Press = (or the Enter key) twice.  The second time you will get the result displayed in scientific notation.

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A couple more:

If two adjacent sides of a rectangle are (5x2 + 25xy + 4y2) and (2x2 – 2xy + 3y2), find its area

Area of a rectangle is just the product of its adjacent sides:

Area = (5x² + 25xy + 4y²)(2x² - 2xy + 3y²)

=  5x² *(2x² - 2xy + 3y²) + 25xy*(2x² - 2xy + 3y²) + 4y²*(2x² - 2xy + 3y²)

= 10x⁴ - 10x³y +15x²y²   +  50x³y -50 x²y² +75xy³   + 8x²y² - 8 xy³ + 12y⁴

I'll leave you to simplify this by collecting like terms together.

A two digit number is three times the sum of its digits. If 45 is added to the number; its digits are reversed. Find the number

 A two digit number can be represented as 10a + b  where a and b are single digits (a>0).

So:  10a + b = 3(a + b)         ...(1)

       10a + b + 45 = 10b + a  ...(2)

 From (1):  10a + b = 3a + 3b  or  7a - 2b = 0      ...(3)

From (2):    9a  - 9b = -45       or     a - b = -5       ...(4)

From (4) we have a = b - 5  ...(5) 

Use (5) in (3): 7(b-5) - 2b = 0  or 7b - 35 - 2b = 0 or 5b = 35  so b = 7.

Put this back into (5): a = 7 - 5  or a = 2.

So the original 2-digit number was 27

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8.2                 

I am sorry Alan but I am still really struggling with this 

I wind up my clock, and as I walk out my door the clock reads 12:00

I know it is slow so the real time is 12:00   +   X minutes

I walk to my friends place  I don't know how long I take but I will call it T minutes

When I arrive his clock reads  12:40         

So

X+T=40 minutes

x=40 minutes - T

I chat for 10 minutes and then return home

I have been away from home for   T+T+10  and my clock tells me that this adds up to 70 minutes

So

2T+10=70

2T=60

T=30 minutes.

I know that  X=40-T  so X=10.   The clock is 10 minutes slow!

WOW I worked it out - Now i just have to work out what you did in your answer  

Yeah....😶

That actually is true...😶

1 score=20

60 

You can also "create" an own fraction.

For example, if you want to find the fraction to 0.121212121212...

Call 0,121212121212... for x

100x=12,1212121212...

100x-x=12

99x=12

x=12/99

Hope you can use this!

Well, for girls, it's actually easier, so if you're a girl, you're in luck. It's been scientifically proven that girls are better at math (and pretty much everything else) than boys.

Spider:   1 head  8 legs

Beetle:   1 head  6 legs

Larva:    1 head  0 legs (?)

S + B + L = 17  ...(1)

S + B > L          ...(2)

8S + 6B = 58    ...(3)

Solving (1) and (3) for S and B we get

S = 3L - 22   ...(4)

B = 39 - 4L   ...(5)

From (4) we see that L must be greater than 7 or S will be negative.

Try L = 8

S = 2,   B = 7    and S + B = 9 which is greater than L consistent with (2)

Try L = 9

S = 5, B = 3   and S + B = 8 which is less than L so not consistent with (2)

L must be less than 10 or B will be negative

Therefore there must be 2 spiders (and 7 beetles and 8 larvae).

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If you have x^a for example then a is the exponent.  For 2^3, 3 is the exponent, for 10^-4, -4 is the exponent etc.

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12/99

$${\frac{{\mathtt{12}}}{{\mathtt{99}}}} = {\frac{{\mathtt{4}}}{{\mathtt{33}}}} = {\mathtt{0.121\: \!212\: \!121\: \!212\: \!121\: \!2}}$$......

13/99

$${\frac{{\mathtt{13}}}{{\mathtt{99}}}} = {\mathtt{0.131\: \!313\: \!131\: \!313\: \!131\: \!3}}$$.....

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Here are a few to be going on with:

(a) (i) Distribute the 2 over the other terms (i.e. just multiply the terms in brackets by 2): 2a + 4b - 6c

(ii) Doesn't show clearly in my browser.

(b) Just use the calculator.

(c) Factors of 24: A = {1, 2, 3, 4, 6, 8, 12, 24}   

     Factors of 30: B = {1, 2, 3, 5, 6, 10, 15, 30} 

    A ∪ B means the union of A and B:  A ∪ B = {1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 24, 30}

    A ∩ B means the intersection of A and B (i.e. the items that are common to both): A ∩ B = {1, 2, 3, 6}

    A - B means the items that are left when you take away from A any items that are also in B: A - B = {4, 8, 12, 24}

   I assume n(A) means the number of items in A:

    n(A) = 8,   n(B) = 8,  n(A ∪ B) = 12, n(A ∩ B) = 4, n(A - B) = 4

    n(A) - n(A ∩ B) = 8 - 4 = 4 = n(A - B)

    n(A ∪ B) - n(B) = 12 - 8 = 4 = n(A - B)

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Yeah it depends --> Sqrt(1.7) = ±1.3

Works for the negative version: -1.3 + 3 = 1.7

Falls apart for the positive version: 1.3 + 3 =4.3

You can always choose to take the negative version of the squareroot thats why I think x=1.70 is a suitable answer.

