Special Symbols

Find the value of the special symbol:

  1. If $3+\triangle=7$ what is the value of $\triangle$? $4$
  2. If $2(\star + 9)=12$ what is the value of $\star$? $-3$
  3. If $2\diamond+4 - 3\diamond=2 + \diamond$, what is the value of $\diamond$? $1$
  4. If $\dfrac{\circledcirc}{3}-11=\dfrac{1}{2}$ what is the value of $\circledcirc$? $34\dfrac{1}{2}$
  5. If $\dfrac{1}{\square}+8=-10$ what is the value of $\square$? $\dfrac{-1}{18}$

Using the rules provided by the equation with the special symbols, find the value of the following expressions:

 

$x\circledS y\circledS z = x+(y)(z)$

  1. $3\circledS 4\circledS 5 =3+(4)(5)=23$
  2. $1\circledS 2\circledS 10= 1+(2)(10)=21 $
  3. $12\circledS 2\circledS 3 =12+(2)(3)=18$

$x\spadesuit y\spadesuit z = z(x^y)$

  1. $1\spadesuit 2\spadesuit 3 = 3(1^2)=3$
  2. $5\spadesuit 1\spadesuit 8 = 8(5^1)=40$
  3. $3\spadesuit 0\spadesuit 100= 100(3^0)=100$

$\dfrac{\heartsuit}{x}=\sqrt{x}+7$

  1. $\dfrac{\heartsuit}{4}=\sqrt{4}+7=9$
  2. $\dfrac{\heartsuit}{64}=\sqrt{64}+7=15$
  3. $\dfrac{\heartsuit}{10} = \sqrt{10}+7$