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Polynomials-and-rational-expressions/548394: In solving the equation (x – 1)(x – 2) = 30, Eric stated that the solution would be
x – 1 = 30 => x = 31
or
(x – 2) = 30 => x = 32
However, at least one of these solutions fails to work when substituted back into the original equation. Why is that? Please help Eric to understand better; solve the problem yourself, and explain your reasoning.
1 solutions

Answer 356980 by Earlsdon(6294) on 2011-12-17 10:21:23 (Show Source):

You can put this solution on YOUR website!
Eric's assumption was incorrect!
He should have done the following:
%28x-1%29%28x-2%29+=+30

Multiply the two factors on the left.
x%5E2-3x%2B2+=+30

Now subtract 30 from both sides.
x%5E2-3x-28+=+0

Solve the quadratic equation by factoring.
%28x%2B4%29%28x-7%29+=+0

Apply the zero product rule.
x%2B4+=+0

so that...
x+=+-4

Triangles/548410: how do you find the base of a triangle when you have the height and area??
the height is 15in.
the area is 120in squared

1 solutions

Answer 356976 by Earlsdon(6294) on 2011-12-17 10:06:22 (Show Source):

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You start with thr formula for the area of a triangle:
A+=+%281%2F2%29b%2Ah

Then you solve this for b, the base:
b+=+2A%2Fh

and finally, you substitute the give values of A (120) and h (15).
b+=+2%28120%29%2F15

inches.

Polynomials-and-rational-expressions/546994: Factor each expression.
1. 216x^3 – 1
2. 8x^3 + 125
3. x^4 – 5x^2 + 4
Please any help???
1 solutions

Answer 356164 by Earlsdon(6294) on 2011-12-13 22:09:13 (Show Source):

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Factor:
1. 216x%5E3-1

This is a difference of two cubes which can be factored thus:
A%5E3-B%5E3+=+%28A-B%29%28A%5E2%2BAB%2BB%5E2%29

highlight%28%286x-1%29%2836x%5E2%2B6x%2B1%29%29

This is a sum of two cubes which can be factored thus:
A%5E3%2BB%5E3+=+%28A%2BB%29%28A%5E2-AB%2BB%5E2%29

8x%5E3%2B125+=+%282x%29%5E3%2B%285%29%5E3

highlight%28%282x%2B5%29%284x%5E2-10x%2B25%29%29

Temporarily change the varible: x%5E2+=+y

Substitute y+=+x%5E2

%28x%5E2-1%29%28x%5E2-4%29+=+highlight%28%28x%2B1%29%28x-1%29%28x%5E2%2B4%29%29

Exponential-and-logarithmic-functions/546826: Find the exact soulution to each equation:
3log(x)=log(x)
What I have so far:
log( x%5E3

)= log(x)
1 solutions

Answer 356097 by Earlsdon(6294) on 2011-12-13 18:25:46 (Show Source):

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Solve for x:
3Log%28x%29+=+Log%28x%29

Divide both sides by Log%29x%29

But

I don't think so! There is no solution to this equation(?).

Number-Line/546805: Please help me solve this equation Thank You ~
The sum of the present ages of Ali and Salimah is 18 years.In 6 years time Ali will be twice as old as Salimah .Find their present ages .
1 solutions

Answer 356095 by Earlsdon(6294) on 2011-12-13 18:19:52 (Show Source):

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Let A = Ali's present age and S = Salimah's present age.
1) A+S = 18 "The sum of the present ages...is 18 years".
2) A+6 = 2(S+6) "In 6 year's time Ali wil be twice as old as Salimah".
Rewrite equation 1) as A = 18-S and substitute into equation 2), then solve for S.
2a) (18-S)+6 = 2(S+6) Simplify.
2b) 24-S = 2S+12 Add S to both sides.
2c) 24 = 3S+12 Subtract 12 from both sides.
2d) 12 = 3S Now divide by 3.
2e) S = 4 and A = 18-4 = 14.
Salimah is 4 years old and Ali is 14 years old.

