Maths-
General
Easy
Question
Prove that AB ≅ DC
![](data:image/png;base64,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)
Hint:
Use angle sum property.
The correct answer is: AB = DC (corresponding parts of congruent triangles)
Complete step by step solution:
Consider 2 triangles, △ AEB and △ CED
From the figure, we have
AE = CE (given)
∠ ABE = ∠ CDE = 55° (alternate angles)
⇒ AB ∥ CD
So, we have ∠EAB=∠ECD=65° (alternate angles, since )
Now, ∠ CED = 180°- (65° + 55°) =180° - 120° = 60° (angle sum property)
∠ CED = ∠ AEB = 60° (vertically opposite angles)
In △ AEB and △ CED,
∠ EAB=∠ECD=65°(alternate angles)
AE = CE (given)
∠ CED = ∠ AEB = 60° (vertically opposite angles)
So, △ AEB ⩭ △ CED by ASA congruence criterion
⇒ AB = DC (corresponding parts of congruent triangles)
Related Questions to study
Maths-
Convert the following fraction to decimal
d) 13/55
Convert the following fraction to decimal
d) 13/55
Maths-General
Maths-
Convert the following fraction to decimal
c) 11/9
Convert the following fraction to decimal
c) 11/9
Maths-General
Maths-
Convert the following fraction to decimal
b) 13/65
Convert the following fraction to decimal
b) 13/65
Maths-General
Maths-
Solve for the value of m of the following-
a. 7m = 343
b. 2m-3 = 1
Solve for the value of m of the following-
a. 7m = 343
b. 2m-3 = 1
Maths-General
Maths-
of an isosceles triangle ABC is acute in which AB = AC and BD
AC . Prove that
![B C squared equals 2 cross times A C cross times C D text . end text](data:image/png;base64,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)
![](data:image/png;base64,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)
of an isosceles triangle ABC is acute in which AB = AC and BD
AC . Prove that
![B C squared equals 2 cross times A C cross times C D text . end text](data:image/png;base64,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)
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)
Maths-General
Maths-
Convert the following fraction to decimal
a) 9/11
Convert the following fraction to decimal
a) 9/11
Maths-General
Maths-
Express the following recurring decimals as vulgar fraction
b) 0.743434343......
