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Functions/178280: This question is from textbook college algebras
Thank you in advance for your help. I do not understand what I need to do to find f^-1 and verify that (f o f^-1)(x)=x and (f^-1 o f )(x)=x
the equation is
f(x)=x/x+1 for x>-1
1 solutions

Answer 133241 by Earlsdon(6287) on 2009-01-24 15:58:15 (Show Source):

You can put this solution on YOUR website!
Verify that f%5E%28-1%29%28f%28x%29%29+=+x

and

for:

for

First, you'll need to find f%5E%28-1%29%28x%29

Start with the given function:
f%28x%29+=+x%2F%28x%2B1%29

Substitute

for

Now exchange x and y.
x+=+y%2F%28y%2B1%29

Next, solve this for y. Multiply both sides by %28y%2B1%29

Expand the left side.
xy%2Bx+=+y

Subtract xy from both sides.
x+=+y-xy

Factor the y from the right side.
x+=+y%281-x%29

Divide both sides by %281-x%29

Now replace the

with

highlight%28f%5E%28-1%29%28x%29+=+x%2F%281-x%29%29

Now you are in a position to find:
f%28f%5E%28-1%29%28x%29%29

Substitute f%5E%28-1%29%28x%29+=+x%2F%281-x%29

recalling that f%28x%29+=+x%2F%28x%2B1%29

f%28x%2F%281-x%29%29+=+%28%28x%2F%281-x%29%29%29%2F%28%28x%2F%281-x%29%29%2B1%29

Notice that where there is an x on the left side, it's replaced with x%2F%28x-1%29

on the right side. Now we'll simplify the right side.
f%28f%5E%28-1%29%28x%29%29+=+%28x%2F%28x-1%29%29%2F%281%2F%28x-1%29%29

Invert and multiply.
f%28f%5E%28-1%29%28x%29%29+=+%28x%2Fcross%28%28x-1%29%29%29%2A%28cross%28%28x-1%29%29%2F1%29

highlight%28f%28f%5E%28-1%29%28x%29%29+=+x%29

Do you think you can manage to show that f%5E%28-1%29%28f%28x%29%29+=+x

Quadratic_Equations/177383: Please help. If the sides of a square are lengthened by 8cm, the area becomes 169cm^2. Find the length of the original square.
Thank you.
1 solutions

Answer 132426 by Earlsdon(6287) on 2009-01-19 12:02:48 (Show Source):

You can put this solution on YOUR website!
Let s = the length of the side of the original square.
If you increase this by 8 cm (s+8) and square it ((s+8)*(s+8)) you get 169 sq.cm. So you can write:
%28s%2B8%29%5E2+=+169

Square the left side.
s%5E2%2B16s%2B64+=+169

Subtract 169 from both sides.
s%5E2%2B16s-105+=+0

Factor this quadratic equation.
%28s-5%29%28s%2B21%29+=+0

Apply the zero product rule:
s-5+=+0

which means that...
s+=+5

Discard the negative solution as the length of the sides can only be positive.
highlight%28s+=+5%29

cm This is the length of the side of the original square.
Check:
%28s%2B8%29%5E2+=+169

OK!

Quadratic_Equations/177348: Could someone please help me answer this question?
If you are looking at a graph of a quadratic equation, how do
you determine where the solutions are?
1 solutions

Answer 132412 by Earlsdon(6287) on 2009-01-19 11:07:27 (Show Source):

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The "solutions" or "roots" to a quadratic equation are the points on the graph of the equation where the graph (a parabola) intersects the x-axis.
Of course, some parabolas will intersect the x-axis in two places (1st. graph) in which case the equation is said to have two real roots.
Some parabolas will have their vertex just touching the x-axis (2nd graph). Such an equation is said to have double root or two identical roots.
Other parabolas will not intersect the x-axis at all (3rd graph), in which case, the equation is said to have no real roots.
graph%28400%2C400%2C-5%2C8%2C-5%2C5%2Cx%5E2-5x%2B2%29

graph%28400%2C400%2C-5%2C8%2C-5%2C5%2Cx%5E2-5x%2B2%29

graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Cx%5E2%2B4x%2B4%29

graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C2x%5E2%2Bx%2B1%29

Trigonometry-basics/177268: This question is from textbook
The highest advertising sign in the world is a large letter I situated at the top of the 73-story First Interstate World Center building in Los Angeles. At a distance of 200 feet from a point directly below the sign, the angle between the ground and the top of the sign is 77.87°. To the nearest tenth, approximate the height of the top of the sign.
1 solutions

Answer 132348 by Earlsdon(6287) on 2009-01-18 18:11:44 (Show Source):

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Using right triangle math, in which the height (h) is the unknown and the base is 200 feet, use the tangent function (opposite over adjacent) to find h.
Tan%2877.87%29+=+h%2F200

Multiply both sides by 200.
200%2ATan%2877.87%29+=+h

feet.