Quadratic_Equations/546819: A rectange shed covers 300 feet of ground. It is 6 feet longer than it is wide. What is the width of the shed to the nearest tenth of a foot?
This is what I tried:
x = width
x + 6 = length
Area of a Rectangle = 300
What I set up: 300 = x(x + 6)
Which then I got: 300 = x^2 +6x
That is all I could figure out.
1 solutions

Answer 356094 by Earlsdon(6294) on 2011-12-13 17:58:10 (Show Source):

You can put this solution on YOUR website!
What you've done so far is good!
Now you need to solve the resulting quadratic equation for x (the width).
x%5E2%2B6x-300+=+0

Use the quadratic formula: x+=+%28b%2B-sqrt%28b%5E2-4ac%29%29%2F2a

where: a = 1, b = 6, and c = -300.
x+=+9-6%2B-sqrt%286%5E2-4%281%29%28-300%29%29%2F2%281%29

which evaluates to:
x+=+-20.578

Discard the negative solution as the width (x) must be a positive value.
x+=+14.6

The width is 14.6 feet (to the nearest tenth of a foot).

Volume/546820: What is the volume of a sphere that has a radius of 2?
1 solutions

Answer 356093 by Earlsdon(6294) on 2011-12-13 17:46:51 (Show Source):

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Try:
V+=+%284%2F3%29pi%2Ar%5E3

Substitute r+=+2

test/545329: How Could You Determine If The Following Measures are The Length Of A Right Triangle? The Measures Are 15in , 8in , 17in
Explain And Show Any Work You Did To Determine If the Measures Are That Of A Right Triangle
1 solutions

Answer 355560 by Earlsdon(6294) on 2011-12-11 13:28:18 (Show Source):

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Use the Pythagorean theorem:
For any right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the two legs.
c%5E2+=+a%5E2%2Bb%5E2

c = the hypotenuse and a and b are the two legs.
In this problem, c = 17, a = 8 and b = 15.
17%5E2+=+289

So the three given sides make a right triangle.

Percentage-and-ratio-word-problems/545336: 1650 students take an english exam. If 42% fail the exam, how many students failed the exam? how many students passed.
(could you show me how to do this problem?)
1 solutions

Answer 355555 by Earlsdon(6294) on 2011-12-11 13:21:23 (Show Source):

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To find 42% of 1650 you first convert the percentage to its decimal eqivalent:
42% = 42/100 = 0.42 then you multiply this by 1650.
0.42(1650) = 693
693 students failed the exam.
To find the number of students who passed, subtract the number who failed (693) from the total number of students (1650).
1650-693 = 957
957 students passed the exam.

Linear-equations/545257: I am lost!!! Can you explain step by step how to solve this problem? Write an equation of the line containing the given point and parellal to the given line.
(-2,6); 9x = 8y + 5
I am totally confused, and even viewing examples, I just cannot understand how the final answer is arrived at.
Thank you so much in advance.
1 solutions

Answer 355550 by Earlsdon(6294) on 2011-12-11 11:57:30 (Show Source):

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Write the equation of the line containing the point (-2,6) and parallel(sp) to the line: 9x = 8y+5
First, find the slope of the given line by putting in the "slope-intercept" form y = mx+b:
9x = 8y+5 Subtract 5 from both sides.
9x-5 = 8y Now divide both sides by 8.
(9/8)x-5/8 = y which you should write as:
y = (9/8)x-5/8 Now compare this with the "slope-intercept" form.
y = mx+b and you can see that the line represented by the given equation has a slope m+=+9%2F8

Now, as you recall from your class, parallel lines have the same slope. This means that the new line whose equation you are going to write must have a slope of m+=+9%2F8

So you can start the new equation, in "slope-intercept" form:
y+=+%289%2F8%29x%2Bb

Now to find b, the y-intercept, you will use the coordinates of the given point (-2,6) and substitute the x- and y-coordinates into your starting equation above:
y+=+%289%2F8%29x%2Bb

Substitute x = -2 and y = 6
6+=+%289%2F8%29%28-2%29%2Bb

Solve for b.
6+=+-9%2F4%2Bb

Add

to both sides.