Express the following recurring decimals as vulgar fraction
b) 0.743434343......
Maths-General
Maths-
ABC is a triangle in which AB = AC. P is any point in its interior such
that
. Prove that AP bisects ![straight angle BAC](data:image/png;base64,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)
![](data:image/png;base64,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)
ABC is a triangle in which AB = AC. P is any point in its interior such
that
. Prove that AP bisects ![straight angle BAC](data:image/png;base64,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)
![](data:image/png;base64,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)
Maths-General
Maths-
Evaluate:
a−3b−4 / a−2b−3
Evaluate:
a−3b−4 / a−2b−3
Maths-General
Maths-
Prove that ∠BAC ≅ ∠CAD
![](data:image/png;base64,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)
Prove that ∠BAC ≅ ∠CAD
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMcAAAC0CAYAAAAgszipAAAgAElEQVR4nO2deVBVZ573P+fce9lkkSUiLii4EgEVN1RcWWQVo53YndiZ6fRUdb/v1PwzXT3/Tc1U9VvTM/Um0zVL1Uxq5u3O9JLpmFGRTQQBFRRXEDVqohh3EBRkk+Xec877Bz7Hc8EkKnAXOJ8UpYQr99xznu/ze37L83skTdM0TExMRiC7+wJMTDwVUxwmJt+A1d0XYPJijKtdTdOQJMnp58O/Nxl7TMvhoWiahsPhQFVVFEVx9+VMSiTTIfdMxGNRVRVJkkzL4QZMy+GBaJqGpmkoisLg4KBpOdyEKQ6PQwVUNM3B48eP+PWvf0NlZRWqqurWxDT2rsF0yD2KIWFIkoosw7Hj1Xz66adERc1g5coVTJ06FUmSkGVzTnMF5l32AFQVVFVDVVVUTUUDOrs6OXnyJLm5OYDGlStXkGUZTRt6ncn4Y4rDA5Gw8NVXX9HT3c3mzZtZsmQJFRUVDAwMmFbDhZh32gOQJFCUIWsgaRqapnL58hdMmxbJ/PkLWLt2HXV1dTQ3N+vWw/Q7xh9THB6ApqnIsoTDYUcD2toeUl9fT3NzC4cPl3HlyhWam5s5c+YMgGk9XIR5lz0ATZNQVRWr1YYky1y6fJk7d+4wPSqS9vbHqKpCUlIStbW1KIpiWg0XYUarPAINkdOzDw7yxeUvmDlzBn/5l39JeNgbKIrGmTOn+ad/+idu375NTEyMey93kmCKwwOQZQmR51NVjcSlS1mxciXBwSGo6pB/sWTJEt577z0cDoeZHXcRZvmIx/H8cSiKgiTJgIQsPxfEiwoRTcYeUxweyFA0Cn2ppWma6YS7AfOOeyBDVuF5uNa0Eu7BFIcHIpZNg4ODtLS0MDAw4JTbMI29azDF4UGI0hDx1d3dTX19PU+ePEFRFFRV1fd4mIw/ps/hQQjrIMrV7XY7AwMD+Pn54evrq79GluUX7vEwGVvMUK4HIkkSTU1NnD17FofDAcDKlSt58803kSTJdNBdhCkOD0IM+vb2dg4cOMDBgoM4lCFxbN26lZ/97Ge88cYb+mtNyzG+mNOPB6AqKpqqYh+0Y7fbOX/2HHUnThIWGkqAnz9R06NoaGigrq4Oi8UCmE65KzDF4SGoqoamarS1tlFcXExAQAApKSn4+/uzdesWQkNDKS4u5ubNm1gsFnNZ5QLMO+wBSLIEmobNZqXu5EkaGhrYunUrb775JqqqEjM3hh07dtDU1ERRUZEZrXIRpjg8AFVRkWSZ5uZm9u7dS1xcHFlZWQQEBCABNpuNrKwsEhISqK6uprGx0d2XPCkwxeEGRD5D5CwkWcLhcFBQUMDjx49JT08neu4c7HY7SBKqphESEkJOTg5dXV0UFRXR09MDoOc/TB9k7DHF4SaMfalkWeZiYyNFRUUkJCSwZcsWYCikO7SEUpElmeTkZFJTU6mpqeHs2bNOORGTsccUhxsQYVjx1dXVzYEDB1BVlZ07dxIeETHsH0goqkJISAhZWVkEBgZSWFjIgwcPAPTch8nYYorDTRjzFBUV5Zw9e5YNGzeyatUqlGeJP/21PLcyb775JhkZGdTX11NVVaU752bOY+wxxeEGhM8hSRJ3797l0KFDhIRO5fvf343N1wdNjHNJfEl6yYifnx+ZmZnMmTOH8vJy7ty5o/8+458mo8cUhxsQA11RFCorK7lx4wbZ2dnMjYlxznxLEhiWXyK3MXfuXLKzs2lubqaoqMipatfsTjJ2mOJwA5qmYbVa+eKLL6ioqGDhwoVs2bIFi8WiW5Rv+7cAaWlpJCUlUV1dzZUrV7BarabvMcaY4nADsizT3d1NZWUljx49YteuXcyaNYvBwUFsNtt3+g+qqhIREUFmZiYDAwMUFBTQ0dEBODv7JqPDFIcLMIZchV9w5swZqqqqWLt2LStWrECWZfz8/IDvdq7F0mn16tVs2rSJc+fOUVtba1qNMcYUhwsQB9AIZ/nRo0eUlJTg4+NDbm4uERERL71Hw/iaKVOmsGvXLsLDwyksLOTu3bv6+5mMHlMcLkAMZk3TsNvt1NTUcPHiRTZs2EBcXNwrz/jG7bIxMTGkpqZy+/ZtKioq6O/vN32PMcIUh4sQ0ak7d+5QUFDAnDlzSE9PJzAw8JUHsnHwy7JMRkYG8+fPp6KiguvXr+tWyGR0mOIYZ4S/IZqxVVZWcu/ePdLS0l7Lagz/vZIkMWPGDHJycnj8+DFVVVV63ZV4nfFPk5fHFIeLsFgsXLt2jcOHDxMXF8e6dev0vMXrzPIWi0X/slqtrFixgrVr11JaWsrp06cBUxijxRSHC5BlGbvdzoEDB+jv72fnzp3Mnj17TB3nyMhIcnNzsdlslJaW0tHRYfoeo8QUh4s4ffo0p0+fZtWqVaxbt07PeI/VAJYkiSVLlrB582ZOnTqld2QH03K8LqY4xgGR0xjqdSvR0tLCf//3f+Pr68vOnTsJCAhwcqjHwnl2OBwEBASQn5/P3Llz+eMf/0hbW5vT7zcus0zBfDemOMYBkc8QM/fRo0e5du0aWVlZxMfHO/WegtFX1Br3hixcuJCsrCyam5spLi6mr69Pz7MYX2vy3ZjiGAfEwLfZbFy8eJHi4mKio6PJzMzEYrGM+QAViUGRgReh3f3793P16lUzKfiamOIYJ2RZ5unTp1RVVXH37l1+8IMf6E74eOQgJEnCYrGgKArTpk1j9+7d2O12CgsLsdvtZt7jNTDFMQ6I+qkLFy5QWVnJ6tWrSU5OHtd2OkYfRlEUVq1axZo1azhz5gzV1dVO721akpfDFMc4IMsyHR0dFBcXA5CTk0NoaKhuNcZj3W/Me8iyzJQpU3jnnXfw9/enpKSE+/fv6+9tboh6OUxxjAMOh4OzZ89y/vx5Nm/ezKpVq5wy2uM1MIc7+IsXLyYtLY2rV69y7NgxBgcHRwQDTL4ZUxzjwL1799i/fz9hYWGkpaXp9VNiaTPe3QqF+Gw2GxkZGcTGxlJWVsa1a9dGvMbkmzHFMUYYcwhVVVU0NTWRkZHB4sWL9TCqq2ZrYZ0URWHOnDnk5+fT0tLC0aNH6evrMzdDvSSmOEaJ8cAZh8PBl19+SXl5OTExMaSlpeHr6+uUDXfFwBTLN1mWkWWZ1atXk5iYSFVVFRcuXDCtxktiimOM0DSN3t5e9u7dS3d3Nzt37mTmzJluaZ1jFKEI7ebn52O32ykrK9Prrky+HVMco0QMQovFQmNjIzU1NSQlJbFp0ybAvWFTVVX1pOPy5cvZtGkTp06dor6+3gznvgSmOF4D47JERKGam5vZt28fU6ZMITc3l4CAAAC3re+NkStZlgkKCiIjI4OoqCj+8Ic/0Nzc7HT9JiMxxfEaiKJC46A6fvw4V65cYcuWLSQkJIzoNeVKxHWJg27E/4uLi2PLli3cvXuXI0eOjNjbbuKMKY5XxNj6RixNbty4QXl5OdOnT39+dMAwJ9yVGN9T/F3TNHx8fNi6dSuxsbHs37+f69ev65/JFMdITHGMAkmS6Ovr4/Dhw9y6dYvc3Fzmzp3rkQNNCGT27Nl873vfo7t7qHm1+JnpoI/EFMcrIgaZGExfffUVFRUVJCQksHHjRmw2m5uv8JsRFmL9+vWsWrWKmpoaTp486WQFTZ5jiuMVMS5Bnjx5QkFBAb29veTk5DB9+nSPXb8b8x6BgYHs2bOH/v5+PvvsMx4/fqxHtczaq+eY4nhFhNVQFIXz589z5MgR0tLS9K2v4LnHARj9oLi4OPLz8/nyyy/1owyEBRECmeyY4nhFxABrb29n3759REZGkpGRQWBgIHa73WtmXFmWycnJYerUqU51V0b/w1s+y3hhiuM1UFWVw4cPc/XqVT10ayxH94ZBJUkSc+fOZc+ePXz99ddUVlbqW2rFZ/FUC+gqTHF8B6KATwwagJs3b1JSUsKCBQvYtWsXPj4+aJrmtJ/C0xFnEa5du5Zly5Zx9OhRLl++DJjHqAk8/ym6GdGtUAijp6eHgoICWlpayMvLY/r06bow3JX0e100TSMiIoKcnBwGBgYoLi6mq6tr0lsMgfc8STchy7JTprm+vp4TJ06wYsUKUlJSxm1P+HgjnG9JkvTPcvbsWerr6/XWpZMdUxzfgXHnXHt7O2VlZQwODvL2228TFBTktTkCMfgVRSE4OJjU1FSCgoL0s9BNTHF8K8Z1t6qqVFdXc+HCBVJTU4mLi8NqtaIoilctpQTC5xCWMT4+ni1btnDlyhW97sq4V2Uy+iDe91TdgCzL3L9/n/LycsLCwvSzwMFzcxrfhQgcCF/J39+f1NRUZs+erZfDGIsSvfVzjgZTHC/BwMAA1dXV3Lhxg7S0NObNm+e0H3wizKqapjFnzhxycnJoa2tj3759DA4O6j/3xqXjaDHF8S2IWP+XX35JSUkJS5YsIS0tDT8/P6/JZ7wKVquV9PR0li5dyrFjx2hoaMBqtXpt0GG0mOIYhvFwS4Du7m7Ky8vp7u4mLy+PWbNmjTixdaIMHE3TmDp1Ktu3b0dVVfbv38+TJ0+conWTCVMcw5AkSQ9lOhwOzp07R0VFBcnJySQlJemvMRbyTRRE5C0xMZFt27Zx4cIFqqqqkGV5UjrlE+fJjhEOhwMYmkV7enooLCwkICCAzMxM3njjjQk/QDRNIygoiLy8PEJDQ6moqODWrVuTshGcKY5hiOiNpmlUVlbS2NjIunXrWLZs2YR2SsXAFwGG6Ohodu7cyaVLl/TczmTDFMcwRNLv/v37/PGPf2TmzJnk5+fj6+vr7ksbV4xOtyRJ+pba+Ph4jhw5wo0bN3R/bCIGI17EpBeHcXOPeOCKonDw4EHu379Pbm4u8+fPB8buFCZPxNjrSnzGadOmkZ2dTUdHB0VFRbS3t+u5DxGwmMhMenEIjC38GxoaqK6uJj4+nq1bt+rO90TeBPRNkbeUlBRSUlI4evQojY2NLmmI7SmY4sC5RLu7u5uSkhJ6e3v54IMPiIiIcNr8M1Etx3DERBAWFkZubi4+Pj4UFhbS3t4OTI6mDKY4cK6hOnbsGHV1daxbt46lS5c6rbEnWuj22zAWJiYmJpKSkqJ3dJws55tP+Cctmq+JdbJx45JYIon9GLdv36a4uJjg4GB27typO+GTYZZ8EWIy8PX15Z133iE6OpqioiLu3bunv2YiO+cTXhyALgRjod3wDPfAwAC1tbVcu3aNnJwcp/qpyYpxQpgzZw6ZmZncu3eP0tJSnj59CjCh/Y8J//RF1leclTf86DFhWa5du8ahQ4dYuHAh69evx9/fX/93kxljKc3mzZuJj4+nvLxc31IrXjMRmRRPXvRkunXrFrW1tfT09OjRJ3Hqa2VlJa2treTm5hITEzNp1tXfhvjswoK88cYb5Ofn09/fT3l5OZ2dnS/dqcQb7+OkEAeA3W6nrq6OX/3qV/zud7/jwYMHugW5ePEix44dIzExkeTkZGw2m1OPp8nK8PoxSZJISkoiJSWF06dPU1tbq1ve4RujjN9764apCS8O8ZAsFgsJCQnExMSwd+9e/vmf/5nGxkba29spKioCIDc3l4iICGD8z+3zBowTgxjYwcHB7Nixg4CAAMrKymhpaXFqSfSiDLq3lrxP+BFgtABLlizh5z//OXl5eZw/f56///u/