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Understanding Quadrilaterals

Short Answer Type

81.

After showing $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ , can you find $space space straight m angle straight I space and space straight m angle straight G$ by any other metod?

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82.

In the figure, ABCD is a parallelogram. Given that OD = 5 cm and AC is 2 cm less than BD. Find OA.

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83.

Given a parallelogram ABCD. Complete each statement along with the definition or property used.

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84.

Can a quadrilateral ABCD be a parallelogram if

(i) $space space space angle straight D plus angle straight B space equals space 180 degree$ ?

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85.
Solve: 2(3x+1) -5x = $7 over 2 minus 2 left parenthesis 2 x plus 7 right parenthesis$ $7 over 2 minus 2 left parenthesis 2 x plus 7 right parenthesis$

First opening the brackets,

                     $LHS space equals space 2 left parenthesis 3 straight x plus 1 right parenthesis minus 5 straight x space space space space space space space space space space equals space 6 straight x space plus 2 space minus space 5 straight x space space space space space space space space space space space equals space left parenthesis 6 minus 5 straight x right parenthesis plus 2 space space space space space space space space space space space space space equals space straight x space plus 2 space space space space space space space space space space space space space space space space space space space space space space space space space space space space$

                     $RHS equals 7 over 2 minus 2 left parenthesis 2 straight x plus 7 right parenthesis space space space space space space space space space equals 7 over 2 minus 4 straight x minus 14 space space space space space space space space space space space equals negative 4 straight x plus open parentheses fraction numerator negative 14 cross times 2 plus 7 over denominator 2 end fraction close parentheses space space space space space space space space space space space space equals negative 4 straight x plus open parentheses fraction numerator negative 28 plus 7 over denominator 2 end fraction close parentheses space space space space space space space space space space space space space equals negative 4 straight x plus open parentheses fraction numerator negative 21 over denominator 2 end fraction close parentheses space space space space space space space space space space space space space equals negative 4 straight x minus 21 over 2 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space$
Now, the equation is

                            $x plus 2 equals negative 4 x minus 21 over 2$

Transposing 2 to RHS and -4x to LHS, we have

                          $x plus 4 x equals negative 21 over 2 minus 2$

or                          $5 straight x equals fraction numerator negative 21 minus 4 over denominator 2 end fraction equals fraction numerator negative 25 over denominator 2 end fraction$

or                           $x equals fraction numerator negative 25 over denominator 2 end fraction cross times 1 fifth$          (Dividing both sides by 5)

∴ $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

Check: LHS = 2(3x+1) -5x

 = $2 open square brackets 3 cross times open parentheses fraction numerator negative 5 over denominator 2 end fraction close parentheses plus 1 close square brackets minus 5 open parentheses fraction numerator negative 5 over denominator 2 end fraction close parentheses$

 = $space space space space 2 open square brackets fraction numerator negative 15 over denominator 2 end fraction plus 1 close square brackets plus 25 over 2$

 = $2 cross times fraction numerator negative 13 over denominator 2 end fraction plus 25 over 2$

 = $fraction numerator negative 26 over denominator 2 end fraction plus 25 over 2 equals fraction numerator negative 1 over denominator 2 end fraction$

 RHS = $space space 7 over 2 minus 2 left square bracket 2 straight x plus 7 right square bracket$

 = $7 over 2 minus 2 open square brackets 2 cross times open parentheses fraction numerator negative 5 over denominator 2 end fraction close parentheses plus 7 close square brackets$

 = $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

= $7 over 2 minus 2 cross times 2 equals 7 over 2 minus 4$

 = $space space fraction numerator 7 minus 8 over denominator 2 end fraction equals negative 1 half$