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Hello,
Since we know the formula is S=2 pi rh+2 pi r2 all we need to do is plug in the values we know to get:
S=2 pi 2.5(8)+ 2 pi 2.5^2 Do the calculation and we get:
S=40 pi + 12.5 pi Combine to get:
S=52.5 pi square cm We could plug in 3.14 for pi to get:
164.9 sq cm (rounded to the nearest tenth)
Make Sense?
RJ Check out a book I wrote on the basics of math:
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Hello,
First let's factor this out (x^2-4x+4) to get:
(x-2)(x-2)=0 Now we know the sides are x-2 so we do this to find the perimeter:
(x-2)+ (x-2) + (x-2) + (x-2)
This will give us:
4x-8 as the perimeter.
RJ www.math-unlock.com

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Hello,
The equation we need to use is:
Distance=7t^2 Plug in 8 for t and we get:
Distance=7(64) Multiplied out to get:
D = 448 feet
RJ
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Hello,
In the following W^2/11w^2-11w - 1/11w-11 we can combine like terms to look like:
W^2/11w^2-122/11(w)-11 The w^2 will cancel out to be:
1/11-122/11(w)-11 Then combine like terms to get:
-122/11(w)-120/11
Make sense?
RJ
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Hello,
Understanding the log is sometimes tough for students. This (Log81^9) is read as:
81 to what exponent will give you 9?
The exponent will be 1/2 and be like this:
81^(1/2)=9 Or you can write it like this:
Square root of 81 = 9
Make sense?
RJ
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Hello,
We can set up 2 equation like this: (Let x be Ricky and y be Roberta)
y=3x
y+5=2(x+5) Solve by substitution:
3x+5=2x+10 Subtract 2x and 5 from both sides to get:
x=5
There we go Ricky is now 5 years old. I'll let you figure out the age of Roberta.
Make sense?
RJ
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Hello,
Let's first rewrite this 2x + 6 / 2x squared + 14x + 24 as:
2x + 6 / 2x^2 + 14x + 24 Both top and bottom and be factored as:
2(x+3)/2(x+3)(x+4) The (x+3) and 2 cancel out to leave us:
1/(x+4)
Make Sense?
RJ
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Hello,
Let "x" represent an even integer. "x+4" will show the largest. Now we can set up an equation to be:
2x=(x+4) Subtract x from both sides to get:
x=4
So the integers are 4,6,8
There we go. Make sense?
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Hello,
First off we can rewrite this as:
(sqrt 64 sqrt x^5) / (sqrt 121 sqrt x^7) Then we can get:
8 sqrt x^5/ 11 sqrt x^7 We can now rewrite this as:
8(x^5/2)/11 (x^7/2) Now bring this denominator up with the numerator:
8 (x^5/2)(x^-7/2)/11 This will result in:
8 (x^-2/2)/11 Now we can rewrite it as:
8/11x
Make sense?
RJ
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Hello,
Moving a negative exponent from numerator to denominator or the other way removes the negative to positive. So in this a^-3(a^3b^4)^-5 divided by b^-3 we get:
b^3/a^3(a^3b^4)^5
There we go, all positive.
Make sense?
RJ
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Hello,
WE can set up a proportion as follows:
4200/60=840/x (Hint: convert hour to minutes)
Cross multiply to get:
4200x=50400 Divide both sides by 4200 to get:
x=12 minutes
Make sense?
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Hello,
The key to adding or subtracting fractions is having the same denominator.
This -5/8-6/-5 we'll set up the denominator to be 40 so it will look like this:
-25/40+48/40 will give us: (hint: 2 negatives gives us a positive)
23/40
Make sense?
RJ
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Hello,
This 25(x-4)+3x=77-2(x-3) can be expanded out to:
25x-100+3x=77-2x+6 Now combine like terms and add 100 to both sides to get:
28x=-2x+183 Add 2x from both sides and divide by 30 to get:
x=183/30 or 6.1
Check the answer in the original to see if it comes out OK.
RJ
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Hello,
Let the width be x and the length will be 2x+8. Now the equation can be:
x+x+2x+8+2X+8=70 Are you with me so far?
Combine terms to get and subtract 16 from both sides:
6x=54 Divide 6 into both sides to get:
x=9 feet There's the width---I'll let you figure out the length.
RJ
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Hello,
There are 2 possible answers, depending on how the 30-60-90 triangle is set in the parallelogram.
Since we know the area is equal to base times height, the height is found by the 30-60-90 formula. It's either 10 cm or 10 sqrt3 cm
So if the height is 10 the area would be:
300 sq cm or
300 sqrt3
RJ
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Hello,
Let's write this (1/x is greater than or equal to 4x) as:
1/x >= 4x Multiply by x on both sides to get:
1>=4x^2 Divide by 4 and then square root both sides to get:
+-1/2>=x
There we go.