Trigonometry-basics/177267: This question is from textbook
Stonehenge in Salisbury Plains, England, was constructed using solid stone blocks weighing over 96000 pounds each. Lifting a single stone required 550 people, who pulled the stone up a ramp inclined at an angle of 9°. To the nearest tenth, approximate the distance that a stone was moved along the ramp in order to raise it to a height of 31 feet.
1 solutions

Answer 132342 by Earlsdon(6287) on 2009-01-18 17:44:48 (Show Source):

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Think of the ramp as a right triangle in which the hypotenuse is the ramp's slope up which the 96000-lb block of stone is to be hauled.
The height (h) of this triangle is the height to which the block is to be raised.
The height is opposite to the angle of 9 degrees, so you can use the sine function to solve this problem and you are trying to find the length of the hypotenuse (c).
sin%289%29+=+h%2Fc

Substitute h = 31 ft.
sin%289%29+=+31%2Fc

Multiply both sides by c.
c%2Asin%289%29+=+31

The sine 0f 9 degrees is 0.156, so...
c%280.156%29+=+31

Divide both sides by 0.156
h+=+198.7179

Round to nearest tenth.
h+=+198.7

feet.

Exponential-and-logarithmic-functions/177270: 6*(7*10^8)
1 solutions

Answer 132340 by Earlsdon(6287) on 2009-01-18 17:26:22 (Show Source):

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Evaluate:
6%2A%287X10%5E8%29

Multiply the 6 times 7 = 42
42X10%5E8

Expand the 10%5E8+=+100000000

Final answer: highlight%284200000000%29

or 4,200,000,000

Money_Word_Problems/177228: This question is from textbook college algebras
thank you in advance for help with this problem. I am not getting it right but would like to know where I am going wrong. Thanks $600 for 10 years at 8.5% compounded annually.
I set it up like this A=600(1+.085)^10
and I end up wiht 656 I know the answer is 1356$ annually. Thank for showing me where I am going wrong.
1 solutions

Answer 132308 by Earlsdon(6287) on 2009-01-18 11:36:26 (Show Source):

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Well, I see nothing wrong with your set up.
A+=+P%281%2Bi%29%5En

and p = 600, i = 0.085, and n = 10 years.
A+=+600%281%2B0.085%29%5E10

So I would double check your order of operations.

Polynomials-and-rational-expressions/177049: Verify algebraically, that (Fof^-1)(x)=x for f(x)=1/(2x+4)
1 solutions

Answer 132304 by Earlsdon(6287) on 2009-01-18 11:07:44 (Show Source):

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Your problem statement is a little unclear! Did you mean to write:
Verify algebraically that f%28f%5E%28-1%29%28x%29%29+=+x

for

I'll assume that you did and we'll proceed.
First, we find f%5E%28-1%29%28x%29

Start with the given function, but replace the f%28x%29

with

Now exchange the x and the y.
x+=+1%2F%282y%2B4%29

Next, solve this for y. Multiply both sides by (2y+4)
x%282y%2B4%29+=+1

Divide both sides by x.
2y%2B4+=+1%2Fx

Subtract 4 from both sides.
2y+=+%281%2Fx%29-4

Simplify the right side.
2y+=+%281-4x%29%2Fx

Now divide both sides by 2.
y+=+%281-4x%29%2F2x

Finally, replace the

with

f%5E%28-1%29%28x%29+=+%28%281-4x%29%2F2x%29

Now you can find f%28f%5E%28-1%29%28x%29%29

f%28f%5E%28-1%29%28x%29%29+=+f%28%281-4x%29%2F2x%29

but

, so...

f%28%281-4x%29%2F2x%29+=+1%2F%28%28cross%282%29%28%281-4x%29%2Fcross%282%29x%29%2B4%29%29

Simplifying this...
f%28%281-4x%29%2F2x%29+=+1%2F%28%281cross%28-4x%29%2Bcross%284x%29%29%2Fx%29

f%28%281-4x%29%2F2x%29+=+1%2F%281%2Fx%29

so...

and so

for

Linear-systems/177176: Al will rent a car for the weekend. He can choose one of two payment plans. The first plan costs $51.98 for two days plus 15 cents per mile. The second plan costs $39.98 for two days plus 20 cents per mile. How many miles does Al need to drive for the two plans to cost the same?

1 solutions

Answer 132244 by Earlsdon(6287) on 2009-01-17 19:09:57 (Show Source):

You can put this solution on YOUR website!
Let's write the cost equations (C) for both car rentals:
C%5B1%5D+=+51.98%2B0.15m

where m = number of miles driven.
C%5B2%5D+=+39.98%2B0.20m

Since you need to know when the costs will be equal, set these two equations equal to each other.
51.98%2B0.15m+=+39.98%2B0.20m

Now you can solve for m, the number of miles. Subtract 0.15m from both sides.
51.98+=+39.98%2B0.05m

Now subtract 39.98 from both sides.
12+=+0.05m

Finally, divide both sides by 0.05
240+=+m

So, Al must drive 240 miles for the costs of both plan to be the same.

Linear-equations/177173: A study showed that, your maximum ideal waist size is directly proportional to your hip size.For a woman with 40-inch hips, the maximum ideal waist size is 32 inches. What is the maximum ideal waist size for a woman with 35-inch hips?
1 solutions

Answer 132243 by Earlsdon(6287) on 2009-01-17 18:59:12 (Show Source):

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First, you will need to write the equation of proportion. Let W = waist size and H = hip size.
W+=+kH

where k is the constant of proportionality. You need to find the value of k, so subtitute W = 32 and H = 40.
32+=+k%2840%29

Divide both sides by 40.
k+=+32%2F40

Now the equation of proportionality is:
W+=+0.8%2AH

To find the ideal maximum waist size (W) for a woman with 35-inch hips, substitute H = 35.
W+=+0.8%2835%29

inches.

Linear-systems/177175: Lena purchased a prepaid phone card for $30. Long distance calls cost 17 cents a minute using this card. Lena used her card only once to make a long distance call. If the remaining credit on her card is $24.05, how many minutes did her call last?

1 solutions

Answer 132241 by Earlsdon(6287) on 2009-01-17 18:50:29 (Show Source):

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Lena has used $30-$24.05 = $5.95 of the total value of the card.
The question is...how many minutes of long-distance call can she get from $5.95 at $0.17 per minute.
To find out, you will need to divide $5.95 by $0.17, so...
5.95%2F0.17+=+35

Lena's long-distance call lasted 35 minutes.

expressions/177171: i am trying to solve this problem..... (3x) to the -1/3 power using log table???
1 solutions

Answer 132239 by Earlsdon(6287) on 2009-01-17 18:44:38 (Show Source):

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It appears as though you have omitted part of the problem statement.
You really need an equation to solve for x...
%283x%29%5E%28-1%2F3%29+=+y

Problems-with-consecutive-odd-even-integers/177196: find three consecutive integers such that the product of the two smaller inters is 2 more than ten times the largest integers.
1 solutions

Answer 132238 by Earlsdon(6287) on 2009-01-17 18:33:30 (Show Source):

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Let the three consecutive integers be: x, (x+1) and (x+2)
x%2A%28x%2B1%29+=+10%28x%2B2%29%2B2

"The product of the two smaller integers (x and (x+1)) is 2 more than 10 times the larger integer (x+3).
x%5E2%2Bx+=+10x%2B20%2B2

Subtract 10x from both sides.
x%5E2-9x+=+22

Subtract 32 from both sides.
x%5E2-9x-22+=+0

Factor this quadratic equation.
%28x-11%29%28x%2B2%29+=+0

Apply the zero product rule.
x-11+=+0

so...

Solutions:
11, 12, and 13
-2, -1, and 0
As you can see, there are two solutions, so let;'s check them both!
x = 11
%2811%29%2A%2812%29+=+10%2813%29%2B2

OK!
x = -2
%28-2%29%2A%28-1%29+=+10%280%29%2B2

OK!

