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*** Thx :-) ***

[n²(n²)]

The outer paranthesis (brackets) are unnecessary:

 n²(n²)

Remember that:

n^a * n^b = n^{a +b}

So we get:

n²(n²) = n⁴

Your answers are always well presented, Tetration......!!!!!

The percent error is given by....

l Approximate Value - Exact Value l / l Exact Value l  x 100%

So we have

l  175 - 97.50 l / l 97.50 l  x 100%  =

77.50 / 97.50  x 100%  =

about 79.5%

$$\frac{5}{6}*30$$

Let's first look at the general case:

$$\frac{a}{b}*k$$

To calculate this, simply multiply the number (in this case k), with the numerator (top, in this case a), and divide the product with the denominator (bottom, in this case b):

$$\frac{a}{b}*k = \frac{a*k}{b}$$

So in our case, we get:

$$\frac{5}{6}*30 = \frac{5*30}{6}=\frac{150}{6}= 25$$

(-3)³ = (-3)(-3)(-3) = 9(-3) = -27

In general we have that (-X)^k = X^k when k is an even number, and (-X)^k = -(X^k) when k is an odd number. 

4x(x-2)=7     let's put this in standard form

4x^2 - 8x - 7 = 0      now, using a =4, b = -8 and c = -7, we have...

x = ( -b ±√ [b^2 - 4ac] ) / 2a

x =  ( 8 ±√ [64 - 4(4)(-7)] ) / 8

x = (8±√ [176]) / 8

x = [8 ±√(16*11)] / 8

x = [ 8 ± 4√11] / 8      ( divide everything by 4 )

x = [2 ± √11] / 2

Remember that -(-x) = +x = x

-11 - (-11) = -11 + 11 = 0

Well....assuming that the Earth's shrinkage and your shrinkage are proportional, you would be 1/12,472th as tall as you are now.......

I'll leave the details to you.....

An increase of 12% means that the original thing is now worth 1.12 as much as it was

A 25% decrease means that it is now worth only .75 as much as it was.....thus....

This will give you your answer...

3200(1.12)(.75)

Good job, h7.....!!!!

19<5p+4<29         subtract 4 from everything

15 < 5p < 25         divide everything by 5

3 <  p   <  5

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x+5>5 and x+4<3

x+5 >5    subtract  5 to both sides                  x+4<3   subtract 4 from both sides

x  > 0                                                           x < -1

"And"  means  "intersection"......in other words, where do these solutions overlap???

Answer:   they don't

Thus, the solution is  { } ....  i.e., the empty set

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(1/20)<(2-3x/20)<(2/5)  ...first, multiply everything by 20 to clear the fractions

1 < 40 - 3x < 8       subtract 40 from both sides

-39 < -3x < -32      divide everything by -3 and remember to "reverse" the inequality signs

13 > x > 32/3

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3x+5<8 or 9x>41

3x+5<8   subtract 5 from both sides                     9x>41  divide both sides by 9                   

3x  < 3    divide both sides by 3                              x > 41/9 

x  < 1                                                  

 "Or"  means "union"

So, the union of these two answers is  (-∞, 1] U (41/9, ∞)

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-25<5(x-5)<4        divide everything by 5

-5 < x-5 < 4/5       add 5 to everything

0 < x < 29/5

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The sum of two numbers is 52. The greater number is 4 more than the smaller number. What equation can be used to solve for the smaller number?

Let x be the greater number and let x-4  be the smaller number...so we have.....

x + (x-4) = 52      ....if we wanted to solve this, first simplify

2x - 4 = 52              add 4 to both sides

2x = 56                   divide by 2

x = 28     this is the larger number

(x - 4)  =( 28 - 4 ) = 24     and this is the smaller number

I am assuming you want this as a decimal but here it is in Decimal and Fraction. Decimal:0.008 Fraction:1/125

1 lolololol

The square root of 7,022,500 is 2650 :)

Since the largest number that divides evenly into both 24 and 16 is 8, factor out 8y:  8y(3 + 2z)

thanks for helping me!

$${\mathtt{80}}{\mathtt{\,\times\,}}{\mathtt{0.65}} = {\mathtt{52}}$$

$${\mathtt{80}}{\mathtt{\,\times\,}}{\mathtt{0.15}} = {\mathtt{12}}$$

52-12=40

Erin who???????

LOL.....I do miss your 666 picture.......or was it 999????

WHOS THEERE??? (deep voice)