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Equations, SM-Bank 056

The formula for converting degrees Celsius to Fahrenheit is  \(F=\dfrac{9C}{5}+32\).

  1. Find \(F\) is \(C=35\).  (2 marks)

  2. Find \(C\) is \(F=68\).  (2 marks)

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a.   \(F=95\)

b.   \(C=20\)

Show Worked Solution
a.    \(F\) \(=\dfrac{9C}{5}+32\)
  \(F\) \(=\dfrac{9\times 35}{5}+32\)
  \(F\) \(=\dfrac{315}{5}+32\)
  \(F\) \(=63+32=95\)

 

b.    \(F\) \(=\dfrac{9C}{5}+32\)
  \(68\) \(=\dfrac{9C}{5}+32\)
  \(\dfrac{9C}{5}\) \(=68-32\)
  \(\dfrac{9C}{5}\) \(=36\)
  \(9C\) \(=36\times 5\)
  \(9C\) \(=180\)
  \(C\) \(=\dfrac{180}{9}=20\)

Equations, SM-Bank 053

Write an algebraic equation for the perimeter of the rectangle below and use it to calculate the value of \(x\) given the perimeter is \(62\).  (2 marks)

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\(x=3\)

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\(P=2l+2w\)

\(62\) \(=2(7x+1)+2\times 3x\)
\(62\) \(=2\times 7x+2\times 1 +6x\)
\(62\) \(=14x+2 +6x\)
\(20x+2\) \(=62\)
\(20x\) \(=60\)
\(x\) \(=3\)

Equations, SM-Bank 052

An isosceles triangle has a perimeter of  \(46\)  and its base is 12. Find the length of its equal sides.  (2 marks)

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\(l=17\)

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\(P\) \(=2l+b\)
\(46\) \(=2l+12\)
\(2l\) \(=34\)
\(l\) \(=\dfrac{34}{2}\)
\(l\) \(=17\)

Equations, SM-Bank 050

Find the value of  \(c\)  in the formula  \(c=\sqrt{a^2+b^2}\)  if  \(a=12\)   and  \(b=5\).  (2 marks)

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\(c=13\)

Show Worked Solution
\(c\) \(=\sqrt{a^2+b^2}\)
\(c\) \(=\sqrt{12^2+5^2}\)
\(c\) \(=\sqrt{144+25}\)
\(c\) \(=\sqrt{169}\)
\(c\) \(=13\)

Equations, SM-Bank 044

Find the value of  \(A\)  in the formula  \(A=\dfrac{h}{2}(a+b)\)  if  \(h=8\),  \(a=7\)   and  \(b=3\).  (2 marks)

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\(A=40\)

Show Worked Solution
\(A\) \(=\dfrac{h}{2}(a+b)\)
\(A\) \(=\dfrac{8}{2}(7+3)\)
\(A\) \(=4\times 10\)
\(A\) \(=40\)