Linear-systems/177177: A total of 285 tickets were sold for the school play. The number of student tickets sold was two times the number of adult tickets sold . How many adult tickets were sold?

1 solutions

Answer 132234 by Earlsdon(6287) on 2009-01-17 18:14:44 (Show Source):

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Let S = the number of student tickets sold and A = the number of adult tickets sold.
From the problem, you can write:
1) S+A = 285 "A total of 285 (student plus adult) tickets were sold..."
2) S = 2A "The number of student tickets (S) sold was two times the number of adult tickets (A) sold."
Substitute equation 2) (S = 2A) for S in equation 1).
(2A+A) = 285 Simplify.
3A = 285 Divide both sides by 3.
A = 95 This is the number of adult tickets sold.
From equation 2)...
S = 2A
S = 2(95)
S = 190 This is the number of student tickets sold.

Linear-equations/177189: I need help with this equation and a explanantion Please.
Determine the slope ans y-intercept of the line x+2y=3. Thank you.
1 solutions

Answer 132231 by Earlsdon(6287) on 2009-01-17 18:05:34 (Show Source):

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First, rewrite the equation in the "slope-intercept" form: y = mx+b:
x%2B2y+=+3

Subtract x from both sides of the equation.
2y+=+-x%2B3

Now divide both sides by 2 to get the y by itself.
y+=+%28-1%2F2%29x%2B3%2F2

Compare this with the general form of the slope-intercept:
y+=+mx%2Bb

and you can see that the slope, highlight%28m+=+%28-1%2F2%29%29

and the y-intercept, highlight%28b+=+3%2F2%29

Linear-systems/177163: Give an ordered pair (x,y) of numbers that satisfy the equation
4x+y=3
1 solutions

Answer 132230 by Earlsdon(6287) on 2009-01-17 17:59:11 (Show Source):

You can put this solution on YOUR website!
Rewrite the equation in the slope-intercept form: y = mx+b
y = -4x+3 Now substitute any value you like for x and you will get the corresponding value of y. Let x = 5
y = -4(5)+3
y = -20+3
y = -17
So one ordered pair would be (5, -17)
As you can see, there are an infinite ordered pairs that would satisfy this equation, you choose the x-value and there will be a corresponding y-value..

Quadratic_Equations/177181: the problem I have is f(t)=2t^2-4t-1 and it asks tosolve the problem if f(2). Can some one show me how this works
1 solutions

Answer 132222 by Earlsdon(6287) on 2009-01-17 17:19:28 (Show Source):

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If:
f%28t%29+=+2t%5E2-4t-1

find f(2): You simply substitute 2 for every t in the equation and evaluate.
f%282%29+=+2%282%29%5E2-4%282%29-1

Linear-systems/176907: This question is from textbook Algebra 1
The farest I have got to this question is 2a= 8 / a+b=2
a=4 on the first linear equations but I don't know where to go from here.
1 solutions

Answer 132218 by Earlsdon(6287) on 2009-01-17 16:10:41 (Show Source):

You can put this solution on YOUR website!

Solve:
2a+=+a

and

Divide both sides by 2.
highlight%28a+=+4%29

Substitute a+=+4

Subtract 4 from both sides.
highlight%28b+=+-2%29

Evaluation_Word_Problems/176891: During the year, Charles read five more books than twice the number of books read by Frank. If together they read a total of 29 books, how many books did each read? Please include a "let statement".
1 solutions

Answer 132217 by Earlsdon(6287) on 2009-01-17 16:06:08 (Show Source):

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Let F = the number of books read by Frank and let C = the number of books read by Charles.
From the problem statement:
1) C = 2F+5 "Charles read five more books than twice the number of books read by Frank"
2) C+F = 29 "...they read a total of 29 books..."
Substitute equation 1) (C = 2F+5) for C in equation 2) (C+F = 29) to get:
2a) (2F+5)+F = 29 Simplify and solve for F by combining like-terms..
2a) 2F+F+5 = 29
2a) 3F+5 = 29 Subtract 5 from both sides of the equation.
2a) 3F = 24 Divide both sides by 3.
2a) highlight%28F+=+8%29

Frank read 8 books.
1) C = 2F+5 Substitute F = 8.
1) C = 2(8)+5
1) C = 16+5
1) highlight%28C+=+21%29

Charles read 21 books.