5+OPP+bixYukpKSwZs0ar3yIrsC4fFqwYAEZGRlcunSJqqoq7Ha7U3Cjp6eHM2fOcPPmTeB5ZYG3JVAnvDiE5RCnL02fPp0/+7M/4yc/+QkAhYWFyLLMsmXLdCfc28y/KzBG9/z8/Ni6dSuLFi2ipKSEW7duYbFY6O/vp6GhgY8++ohf/OIX1NTU0N/fDzyvWfMmrO6+gPFm+APRNA1/f3927dpFc3MzX3/9Nb29vRQVFTFz5kwWLVoEMCIHMul5Nl9Iz/4+LyaW3OwcPvroI07XnSLAP4CKIxXs3bsXu93OsmXLSEpK8uqCzQkvjuHLJE3TsFqtXLp0iaNHj7JgwQKWLFnC8ePH+eu//mv27NlDWloa/v7++lLAFAdoaGiKCobQ+KpVq1m5ciWffPIJhYWFPO5oJz4+ntzcXJKTkwkKCnIqufG2JeuEF8eLePr0KZ9//jmdnZ389Kc/JSUlhfj4ePbu3cu//Mu/0NTUxK5du4iJifG6Bzpe6PdB05AtFjra27l69SpPnnTS09ODpmn86McfkJGRQWRkJA6HA4fD4XS6lbfVpk06cciyzKlTp6irqyM5OZm1a9fi4+NDTk4O0dHR/OEPf6CwsJD79++ze/duli1bhp+fn7sv2+1o6tDy8mlfH9caGykrK6OmpobAwEAWLVpEW1sboaGhRERE6N3mjX2DvU0YMAnEIbK7ImrV0tJCYWEhPj4+ekhSPLilS5cSGRnJwYMH2bdvH7/85S9599132bFjBz4+PvrvmUzo56gjcevWLUpKSqisrKSnp4d169bx1ltvYbPZ+Lu/+zs+++wzFi9eTGxs7ITo1D7hxWEMQTocDmpqamhsbOT9998nPj5+RIZ3+vTp/OAHP2D27Nn8/ve/5+LFi3rJ9vCM8UTGmMxra2vj2LFjHKmo4M7tOyxcuJC8vDxWrFxJRHg4SBLp6en85r8+obKykujoaL2GzZuZ8OIwJgG/+uoriouLiY6OZuPGjS+0BqqqEhAQQHp6OrGxsSiKgp+fH4qieP1M+CpIkkR3dzf19fUcPHiQy5cvM31aJH/yJ3/Cli1biIyMRLZYcCgKaBqpaWnUnKilvKKcVatWsXz5cnd/hFEz4cUhKnH7+vr0Thp/8Rd/QXR0NIqijDjg0pjhjY2NHVHFO1miV5Ikcf36df71X/8Vu91OTk4OOdk5zImOBnE/nr0OSWJ6ZCR79uzhH/7hHygrK2PBggUEBQW5+2OMigktDmMZgzj7LjExkXXr1mGz2Zy2fAokSXLq8jf8596WyBoNM2bMYPv27cTGxrJy5Ur8/f3RVBVNA0mWUFWxzATZZmX58uWsXLmSEydOsGrVKlJTU50qoL3N8k7YJ220AO3t7ezfv5+BgQGys7OJiooCXvywxP8b3mh5+B6QyUBkZCQ//OEP2bBhA/7+/gBIsoxsGQrPyhYZi9WC/OweBQUFkZ+fj9Vq5dChQ3rdlQiKmOUjHkhdXR21tbVs2rSJTZs2mSemvgTDCwdfpiRd0zTi4uLIzMzk4sWLnDx5ksHBQaxW71ygTFhxiFm+ubmZ4uJiIiIi2LZtGwEBAU4/N+uoXszwpebLCERRFP0ogzlz5lBYWMj169eRJAm73e51S1LvutqXQOwVF6HbiooKbt68SUZGBosWLXph1tbkxRjv03ftbRFLUUmSiI2NJTs7m/v373P8+HG6urr0DWfexIQTh3FzzvXr16msrGT27NlkZWXpmW5jrY+3zWau5FU7yQsLY7VaSU5OJj4+nkOHDnHjxg2v9Ncm3MgQ5r+3t5fCwkIePXpEXl4ekZGR5p7wccTYvkhVVaKiosjNzUXTNPbv309vb6+7L/GVmXAjRcxQDQ0N1NbWsnTpUlJSUrxy5vI2jC2QJEli3bp1JCcnc+rUKc6dO+d193/CiMOYs2hpaaG0tBRVVdm+fTuhoaFeWfjmTRj9EuFfTJkyhczMTEJCQvj9739Pa2vrC3sTeypeLQ7jKUzGbiG1tbWcOnWKtLQ0EhMTdT/E9DHGF3GfxZc4CCc9PZ179+5RVFSk+yXeEEb3+pEyfPa5d+8eJSUlTJ8+nZycnBEbbkxch7jn2dnZTJs2jYqKCi5duuQ15TdeLQ4RihU9qAYHBzl8+DDXr19n27ZtxMTEeMUMNRExFnzOnDmTd999l9bWVg4cOKB3