Now you can complete your equation:
y+=+%289%2F8%29x%2B1%2F4

Radicals/545264: 2. The equation D=1.2square root h ,gives the distance, D, in miles that a person can see to the horizon from a height, h, in feet.
a. Solve this equation for h.
b. Long’s Peak in Rocky Mountain National Park, is 14,255 feet in elevation. How far can you see to the horizon from the top of Long’s Peak? Can you see Cheyenne, Wyoming (about 89 miles away)? Explain your answer.

1 solutions

Answer 355548 by Earlsdon(6294) on 2011-12-11 11:30:45 (Show Source):

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Given:
a) D+=+1.2sqrt%28h%29

Solve for h. Divide both sides by 1.2
D%2F1.2+=+sqrt%28h%29

Now square both sides.
%28D%2F1.2%29%5E2+=+h

Substitute h = 14,255
D+=+1.2sqrt%2814255%29

miles Approx.
I'll leave the explanation toyou.

logarithm/545258: How do you solve 5+2lnx=4??? NEED ANSWER STEP BY STEP ASAP!
1 solutions

Answer 355547 by Earlsdon(6294) on 2011-12-11 11:22:19 (Show Source):

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Solve for x:
5%2B2ln%28x%29+=+4

Subtract 5 from both sides.
2ln%28x%29+=+-1

Divide by 2.
ln%28x%29+=+-1%2F2

Rewrite this in exponential form.
e%5E%28-1%2F2%29+=+x

Evaluate using your calculator.
x+=+0.6065

Approx.

Quadratic_Equations/545038:
what is the graph for +y=x%5E2+%2B+2x+%2B+6+

?
The vertex is (0, -7), and the axis of symmetry is x=0.
1 solutions

Answer 355482 by Earlsdon(6294) on 2011-12-10 21:30:42 (Show Source):

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For the parabola given by:
y+=+x%5E2%2B2x%2B6

The vertex is at (-1, 5) and the equation of the axis of symmetry is: x+=+-1

graph%28400%2C400%2C-5%2C5%2C-5%2C10%2Cx%5E2%2B2x%2B6%29

logarithm/545127: solve the logarithmic equation.
log base 6 (x+1)=3.
Please help me I and drawing a blank and cant remember what to do. I got to (x+1)log base 6=3 but dont remeber whats next.
1 solutions

Answer 355478 by Earlsdon(6294) on 2011-12-10 21:13:25 (Show Source):

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Solve for x:
Log%5B6%5D%28x%2B1%29+=+3

Rewrite this in "exponential" form: Log%5Bb%5D%28x%29+=+y

---->

Subtract 1.
215+=+x

Numbers_Word_Problems/545130: The sum of two numbers is 32, and their product is 96. What is the sum of the reciprocals of the two numbers.
1 solutions

Answer 355476 by Earlsdon(6294) on 2011-12-10 21:07:32 (Show Source):

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The sum of the reciprocals of two numbers a and b can be found by:
1%2Fa+%2B+1%2Fb+=+%28a%2Bb%29%2F%28a%2Ab%29

In other words, the sum (32) over the product (96).
32%2F96+=+1%2F3

Exponential-and-logarithmic-functions/545107: how do we solve log8=logx+log(2x)
1 solutions

Answer 355475 by Earlsdon(6294) on 2011-12-10 21:01:34 (Show Source):

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Solve for x:
Log%288%29+=+Log%28x%29%2BLog%282x%29

Apply the "Product rule" to the right side:
Log%5Bb%5D%28M%29%2BLog%5Bb%5D%28N%29+=+Log%5Bb%5D%28M%2AN%29

then

Divide by 2.
4+=+x%5E2

Take the square root.
2+=+x

Quadratic_Equations/544882: write a quadratic function in standard form for the given set of zeros: -5 and 4.
1 solutions

Answer 355358 by Earlsdon(6294) on 2011-12-10 10:32:10 (Show Source):

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The zeros are given as:
x+=+-5

and

so the factors will be:
x%2B5+=+0

and

Multiply these factors to get the original quadratic equation:
%28x%2B5%29%28x-4%29+=+0

Geometry_Word_Problems/544405: If a square has an area of a 100 and theres a circle inside of it, how is the circle's area 80
1 solutions

Answer 355078 by Earlsdon(6294) on 2011-12-08 21:14:52 (Show Source):

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It isn't, exactly!
If the square has an area of 100, then the side of the square must be 10 (A = 10*10 = 100).
The inscribed circle must have a radius equal to half the length of the side of the square (10/2 = 5
The area of a circle whose radius is 5 is:
A+=+%28pi%29r%5E2

Approximately.

