 (Show Source):


Linear_Equations_And_Systems_Word_Problems/311000: Use a calculator to approximate the square roots. Round to three decimal places.
-567788.
1 solutions

Answer 222424 by Fombitz(13828) About Me  on 2010-06-03 13:07:18 (Show Source):
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You cannot take the square root of any number less than zero.
Undefined.


Numbers_Word_Problems/310964: of 3 numbers, the second is two less than the first. the third number is 4 less than the first. if all 3 numbers sum to 45, find each number.
1 solutions

Answer 222423 by Fombitz(13828) About Me  on 2010-06-03 13:06:31 (Show Source):
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A-first number
B-second number
C-third number
.
.
.
"the second is two less than the first"
B=A-2
"the third number is 4 less than the first"
C=A-4
"all 3 numbers sum to 45"
A%2BB%2BC=45
A%2B%28A-2%29%2B%28A-4%29=45
3A-6=45
3A=51
highlight%28+A=17+%29
.
.
B=A-2%29
highlight%28+B=15%29
.
.
C=A-4
highlight%28+C=11%29


Geometry_Word_Problems/310982: What is the perimeter of an epuilateral triangle with a side measuring 5.2 millimeters?
1 solutions

Answer 222422 by Fombitz(13828) About Me  on 2010-06-03 13:02:42 (Show Source):
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Equilateral triangles have 3 equal length sides.
P=3s=3%285.2%29=15.6
The perimeter is 15.6 mm.


Inequalities/310996: 0.7 Find a value for x that satisfies the inequality
1 solutions

Answer 222421 by Fombitz(13828) About Me  on 2010-06-03 13:01:34 (Show Source):
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No inequality given.
Please re-post.


Exponential-and-logarithmic-functions/310905: In a triangle which the length of one side is not given b=1, and c= square root of 17
a^2+b^2=C^2
a^2+1=sqrt of 17
17^2+1=sqrt of 17
290=sqrt of 17
17=17
is this correct?

1 solutions

Answer 222420 by Fombitz(13828) About Me  on 2010-06-03 13:01:09 (Show Source):
You can put this solution on YOUR website!
Wait, what happened to a%5E2?
Also, you made a mistake here
a%5E2%2B1=sqrt%2817%29
It should be
a%5E2%2B1=17 since you squared c.
From there, you should be able to solve for a directly.
Re-post if you get stuck.


Equations/310997: How would I perform this indicated operation?
(5x^-3)^-2 (15x^5)^2 (25x^14)^-1
1 solutions

Answer 222419 by Fombitz(13828) About Me  on 2010-06-03 12:58:24 (Show Source):


Polynomials-and-rational-expressions/310988: Two negative, even consecutive integers have a product of 224. Find the smaller integer.
a) -12
b) -14
c) -16
d) -18

1 solutions

Answer 222418 by Fombitz(13828) About Me  on 2010-06-03 12:54:34 (Show Source):
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N%28N%2B2%29=224
N%5E2%2B2N-224=0
%28N-14%29%28N%2B16%29=0
N%2B16=0
highlight%28+N=-16%29+
highlight%28+N%2B2=-14%29+
c) The smaller integer is -16.


Miscellaneous_Word_Problems/310870: A class containing a number P students has a test average of 70%. Another class containing a number N students has a test average of 92%. When the classes are combined, the new average is 86%. What is the value of P/N?
It's the only problem in my homework assignment I can't solve. I think it should be set up as:
[(P X .70) + (N X .92)]/P + N equals .86
But how do I solve for P or N?
1 solutions

Answer 222406 by Fombitz(13828) About Me  on 2010-06-03 11:14:46 (Show Source):
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Don't solve for them, solve for P/N.
(x1+x2+x3+...+xp)/P=70
(y1+y2+y3+...+yn)/N=92
(x1+x2+...+xn+y1+y2+...yp)/(P+N)=86
.
.
.
(x1+x2+x3+...+xp)=70P
(y1+y2+y3+...+yn)=92N
(x1+x2+...+xn+y1+y2+...yp)=86%28P%2BN%29
+70P%2B92N=86P%2B86N+
+-16P=-6N
+P%2FN=6%2F16=3%2F8


Radicals/310971: I homeschool my 9th grader and we have one more question on simplifying radicals. He is supposed to simplify index 3 of square root 160. My teacher's manual says the answer is: 2 (index 3) of square root 20. My son and I feel that 20 could be simplified. Is the teacher's manual wrong or are we. thank you. Joan and her son Jed
1 solutions

Answer 222405 by Fombitz(13828) About Me  on 2010-06-03 11:08:38 (Show Source):
You can put this solution on YOUR website!
I think you're getting confused on the symbols.
It's not the square root, it's the cube root.
I think that's what you mean by index 3 square root.
Just like square root is to the (1%2F2) power, cube root is to the (1%2F3) power.
You can pull the 8 out because 2%5E3=8 so the cube root of 8 is 2.
You have no other factors in 20 that are cube roots so it's as simplified as it can be.



Quadratic-relations-and-conic-sections/310974: identify the conic section given by 121x^2=49+144y^2
1 solutions

Answer 222404 by Fombitz(13828) About Me  on 2010-06-03 11:03:58 (Show Source):
You can put this solution on YOUR website!
121x%5E2-144y%5E2=49
%28121%2F49%29x%5E2-%28144%2F49%29y%5E2=1
Unequal coefficients for x%5E2 and y%5E2 with unequal signs points to a hyperbola.


Equations/310970: How would I perform this indicated operation?
(14a^2 – 29ab – 13b^2) – (9a^2 – 16ab + 17b^2)
1 solutions

Answer 222403 by Fombitz(13828) About Me  on 2010-06-03 11:00:35 (Show Source):
You can put this solution on YOUR website!
Distribute the (-1) on the right hand side,

Group like terms,

Add and simplify,

%2814a%5E2-29ab-13b%5E2%29-%289a%5E2-16ab%2B17b%5E2%29=+5a%5E2-13ab-30b%5E2


Bodies-in-space/310953: If a cone shape is 5' high and contains 15 cubic feet what is the bottom diameter? Thank you.
1 solutions

Answer 222402 by Fombitz(13828) About Me  on 2010-06-03 10:55:03 (Show Source):
You can put this solution on YOUR website!
The volume of a cone is given as,
Vcone=%28pi%2F3%29r%5E2%2Ah
15=%28pi%2F3%29r%5E2%2A5
r%5E2=9%2F%28pi%29
r=3%2Fsqrt%28pi%29
d=2r=6%2Fsqrt%28pi%29