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Combinations (stats and prob)
$(6-2)!=4!$ $4!= 4\times 3 \times 2 \times 1=24$
See lessSimplify the Equation
$y-(x-5)(x+5)=2y-(x+6)(x+6)$ Open up the brackets $y-(x^{2}-25)=2y-(x^{2}+12x+36)$ $y-x^{2}+25=2y-x^{2}-12x-36$ $x^{2}-x^{2}+12x=2y-y-36-25$ $12x=y-61$ $\therefore 12x-y=-61$
Open up the brackets
See lessSolve the equation
$\dfrac{4a}{12}+\dfrac{6a}{18}=\dfrac{12a}{24}-\dfrac{16a}{32}$ Divide by the common terms $\dfrac{a}{3}+\dfrac{a}{3}=\dfrac{a}{2}-\dfrac{a}{2}$ $\dfrac{2a}{3}=0$ Cross multiply $2a=0$ $\therefore a=0$
Divide by the common terms
Cross multiply
See lessWhat is the Center and radius of a Circle
$(x+4)^{2}+(x+1)^{2}=9$ The general equation of a circle is given as $(x-a)^{2}+(x-b)^{2}=r^{2}$ By comparison $a=-4, b=-1$ and $r=\sqrt {9}=3$ $\therefore$ center (-4, -1) and radius =3
The general equation of a circle is given as
By comparison
center (-4, -1) and radius =3
See lessOn a six-sided die, each side has a number between 1 and 6. What is the probability of throwing a 3 or a 4?
Sample space=${1,2,3,4,5,6}$ $\rightarrow$ Prob.(3) or Prob.(4) $\rightarrow \dfrac{1}{6}+\dfrac{1}{6}$ $\rightarrow \dfrac{2}{6}=\dfrac{1}{3}$
Sample space=
See lessWhat is the square root of 2525?
$\sqrt {2525}$ $\sqrt {25 \times 101}$ $\sqrt {25} \times \sqrt {101}$ $5 \times \sqrt {101}$ $5\sqrt {101}=50.25$
See lessSimplifying fractions
$2^{-3} \div 2^{2}$ Applying law of indices $2^{-3-2}=2^{-5}=\dfrac{1}{2^{5}}=\dfrac{1}{32}$
Applying law of indices
See lessSimplifying multiplication
In $-9^{2}$, the square did not affect the minus sign. While in $(-9)^{2}$, the square affects the minus sign and change it to plus sign. Also difference in mathematics means minus Hence, $-9^{2}-(-9)^{2}$ $-81-81=-162$
In
, the square did not affect the minus sign. While in 
, the square affects the minus sign and change it to plus sign.
Also difference in mathematics means minus
Hence,
See lessCalculus: Integral
$\int (10x^{3}-2\sec ^{2}x)dx$ $\int 10x^{3}dx -2\int \sec ^{2}xdx$ $10\int x^{3}dx -2\int \sec ^{2}xdx$ $10\dfrac {x^{3+1}}{3+1}-2tan x+C$ $10\dfrac {x^{4}}{4}-2tan x+C$
See lessWhat is the formula of Arithmetic sequence?
Arithmetic sequence $T_{n}= a+(n-1)d$ Where a= first term n= number of terms d= common difference
Arithmetic sequence
Where
a= first term
n= number of terms
d= common difference
See less