Geometry_Word_Problems/544358: if you have a 3 cup container and a 5 cup container ,how can you measure exactly 1 cup?
1 solutions

Answer 355072 by Earlsdon(6294) on 2011-12-08 21:06:26 (Show Source):

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Fill the 3-cup container and empty it into the (empty) 5-cup container.
The 5-cup container now holds 3 cups.
Fill the 3-cup container again and pour enough from the 3-cup container into the 5-cup container to exactly fill the 5-cup container.
You will have poured 2 cups from the full 3-cup container to leave exactly 1 cup.

Quadratic_Equations/543688: Solve this problem by completing the square show your work: 3x^2 - 12x + 11 = 0
This is what I have done:
3(x^2 - 4x + 4) = -11
3(x^2 - 4x + 4) = -11 + 12
3(x^2 - 4x + 4) = 1
(x^2 - 4x + 4) = 1/3
(x - 2)^2 = 1/3
(x - 2) = (1/3)^1/2
x = 2 +- (1/3)^1/2
But the answer in the back oh my book reads x = 2 +- (square root of 3) / 3
1 solutions

Answer 354903 by Earlsdon(6294) on 2011-12-07 20:27:57 (Show Source):

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You have the correct answer but it needs one more step to simplify it further"
x+=+2%2B-sqrt%281%2F3%29

Simplify.

Rationalize the denominator by multiplying the second term by sqrt%283%29%2Fsqrt%283%29

Quadratic_Equations/542571: Solve the equation by making an appropriate substitution.
x-512-16sqrtx=0
here is what I have tried:
x^1-16x^1/2-512
(x^1/2)^2-16^1/2-512
subsitute x for u
u^2-16u-512
factor (I cannot find a factor for this problem so I divide everything by 2)
u^2-8u-256
using the formula
8 +-sqrt8^2-4(1)(256)/2(1)
8 +-sqrrt1088 / 2
reduced
4+12sqrrt17, 4-12sqrrt17
my answer choices are
{768}
{2068}
{1024}
{512}

1 solutions

Answer 354636 by Earlsdon(6294) on 2011-12-06 12:52:10 (Show Source):

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You're ok up the point of substituting u+=+x%5E%281%2F2%29

This wil factor:
%28u%2B16%29%28u-32%29+=+0

Apply the zero product rule.
u%2B16+=+0

so...

Substitute u+=+sqrt%28x%29

Square both sides in each case.
highlight%28x+=+256%29

You should check these solutions because, in squaring, you may have inadvertently introduced invalid solutions.
x-512-16sqrt%28x%29+=+0

Substitute x+=+256

Surface-area/542542: In a triangle whose area is 72in. sq., the base has a length of 8in. Find the length of the corresponding altitude.
1 solutions

Answer 354634 by Earlsdon(6294) on 2011-12-06 12:28:12 (Show Source):

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You could start with:
A+=+%281%2F2%29bh

The area of a triangle where b = base (8) and h = height (altitude).
72+=+%281%2F2%29%2A8%2Ah

Divide by 4.
18+=+h

The altitude is 18 inches.

