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As long as "a" is not equal to 0....notice that:   a⁰  =  a^n-n = aⁿ / aⁿ  =  1

So....3⁰  = 3^{n - n}  =   3ⁿ / 3ⁿ  =  1

8 x 10⁷

\(\dfrac{-20}{10}\\=-2\)

Slope intercept form is the form of y = mx + b.

e.g.: y = 3x + 2 is in slope-intercept form.

2y = 3/2 x + 5 is not in slope-intercept form.

y = 3/4 x + 5/2 is the slope-intercept form for 2y = 3/2 x + 5.

\(80:x=5\times a\\ x:80 = 1:5a\\ x = 80:5a = 16:a\\ a = 16:x\)

He still has 6 apples!! 

15 x 9

= 10 x 9 + 5 x 9

= 90 + 45

= 135.

I learn maths like this.

7sqrt2 = sqrt(2 x 7^2) = sqrt(98) which is very close to 10. :)

You make things all go to one side and x go to another side to make the subject x.

Example:

Make a the subject.

 \(ax = \dfrac{ab -1 }{2}\\ 2ax = ab - 1\\ 2ax - ab = -1\\ a(2x - b) = -1\\ a =\dfrac{-1}{2x -b}\\ \;\;=\dfrac{1}{b-2x}\)

Good quote Guest, but it should be math related.

\(S = {aP}\)

The level of slippery of the snail will increase when the rain amount increase!! :P So is that snail dangerous walking on the leaf?

-10 + 7x + 24 - 2

= 7x + 24 - 2 - 10

= 7x + 24 - 12

= 7x + 12

Same answer as higgsb

You typed\(\theta1 = 63 \\\theta2 = 38 \\Mass = 25 KG\\ \epsilon Fx = cos 63 (T{}_{}2)- cos 38 (T1) = 0 \\\epsilon Fy = sin 63 (T{}_{}2)- sin 38 (T1) =\)

You didn't finish typing!!

By the way use \\ command to seperate lines.

e.g.: 2 + 2 \\ = 4 will appear as \(2+2\\=4\)

22 , 44, 66, 88, 110. :)

2x + xy = xz + 3

2x + xy - xz = 3

x (2 + y - z) = 3

x = 3/(2 + y - z) 

Same answer as Guest #1

1/x + 1/2 = y

1/x = y - 1/2 = (2y-1)/2

x = 2/(2y - 1)

Guest #1 did not simplify that fraction.......

\(2|270\\ 5|135\\ 3|27\\ 3|9\\ 3|3\\ \;\;\;1\)

That is a short division hope you understand :)

Therefore 270 = \(2\times3^3\times 5\)

Visual representation:

\(\dfrac{86}{\not{\!\!97}}\times \not{\!\!97}\\ =86\)

1)

\(7=-\dfrac{3}{4x}\\ 28x = -3\\ x = -\dfrac{3}{28}\)

2)

\(50 = -2 + 13q\\ 13q = 52\\ q = 4\)

3)

\(5-\dfrac{9}{2d}=32\\ \dfrac{9}{2d}=5-32\\ \;\;\quad\!=-27\\ 2d = -\dfrac{9}{27}\\ \;\;\;\;\!\;\!=-\dfrac{1}{3}\\ d = -\dfrac{1}{6}\)

4)\(\dfrac{7a+1}{2}=18\\ 7a + 1 = 36\\ 7a = 35\\ a = 5\)

Since the tall building is 35 feet tall and the shorter building is 25 feet tall, then the difference between the roof of the shorter building to the roof of the taller building is:

35 - 25 =10 feet, which is the opposite side of a right-angle triangle.

Since they are 20 feet apart, that is the adjacent side of the triangle. Then by Pythagoras's theorem we have: Ladder(hypotenuse)^2 =10^2 + 20^2, so the ladder will be:

L^2 =100 + 400=500

L =sqrt(500)=22.36 feet - Length of the ladder.

3b + 4 = 24

3b = 20

b = 20/3 OR b = 6 2/3 it's equivalent.

5y + 4 - 2y = 9

3y + 4 = 9

3y = 5

y = 5/3 OR y = 1 2/3 it's equivalent.

OOOHHH NOOOOO AAARRRGGGHHHH NEEEE-NAAAAAWWW-NEEEEEE-NAW CRASH BANG KABOOM SMASH

ok, lets be serious now.

the question is 156/18=x which equals 8 ^r 12 so u each have 8 berries there are 12 left over.

Hi Anon,

\(\pi \times \text{the reciprocal of }\dfrac{2}{3} + 9.089\\ =\dfrac{3\pi}{2}+\dfrac{9089}{1000}\\ =\dfrac{1500\pi + 9089}{1000}\)

2 - 8/(-2) -2 - (-12)/(-6) x (-2)

= 2 - (-4) - 2 - 2 x (-2)

= 2 + 4 - 2 - (-4)

= 2 + 4 - 2 + 4

= 6 - 2 + 4

= 4 + 4 

= 8.

\(\left(-16-(-2+1)\right)\times\dfrac{2}{5}\\ =\dfrac{2(-16-(-1))}{5}\\ =\dfrac{2(-15)}{5}\\ =\dfrac{-30}{5}\\ =-6\)

\((\dfrac{b^{-2}}{b^{-3}})^2\\ =(\dfrac{b^3}{b^2})^2\\ =\dfrac{b^6}{b^4}\\ =b^2\)

That's about Pythagoras' theorem OR Pythagorean theorem.

Difference between the heights of the buildings = 35 - 25 = 10m

\(10^2 + 20^2 = (\text{length of ladder})^2\\ \text{length of ladder} = \sqrt{100+400} = \sqrt{500}=10\sqrt5\text{ m}\)

Length of ladder should be at least 10sqrt(5) meters.