Make sense?
RJ Check out a book at:
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Hello,
Let's have "x" be the width and "2x+3" represent the length so we can set up the following equation:
x+x+2x+3+2x+3=114 Combine like terms to get:
6x+6=114 Subtract 6 divide by 6 both sides to get:
x=18 feet
I'll let you figure out the length.
Make sense?
RJ I wrote a book you should check out:
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Hello,
I'll help you out with the first one (Log base 5 (r+2) + log base 5 (r-2) = 1)
This can be rewritten as:
Log base 5 (r+2)(r-2) = 1
Now let's exponentiate both sides by using base 5 to get:
5^log5(r+2)(r-2)=5^1 This can then be written as:
(r+2)(r-2)=5 Expand this out to get:
r^2-4=5 Add 4 to both sides to get:
r^2=9 Square root both sides will result in:
r=+-3
Make sense?
RJ
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Hello,
This / can be written as follows:
{(5x^2+21x+4)/(x^2-16)} multiplied by {(x-2)/(5x+1)} The first fraction can be rewritten as:
{(5x+1)(x+4)/(x-4)(x+4)}times{(x-2)/(5x+1)} Notice the (5x+1) and the (x+4)cancels out to leave us with:
(x-2)/(x-4)
Make sense?
RJ
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This makes no sense. Did you forget part of the problem?
RJ

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Hello,
What we need to do is find a negative number that would be multiplied by itself 3 times to get -64. Any idea.
Try -4
RJ
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Hello,
t^2+6t+8=0
We can factor this as:
(t+4)(t=2)=0
Solve for t to get:
t=-4
t=-2
There you go!
Make sense?
RJ
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Hello,
Let's show the numbers as "x" and "x+2" then we can solve this as:
x(x+2)=168 Subtract 168 from both sides to get:
x^2+2x-168=0
Now factor this:
(x-12)(x+14)=0 Now solve x to get:
x=12
x=-14
Obviously the only positive number would be:
12 and the other number is 14
Make sense?
RJ
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Hello,
Let's first off regroup this 2x^3-x^2-18x+9=0 to give us:
x^2(2x-1)-9(2x-1)=0 From this we have (2x-1) being multiplied by x^2 and -9 so we can use the distributive property to rewrite this as:
(x^2-9)(2x-1)=0 We can factor (x^2-9) to get the following:
(x-3)(x+3)(2x-1)=0 Are you with me so far?
Now we can solve for x to get:
x=3
x=-3
x=1/2
Of course, to check if these are correct, just plug them into the original equation.
Make sense?
RJ
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Hello,
Let's have "x" be the time involved so the equation would be:
2/3(x)+12>113/3 Multiply both sides by 3 to get:
2x+36>113 Subtract 36 from both sides to get:
2x>77 Divide by 2 to get:
x>38.5 weeks
Make sense?
RJ
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Hello,
We can set up a proportion as follows: (hint: we need to have both be the same measurements, either feet or inches)
8/2=144/x Cross multiply to get:
x=36 pounds
Make sense?
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Hello,
We can set up 2 equations and solve it from there. Let "x" be adults and "y" represent children.
x+y=400
6x+4.5y=2100
Multiply the first equation by -6 and add it to the second equation:
-6x-6y=-2400
6x+4.5y=2100
This will give us:
-1.5y=-300 Divide each side by -1.5 to get:
y=200 children tickets. Now plug this into the first equation to find x:
x=200 adult tickets
Make sense?
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Hello,
The formula is nPr=n!/(n-r)!
So it would look like this:
15!/(15-3)! This expands out to:
(15x14x13x12x11x10x9x8x7x6x5x4x3x2x1)/(12x11x10x9x8x7x6x5x4x3x2x1)
I'll let you do the calculations from here.
Make sense?
RJ
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Hello,
With this 3x/4-3=x/2+2 let's first get rid of the fractions by multiplying both sides by 4 to get:
3x-12=2x+8 Now we can add 12 and subtract 2x from both sides to get:
x=20
Make sense?
RJ
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Hello,
Yes, you got the right idea but missed an important value. Let's do step by step so it's clear.
We know the area of a triangle is 1/2(base x height) so we can plug in the values known as:
28=x(x)(1/2) Or rewritten as:
28=x^2/2 Multiply each side by 2 to get:
56=x^2 Square root each side to get:
x=sqrt 56 Or
x=7.48 inches (rounded off)
RJ
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Hello,
You better ask what you want done with these two points. Slope? Equation?
RJ