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Volume = x^3

Area = 6x^2

Final area = 2(6x^2) - 2x^2 = 10x^2

There's a curious pattern... see if you can find it. 

Hint: 11 *  b+8 = ?

11 * 16 = 176

There are many ways to fill the license plate in. To demonstrate it, we create a template:

_ _ _ _ _ _ = 26 * 26 * 26 * 10 * 10 * 10

There are $26^3$ ways to choose the letters and $10^3$ ways to choose the numbers. Thus, the number of license plates are $26^3 \cdot 10^3= 17576000.$

Surface area of a sphere  $ = 4 \pi r$

Volume = $\frac{4}{3} \pi r$

Because they are three digits and whole, we know that r is divisible by 3. In other words, $r=3n$ where n is all integers.

Looking at the three digit part, we have $r = 300x+30y+3z,$ where x, y, and z are integer digits 0-9. 

It is impossible to determine a unique value for r and thus the question needs more information.

1   that has an odd number

2=2*1 that has 2 that is no good

In fact, all prime numbers have 2 so none of those match the criterior

4  has 1,2, and 4    That has an odd number

6 is no good either,    1*6,2*3

So at least one of the factors must be a squared number.

Think about that!

That is incorrect :(

In triangle ABC, AB=5, AC=6, and BC=9. Circles are drawn with centers A, B, and C so that any two circles are externally tangent. Find the sum of the areas of the circles.

This problem is a common example of clever manipulations. 

The question: $$\frac{1}{a} + \frac{1}{b} \cdot (a-b) = 1 \text{ and } a \cdot b = 5. \text { What is } a^2 + b^2 ? $$

The solution: 

This can be simplified to $(a^2-b^2) = ab$, but we know that $ab=5,$ so $a^2-b^2=5.$ We now know that by substitution, $$a^2+b^2=2a^2+5.$$ 

Be careful asinus, I think you made a mistake!

$a^2+b^2=5\sqrt{5}!$

Horse has 3/4 of  circle of radius 15m

  and has two quarter (a half circle) cirlces of radius 5

area of a full cirlce = pi r²

Put in '2' for x in the f(x) function = 9

   put '9' in the g(x) function  = 0

     put 0 in the f(x) function = 5       = h(2)

Suppose [(1/a)+(1/b)] * (a-b) equals to 1. And a*b=5. What is a^2+b^2?

Hello Guest!

\(\color{BrickRed} (\frac{1}{a}+\frac{1}{b})(a-b)=1\\ \frac{a}{a}-\frac{b}{a}+\frac{a}{b}-\frac{b}{b}=1\\ \color{blue}\frac{a}{b}-\frac{b}{a}=1\)

\(a\cdot b=5\)

\(b=\frac{5}{a}\)

\(\frac{2a}{5}-\frac{5}{a^2}=1\\ \frac{2a^3-25}{a^2}=1\\ 2a^3-25=a^2 \)

\(2a^3-a^2-25=0\)

\(a=2.5\\ b=2\\ a^2+b^2=10.25\)

  !

First, we evaluate the result of the equations without k. We get:

$$y = 6 x - 12, z = 22/3 - (7 x)/3$$

$$ x = 1/7 (22 - 3 z)$$

For $kx+z=3$ to agree with these equations, we need to solve for k.

Solving for k in terms of z, $$ k = \frac{ 7 (z - 3)}{3 z - 22}.$$

However, we want $kx+z \ne 3.$ 

See if you can work more on this on your own!

Look for patterns!

$$99 \cdot 99=9801$$

$$ 999 \cdot 999 = 998001$$

When looking at the patterns, we see that the formula for the square a number consisting of $n$ $9's$ is:

Number of 9s in the number = Add $n-1$ 9s

Then add an 8

Number of 0s in the number = Add $n-1$ 0s

Then add a 1.

There are 16 digits in the number $999999999999999999.$ So, $$\boxed{999999999999999999^2 = 999999999999999998000000000000000001}$$

a) PEMDAS gives 23

b) 15/3 = 5

c) 3 by PEMDAS

No matter what the value of "a" is, the GCD of  a + 3 and 2a + 13 is always = 1

Let AF be x

x / 12-x = 18 / 12 

x = ?

17 , 25 , 33 , 41 , 49 , 57 , 65 , 73 , 81 , 89 , 97 , Total =  11 such numbers

First the cow gets to meander about 1/4 of a full circle    radius 120 ft     1/4  pi (120²⁾

  when it gets up just right of 'a'  the rope is now shorter by length 'b'  so   60 ft

       mooster gets 1/4 of a circle   radius 60 ft         1/4 pi (60²⁾

             gets to the left of 'a' rope is shorter again by 'a'       so  30 ft

                   area is 1/4 of a circle radius 30    1/4 pi 30²

When it gets to intersection of d and e the rope gets 70 ft shorter    so   50 ft long

   1/4 of circle radius 50 ft       1/4 pi 50²  

^{TOTAL area is the sum of the REDS above......}

TOTAL cicuference = pi * d     which is  pi * 2 * r

 fraction of the circumference is   5 / (pi * 2 * r)       multiply THIS number by 360^o to get the central angle measure

t convert the central angle measure^o you got in the first part   multiply it  by ( 2pi R) /360^o        ('R' here is radians)

Circumference of wheel/tire in FEET =   2 * r * pi  / 12

now the tire travels 800 of these distances PER MINUTE

   800   *   2  * r*pi  / 12          multiply this by 60 minutes in an hour to get feet per hour

60 * 800* 2*r*pi / 12               divide this number by 5280 feet in a mile to get miles per hour

This is a fraction of the whole earth circumference   (pi * 2 * 3960)

   39 - 15 = 24^o  of the entire 360

24/360   x    (pi * 2 * 3960) = ....... miles apart