Exponents/542566: Instructions simply say to simplify (8+5)^0. I think the answer is 1 but not sure. Can someone please help and show me how these are done?
1 solutions

Answer 354632 by Earlsdon(6294) on 2011-12-06 12:18:47 (Show Source):

You can put this solution on YOUR website!
Anything to the zeroth power is one!
%288%2B5%29%5E0+=+13%5E0+

Quadratic-relations-and-conic-sections/542528: I have to find the vertex, axis of symmetry, minimum or maximum value, and range of the parabola. the formula is y=ax^2+bx+c
Question: y=2x^2-6x+3
What i have so far:
y=2x^2-6x+3
-b/2a=-(-6)/2(2)=6/4=3/2
y=2(3/2)^2-6(3/2)+3
2(9/4)-(-18)/2
I am stuck, I'm not sure if im doing it right but if you could help explain it to me that would be awsome! thank you!
1 solutions

Answer 354630 by Earlsdon(6294) on 2011-12-06 12:07:35 (Show Source):

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y+=+2x%5E2-6x%2B3

You have correctly found the x-coordinate of the vertex:
x+=+3%2F2

and you have made a start on finding the corresponding y-coordinate by substituting x+=+3%2F2

into the given quadratic equation to solve for y.
y+=+2%283%2F2%29%5E2-6%283%2F2%29%2B3

Simplify.

The coordinates of the vertex are: (3/2, -3/2)
The vertex is a minimum (the parabola opens upward) which is indicated by the positive coefficient of the x%5E2

term.
The axis of symmetry is give by x+=+3%2F2

which is the equation of the vertical line passing through the point (3/2, -3/2). (the vertex.)
The range consists of all of the valid y-values.
Since the y=coordinate of the vertex (a minimum) is y+=+-3%2F2

it is clear that the range is -3%2F2

and above.
So the range can be written as:
y%3E=-3%2F2

You can see this from the graph:
graph%28400%2C400%2C-5%2C5%2C-3%2C10%2C2x%5E2-6x%2B3%29

Exponential-and-logarithmic-functions/542546: I need help on how to solve this and how to solve this with a calculator. Can someone please help me?
2.0e^(-1.5x)=1
1 solutions

Answer 354626 by Earlsdon(6294) on 2011-12-06 11:40:37 (Show Source):

You can put this solution on YOUR website!
Solve for x:
2.0e%5E%28-1.5x%29+=+1

First, divide both sides by 2.
e%5E%28-1.5x%29+=+1%2F2

Substitute 1%2F2+=+0.5

Now take the natural logarithm of both sides.
ln%28e%5E%28-1.5x%29%29+=+ln%280.5%29

Apply the "power rule" to the left side.
-1.5xln%28e%29+=+ln%280.5%29

Substitute ln%28e%29+=+1

Divide both sides by -1.5
x+=+ln%280.5%29%2F-1.5

Evaluate.

Approx.

Miscellaneous_Word_Problems/542054: My daughter got the following word problem for homework, but neither of us can recall how to solve this sort of problem:
Ben sold some tickets for a basketball game. Adult tickets were $5 and student tickets were $3. Ben collected $180 for the 50 tickets he sold. How many adult and child tickets did he sell?
If you could point us in the right direction, I would greatly appreciate it!
1 solutions

Answer 354407 by Earlsdon(6294) on 2011-12-05 17:39:00 (Show Source):

You can put this solution on YOUR website!
Start by letting A = the number of adult tickets and S = the number of student tickets.
The adult tickets cost $5.00 each so the total collected from the adult ticket sales is: $5.00(A) and, similarly, the total amount collected from the student ticket sales is $3.00(S) and the sum of these two amounts is given as $180.00
Also, the total number of tickets sold was 50 so A+S = 50.
Now you can write the necessary equations to answer the question posed by the problem.
$5*A+$3*S = $180 and...
A+S = 50 Rewrite this as S = 50-A and substitute into the first equation.
$5*A+$3*(50-A) = $180 Simplify.
5A+150-3A = 180 Combine the A's
2A+150 = 180 Subtract 150 from both sides.
2A = 30 Divide both sides by 2.
A = 15 This is the number of adult tickets sold.
S = 50-A
S = 50-15
S = 35 This is the number of student tickets sold.

logarithm/541556: writing an expression as a single logarithm 5%28ln+x+%2B+ln+7%29+-+3%28ln+x%2B+ln+5%29

1 solutions

Answer 354220 by Earlsdon(6294) on 2011-12-04 21:12:16 (Show Source):