Linear-equations/177137: Please help me with this question.
1. Gas laws. The volume of a gas is inversely proportional to the pressure on the gas.If the volume is 6 cubic centimeters when the pressure on the gas is 8 kilograms per square centimeter, then what is the volume when the pressure is 12 kilograms per square centimeter?

1 solutions

Answer 132192 by Earlsdon(6287) on 2009-01-17 12:39:17 (Show Source):

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Write the equation of variation:
V+=+k%2FP

where: P = pressure, V = volume, and k is the constant of variation. Substitute the given V = 6 and P = 8 to find the value of k.
6+=+k%2F8

so...

Now the equation of variation is:
V+=+48%2FP

Now substitute P = 12 to find the new volume (V).
V+=+48%2F12

Cubic centimeters

absolute-value/177129: This question is from textbook
Factor. Write prime if the expression cannot be factored: 12w^2+10w-8
1 solutions

Answer 132189 by Earlsdon(6287) on 2009-01-17 11:26:02 (Show Source):

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Factor:
12w%5E2%2B10w-8

First, factor a 2.
2%286w%5E2%2B5w-4%29

Now factor the parentheses.
highlight%282%282w-1%29%283w%2B4%29%29

Miscellaneous_Word_Problems/177073: This question is from textbook
Car rental agency A will rent a compact car for $35 per day and an additional charge of $0.24 per mile. Car rental agency B will charge only $0.16 per mile but charges $41 per day. If Adam wanted to rent a car for three days, how many miles would Adam have to drive to make car rental agency B a better bargain?
1 solutions

Answer 132145 by Earlsdon(6287) on 2009-01-16 20:44:33 (Show Source):

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Let C%5BA%5D

be the cost for agency A and C%5BB%5D

be the cost for agency B.
For agency A:
C%5BA%5D+=+35%2Ad%2B0.24%2Am

where d = number of days rented and m = number of miles driven.
For agency B:
C%5BB%5D+=+41d%2B0.16m

Adam wants to rent for 3 days so d = 3 and we want to see for how many miles agency B would be cheaper than agency A, or when is...
C%5BB%5D+%3C+C%5BA%5D

Substituting the above equations with d=3,
41%283%29%2B0.16m+%3C+35%283%29%2B0.24m

Simplify and solve for m.
123%2B0.16m+%3C+105%2B0.24m

Subtract 105 from both sides.
18%2B0.16m+%3C+0.24m

Subtract 0.16m from both sides.
18+%3C+0.08m

Divide both sides by 0.08
225+%3C+m

Adam would have to drive more than 225 miles to make agency B a better (cheaper) bargain.

Polynomials-and-rational-expressions/177023: Which numbers cannot be used in place of the variable in each rational expession?
2y+1/y^2-y-6
=
1 solutions

Answer 132070 by Earlsdon(6287) on 2009-01-16 11:37:34 (Show Source):

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Which numbers are not allowed in the denominator? The values of y that make the denominator = zero. So, set the denominator = to zero and solve for the values of y that satisfy the equation.
y%5E2-y-6+=+0

Factor the equation.
%28y%2B2%29%28y-3%29+=+0

Apply the zero product rule.
y%2B2+=+0

so...

These are the "excluded" values of y.

Equations/176965: This question is from textbook pre-algebra
S-3 over 7 = S+5 over 9
1 solutions

Answer 132032 by Earlsdon(6287) on 2009-01-15 22:21:34 (Show Source):

You can put this solution on YOUR website!
Solve for S:
%28S-3%29%2F7+=+%28S%2B5%29%2F9

Multiply both sides by 7 and by 9.
9%28S-3%29%2Across%287%29%2Fcross%287%29+=+7%28S%2B5%29%2Across%289%29%2Fcross%289%29

Cancel as indicated.
9%28S-3%29+=+7%28S%2B5%29

Perform the distributive property.
9S-27+=+7S%2B35

Add 27 to both side.
9S+=+7S%2B62

Subtract 7S from both sides.
2S+=+62

Divide both sides by 2.
highlight%28S+=+31%29

Rational-functions/176969: I need assistance in figuring out the following:
8sqrt%282%29%28sqrt%288%29-3sqrt%282%29%2B7sqrt%2832%29%29

I have an algebra test tomorrow and nearly no one in my class really understands the math material we are being tested on, so this would be extremely helpful and I would be veryyyyyyyy grateful for any help!
1 solutions