Maybe hard to learn, but definitely one of the easiest subjects once you have managed to learn it!

is right, but consider that 1.70 is a false root.

sqrt(1.70)=1.30

1.70-1.30<3.0

Equation is: sqrt(x) = x - 3

--> x = x^2 -6x + 9

--> 0 = x^2 -7x + 9

Use quadratic formula where a=1 , b=-7, c=9 :

x = (7±sqrt(49-4(1)(9)) / 2 = (7±sqrt(13)) / 2

x = 1.70 or x = 5.30

Just substitute in the values for x and y then you have an equation for a:

           8 - a = sqrt(-2(-8+a))

a^2 -16a+64=-2(a-8)

a^2 -14a+48=0

     (a-6)(a-8)=0 Therefore a = 6 or a = 8

what is the fraction of 6 over 1000

       It's   3/500

If three points of a parallelogram are located at (1,0), (4,3), and (5,-2) what is the fourth coordinate ?

$$\small{\text{$
\begin{array}{rclclclcl}
\vec{P_1}=\begin{pmatrix} 1 \\ 0 \end{pmatrix} \qquad
\vec{P_2}=\begin{pmatrix} 4 \\ 3 \end{pmatrix} \qquad
\vec{P_3}=\begin{pmatrix} 5 \\ -2 \end{pmatrix} \\\\\\
\vec{P_4}&=& &-&\vec{P_1} &+& \vec{P_2} &+& \vec{P_3}
=\begin{pmatrix} -1+4+5 \\ 0+3-2 \end{pmatrix} = \begin{pmatrix} 8 \\ 1 \end{pmatrix}\\\\
\vec{P_4}&=& &&\vec{P_1} &-& \vec{P_2} &+& \vec{P_3}
=\begin{pmatrix} 1-4+5 \\ 0-3-2 \end{pmatrix} = \begin{pmatrix} 2 \\ -5 \end{pmatrix}\\\\
\vec{P_4}&=& &&\vec{P_1} &+& \vec{P_2} &-& \vec{P_3}
=\begin{pmatrix} 1+4-5 \\ 0+3+2 \end{pmatrix} = \begin{pmatrix} 0 \\ 5 \end{pmatrix}\\\\
\end{array}
$}}$$

Thank you :)

Now I have to go school to learn some more maths!!! :D

Bye Melody :)

Thanks Civonamzuk,

Your presentation was brilliant, you just made a little mistake somewhere - it is no big deal :)

Thank you Heureka  

In the figure below, AB = AC = 50, AD = 52, and bc = 28. Determine cd.

I. Herons Formula: Area A (ABC):

$$\small{\text{$
\begin{array}{l|l}
A=\sqrt{s\cdot (s-a)\cdot(s-b)\cdot (s-c)} & \qquad \overline{AB} = a=50, ~ \overline{AC} = b=50,~ \overline{AD} =c=28\\\\
& \qquad s = \frac{a+b+c}{2}=\frac{50+50+28}{2}=\frac{128}{2}=64 \\
A=\sqrt{s\cdot (s-50)\cdot(s-50)\cdot (s-28)} \\
A= \sqrt{64\cdot (64-50)\cdot(64-50)\cdot (64-28)} \\
A= \sqrt{64\cdot 14 \cdot 14 \cdot 36} \\
A= \sqrt{8^2\cdot 14^2 \cdot 6^2} \\
A= 8\cdot 14 \cdot 6 \\
A=672
\end{array}
$}}$$$$$$

II: Height h of (ABC):

$$\small{\text{$
\begin{array}{rcl}
c\cdot h &=& 2\cdot A\\\\
h&=& \dfrac{2\cdot A}{c} \\\\
h&=& \dfrac{2\cdot 672}{28}\\\\
h &= &48
\end{array}
$}}$$

III. Pythagoras:

$$\small{\text{$
x = \overline{CD}
$}}\\\\
\small{\text{$
\begin{array}{rcl}
h^2 + \left( \dfrac{c}{2}+x \right) ^2 &=& 52^2 \\\\
48^2 + \left( 14 +x \right) ^2 &=& 52^2 \\\\
\left( 14 +x \right) ^2 &=& 52^2 - 48^2\\\\
\left( 14 +x \right) ^2 &=& 20^2\\\\
14 +x &=& 20\\\\
x &=& 20-14\\\\
x &=& 6
\end{array}
$}}$$

CD = 6