You can put this solution on YOUR website!
5%2A%28lnx%2Bln7%29-3%2A%28lnx%2Bln5%29

Apply the distributive property to both terms.
%285%2Alnx%2B5%2Aln7%29-%283%2Alnx%2B3%2Aln5%29

Now apply the "power rule" for logarithms.
%28lnx%5E5%2Bln7%5E5%29-%28lnx%5E3%2Bln5%5E3%29

Now apply the "product rule".
ln%28x%5E5%2A7%5E5%29-ln%28x%5E3%2A5%5E3%29

Simplify using: 7%5E5+=+16807

and

Now apply the "quotient rule".
ln%2816807x%5E5%2F125x%5E3%29

Simplify.

Miscellaneous_Word_Problems/541593: A rectangular piece of metal is 10cm longer than it is wide. Squares with sides of 2cm long are cut from the four corners of the piece of metal, and the flaps are folded upward to form an open box. If the volume of the box is 832cm cubed, what were the demensions of the original piece of metal? (V=LWH)
1 solutions

Answer 354217 by Earlsdon(6294) on 2011-12-04 20:49:42 (Show Source):

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The dimensions of the box, in terms of W, the width would be:
V+=+L%2AW%2Ah

Substitute: L = W+10, h = 2, and V = 832.
832+=+%28W%2B10-4%29%28W-4%29%2A2

Simplify.

Divide both sides by 2.
416+=+W%5E2%2B2W-24

Subtract 416 from both sides.
W%5E2%2B2W-440+=+0

Factor.

Apply the "zero product rule".
W-20+=+0

so...

Discard the negative solution as the width, W, is a positive quantity.
W+=+20

cm. and...
L+=+W%2B10

cm.

Quadratic_Equations/541523: find all solutions by factoring: 4t^6-t^4=0
1 solutions

Answer 354200 by Earlsdon(6294) on 2011-12-04 18:56:08 (Show Source):

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Find all solutions: (You should expect to get 6 solutions, some of which might be identical)
4t%5E6-t%5E4+=+0

Factor out t%5E4

Apply the "zero product rule".
t%5E4+=+0

then

and

is a solution four times.
4t%5E2-1+=+0

Factor this.
%282t%2B1%29%282t-1%29+=+0

Apply the "zero product rule"'
2t%2B1+=+0

so...

and

and

The six solutions (four of which are identical) are:
t+=+0

To give some idea of the graphical soltions:
graph%28400%2C400%2C-3%2C3%2C-5%2C5%2C4x%5E6-x%5E4%29

Money_Word_Problems/541499: Rowan invested a certain amount of money at 5% per year and an amount thrice as large at 8% per year. The total annual income from the two investment was 17,400 Php. Find the amount invested at each rate.
1 solutions

Answer 354195 by Earlsdon(6294) on 2011-12-04 18:40:30 (Show Source):

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Let x = the number of Php invested at 5% per annum and 3x = the amount invested at 8% per annum. The sum of the earnings on these two amounts is given as 17,400 Php. (I don't know what these are but we can still work the problem).
First we write down the expressions for the earnings on each amount. Change the percentages to their decimal equivalents: 5% = 0.05 and 8% = 0.08, then...
0.05x+0.08(3x) = 17,400 Simplify and solve for x.
0.05x+0.24x = 17,400 Combine the x's.
0.29x = 17,400 Divide both sides by 0.29
x = 60,000 Php and 3x = 180,000 Php.
60,000 Php was invested at 5% per annum and 180,000 Php was invested at 8% per annum.

Polynomials-and-rational-expressions/541506: (5x-1)^2
I know the answer is 25x^2-10x+1
But when I try to solve I only come up with 25x^2+1
I don't understand where the -10x comes from,
I appreciate any help,
thank you!!
1 solutions

Answer 354193 by Earlsdon(6294) on 2011-12-04 18:26:19 (Show Source):

You can put this solution on YOUR website!
Use the FOIL method to multiply the binomials:
%285x-1%29%285x-1%29+=+25x%5E2-5x-5x%2B1

Simplify to:
25x%5E2-10x%2B1

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