Answer 132030 by Earlsdon(6287) on 2009-01-15 22:09:03 (Show Source):

You can put this solution on YOUR website!
Evaluate:
%288sqrt%282%29%29%28sqrt%288%29-3sqrt%282%29%2B7sqrt%2832%29%29

Ok, the key thing here is to get all of the radicands (the numbers inside of the square root symbols) to = 2, if possible. Well, since you know that 8 and 32 are multiples of 2 this is possible. So here we go, step-by-step!
%288sqrt%282%29%29%28sqrt%284%2A2%29-3sqrt%282%29%2B7sqrt%2816%2A2%29%29

%288sqrt%282%29%29%28sqrt%284%2A2%29-3sqrt%282%29%2B7sqrt%2816%2A2%29%29

Now,

so you can move that outside of the radical but leave the 2 inside. And, sqrt%2816%29+=+4

so you can move that outside of the radical leaving the 2 inside:
%288sqrt%282%29%29%282sqrt%282%29-3sqrt%282%29%2B7%2A4sqrt%282%29%29

Multiply the 7*4 = 28
%288sqrt%282%29%29%282sqrt%282%29-3sqrt%282%29%2B28sqrt%282%29%29

In the second set of parentheses, collect all of the sqrt%282%29

's together.
%288sqrt%282%29%29%2827sqrt%282%29%29

Finally, perform the indicated multiplication, do the numbers first (8*27 = 216) then the radicals ( sqrt%282%29%2Asqrt%282%29+=+2

to get:

Quadratic_Equations/176899: Please help with this one...the directions are to find the vertex, the line of symmetry, the minimum and maximum value of the quadratic equation and then graph it. I know that once I get the vertex, I can find the rest. I have solved it close to the end, but I am not sure where to go from here...
f(x)=-2x^2+2x+7
I used the equation -b+- the square root of b^2-4ac divided by 2a
I got to -2+-the square root of 60 divided by 4. Now I am stuck...thank you for the help.
1 solutions

Answer 132019 by Earlsdon(6287) on 2009-01-15 21:48:36 (Show Source):

You can put this solution on YOUR website!
Find the vertex, line-of-symmetry, minimum or (not and) maximum of:
f%28x%29+=+-2x%5E2%2B2x%2B7

First, since your are not asked to find the x-intercepts, you didn't need to use the quadratic formula x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a

Notice that the coefficient of the x%5E2

term is negative (-2), so this means that the parabola opens downward and, cosequently, the parabola will have a maximum, not a minimum.
Note, a parabola cannot have both a maximum and a minimum.
The maximum point will occur at the vertex of the parabola, so let's find the location of the vertex.
The x-coordinate of the vertex is given by: x+=+%28-b%29%2F2a

and, in this equation, a = -2, b = 2, so...
x+=+%28-2%29%2F2%28-2%29

Simplifying, we get:
x+=+1%2F2

Now to find the y-coordinate, substitute this into the given equation, after replacing f(x) with y:
y+=+-2%281%2F2%29%5E2%2B2%281%2F2%29%2B7

Simplify this.
y+=+-2%281%2F4%29%2B2%281%2F2%29%2B7

The vertex location is (0.5, 7.5) and this is also the location of the maximum point of the parabola.
The equation of the line of symmetry is simply the equation of the vertical line that passes through the vertex, or x+=+0.5

Now let's look at the graph:
graph%28400%2C400%2C-5%2C5%2C-5%2C10%2C-2x%5E2%2B2x%2B7%29

Rational-functions/176964: the resistance of copper wire varies directly with its length. a copper wire 275 feet long has a resistance of 950 ohms. what is the resistance of 1575 feet of copper wire
1 solutions

Answer 132013 by Earlsdon(6287) on 2009-01-15 21:22:22 (Show Source):

You can put this solution on YOUR website!
You can start by writing the equation of variation in which R = resistance in ohms and L = wire length in feet, and k = the constant of variation:
R+=+k%2AL

Solve for k.
k+=+R%2FL

Substitute the given R = 950 ohms and L = 275 feet and solve for k.
k+=+950%2F275

Simplify.

, so...

Substitute L = 1575 feet and solve for R.
R+=+%2838%2F11%29%281575%29

ohms.

