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777dan777 [17]
3 years ago
15

2.Solve the following quadratic equations i. 9x^2 - 1/16 ii. 2h^2 - 3h - 27

Mathematics
1 answer:
Juli2301 [7.4K]3 years ago
4 0
i)~9x^2-\dfrac{1}{16}=0\iff9x^2=\dfrac{1}{16}\iff x^2=\dfrac{1}{9\cdot16}\iff \\\\x^2=\dfrac{1}{144}\iff x=\pm\sqrt{\dfrac{1}{144}}=\pm\dfrac{1}{12}\Longrightarrow\boxed{x=\pm\dfrac{1}{12}}


ii)~2h^2-3h-27=0\\\\\Delta=b^2-4ac\to \Delta=(-3)^2-4\cdot2\cdot(-27)\to\Delta=9+216=225\\\\
\Longrightarrow h=\dfrac{-b\pm\sqrt{\Delta}}{2a}=\dfrac{-(-3)\pm\sqrt{225}}{2\cdot2}=\dfrac{3\pm15}{4}\\\\\begin{cases}h_1=\dfrac{3+15}{4}=\dfrac{18}{4}\iff \boxed{h_1=\dfrac{9}{2}}\\h_2=\dfrac{3-15}{4}=\dfrac{-12}{4}\iff\boxed{h_2=-3}\end{cases}

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The height of the painting h , the diagonal, and the width of the painting forms a right triangle with the diagonal being the hypotenuse.

From the Pythagoras Theorem,

{w}^{2}  +  {42}^{2}  = {62}^{2}

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The width of the painting is 45.6cm to the nearest tenth.

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laurie will draw a scale model of the garden she wants to plant. Her scale will be 1cm = 2.5 ft. what will be the actual dimensi
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3 years ago
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The length of a rectangular garden is 5 times its width.
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<h3>Given</h3>
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