Exponential-and-logarithmic-functions/176826: This question is from textbook college algebras
Thank you in advance for helping me with this problem. (4^x)(16^3x-1)=8
This is what I have done.
(2^2x)(2^4(3x-1))=2^3
in the end I got 2/7??? am I on the right track? thanks for your help.

1 solutions

Answer 131900 by Earlsdon(6287) on 2009-01-15 11:25:22 (Show Source):

You can put this solution on YOUR website!
Solve for x:
%284%5Ex%29%2816%5E%283x-1%29%29+=+8

Your first step is good!
%282%5E%282x%29%29%282%5E%284%283x-1%29%29%29+=+2%5E3

Expand the second exponent.
%282%5E%282x%29%29%282%5E%2812x-4%29%29+=+2%5E8

The second factor on the left shows the exponents being subtracted so this means division:
%282%5E%282x%29%29%28%282%5E%2812x%29%29%2F2%5E4%29+=+2%5E3

Multiply both sides by 2%5E4

%282%5E%282x%29%29%282%5E%2812x%29%29+=+%282%5E3%29%282%5E4%29

Perform the indicated multiplication by adding the exponents.
2%5E%2814x%29+=+2%5E7

The bases (2) are equal so the exponents are equal.
14x+=+7

Divide both sides by 14.
highlight%28x+=+1%2F2%29

Mixture_Word_Problems/176700: In January of the year 2000, my husband John was 11 times as old as my son william. In January of 2012, he will be three times as old as my son. How old was my son in January of 2000?
Can you show me step by step to solve it in a system of equations?
1 solutions

Answer 131775 by Earlsdon(6287) on 2009-01-14 18:23:59 (Show Source):

You can put this solution on YOUR website!
Let J = the age of your husband, John, in 2000 and let W = the age of your son, William in 2000.
From the problem description, you can write:
In 2000:
J+=+11W

"...John was 11 times as old as...William."
12 years later in 2012, when both of them are 12 years older, you can say:
J%2B12+=+3%28W%2B12%29

Simplifying this, we get:
J%2B12+=+3W%2B36

Now we substitute, from above, J+=+11W

Subtract 3W form both sides of this equation.
8W%2B12+=+36

Now subtract 12 from both sides.
8W+=+24

Finally, divide both sides by 8.
W+=+3

Your son was 3 years old in 2000.

Triangles/176703: This question is from textbook Geometry
The legs of an isosceles triangle are 5 units long and the base is 4 units long, what is the length of the base?
Please help I have been trying to pass Geometry for the last two months it is the last class I have to complete to receive my diploma I am finished with everything else. Please help!
1 solutions

Answer 131763 by Earlsdon(6287) on 2009-01-14 18:10:40 (Show Source):

You can put this solution on YOUR website!
This is like asking "Who's buried in Grant's tomb?"
You are given all of the dimensions of the isosceles triangle!
The legs are each 5 units long and the length of the base is given as 4 units long. What more is there to know besides what units are being used.

Numbers_Word_Problems/176693: Farmer Billy Bob has 210m of fencing to enclose his pig pen on all 4 sides. What dimensions should his pig pen be to enclose the largest possible area?
1 solutions

Answer 131761 by Earlsdon(6287) on 2009-01-14 18:05:49 (Show Source):

You can put this solution on YOUR website!
Start by writing the formula for the perimeter of a rectangle (assuming, of course, that the pen will be rectangular):
P+=+2%28L%2BW%29

Substitute the given P = 210.
210+=+2%28L%2BW%29

Divide both sides by 2.
105+=+L%2BW

and rewite this as:
L+=+105-W

Now the area of a rectangle is given by:
A+=+L%2AW

Substitute, from above, L = 105-W.
A+=+%28105-W%29%2AW

Simplify.

Rewrite as:
A+=+-W%5E2%2B105W

This is a quadratic equation that represents the area and the maximum point will be at the vertex of the parabola.
This point is given by:
W+=+%28-b%29%2F2a

where: a = -1 and b = 105, so...
W+=+%28-105%29%2F2%28-1%29

meters. This will be the dimension of the width of the pen.
The length is given (from above) by:
L+=+105-W

meters. This will be the dimension of the length of the pen.
This answer should come as no surprise to you as it is well known that the largest rectangular area enclosed by a given perimeter is in the form of a square.
Check:
P+=+2%28L%2BW%29

Substitute L = 52.5 and W = 52.5
P+=+2%2852.5%2B52.5%29

meters, the given perimeter.

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