S/R0vFoc8NxyqKpKU1MTJSUlrF69mqysLKxWq8evaycqwmqIE6E2b95MUlISZ86c4cKFC1gsFo/3PbxeHOIh9PX1ceDAAfr6+sjMzCQyMtKpM7oZrXI9FosFX19fJEnC19eXXbt2oWkaBQUFtLa2enxi0KvFYSwuPHfuHEeOHNE78pnLKc9ClmWWLl1KZmYm58+f5+TJk3rI19gh0ZPE4tXiELS2tlJQUEBgYCDf+973nLa+mtbC/YgIoZ+fH+np6cyYMYPi4mKampqcXudpgROvE4dxZhFhwfLycq5evUpaWhpLlixxKpH2pJloMjK8/GTOnDlkZWVx+/Ztjhw5Qn9/vx5Q8SRhgJeKQ1VVHA4HmqbR1NTEkSNHiIqK4q233sLHxweLxaLvx/C0Gz6ZET3DNm7cSFxcHMeOHeP69et63sPTnpVXikPw9OlTysvL9VNfp02b5tVNxCYDkiQxa9Ys0tPT6erqorCwkK6uLsDzNkN5nThgaN+A1WrlwoUL+tEBmzZtcuqRZOK5aJrGhg0bSE5O5vjx4zQ0NOhLK0/Cq8Qhbp7FYqGtrY3Dhw8zODjIrl27CA8P18/VMPFMjJumpk6dSlZWFv7+/uzfv18P7Qo8QSheJQ6BpmnU1dVx5swZNmzYQEJCgp5UetU9CCauQ5ZlfHx8dCuRmJjI5s2b+eKLLzhy5MiIkK67BeJV4hAVnw8fPqS0tJTQ0FCys7MJDg4GJvbJphMJMWmJxOCsWbMoLS3l9u3bHrU706vEATAwMEB1dTU3btxgy5YtzJ8/X7+ZZnTK+5g9eza5ubm0trbqm6I8pem0V4jDOJM0NTWxb98+Fi5cSHp6Or6+vropFmXSJt6BCOFu2bKFpKQkKisraWxs1Cc5d1sQjxaH8dBFRVHo6+ujuLiYrq4usrKymDt3rlOPKZhcTde8GWOP4tDQUHJzcxkYGKC8vJyOjg6PiDx69EgyOtaqqlJfX8/hw4dZtmwZa9asGfEaE+9DWAhRd1VTU0NNTY3T5jV34dHiMJajDwwM8PnnnzNlyhTefvttIiIizPIQL8fYezg4OJi8vDxCQ0M5dOgQzc3N7r48zxYHPI9AVVRU0NjYyIYNG0hKSppUxwFMVIx9iQHmzp1LWloaV65cobKyksHBQbc+X48Uh7EU3WKxcPfuXQoLCwkODmbXrl16TsNkYmCs2s3OzmbRokUUFxdz584dvdeuO/ade5Q4jB1ExFd/fz/l5eU0NTWxe/du/Zw+oxNu4p0M76aoaRrR0dHk5eXR0dFBQUEB3d3dKIqiC8SVeOzoEiJpaGigoqKCRYsWkZ6ebi6jJjBCIOvWrWPFihVUVFRw/vx5tzWi9ihxiIEvZojHjx9z+PBhnj59ynvvvUd4ePgI62IycRCh+9DQUPLy8vDz86O4uJj29vYRx9O5Ao8Sh0CY0fr6ek6fPs3atWtZuXKlGZmaBIhJLzExkZSUFC5fvszx48dxOBz6z12Fx4lDOOGifsrf35/09HQCAwNfuuO3iXdibLoXEBDA9u3biYiI4ODBgzQ3N+vdZFw1SXqcOMRZDnV1dVy5coWMjAwSEhLMnMYkYPiBQvPmzWPbtm3cu3ePw4cP09/f79Lr8UhxfP311xw8eJCoqChSU1MJDAzUO1WYTFyMfoWwIps2bWLRokWUl5dz+fJlp24l441bxWGsnRLfi66FbW1t5Obm6l0LvaWFpMnoMIbxZVlmxowZvP322zx9+pSysjI6Ozt1gYhGGuOFR1gO8UFVVeXSpUtUVlayePFiNm3ahNVqdWpObDKxMUYhRaV1YmIia9eu5fjx49TV1bms7srto02YUE3T6Ozs5NNPP0XTNHbs2EFERIS7L8/EjYjVgjG0W1payoMHD1yyxHarOMQHFA0T6urqOH/+POvXr2f16tWmjzHJEcttVVWJi4tj27ZtnDt3jgsXLgDjvz3BreIQESir1cr9+/fZt28fYWFh5OTk4O/v75JygeGmefgRw5Od4VFC4z0R/uJ4RRLF5CjLsn5K7aJFi/j1r39NU1PTiPce62tw+7JKUFpaytdff01+fj4LFy7Um7aNN6qq8vTpUx4+fEhnZycOh4POzk5aWlro7+8fd6fPkxED78mTJ7S1tdHf34/dbqejo4O2tjb6+vr0BnvjMZEIp1xYiMWLF5OXl0d7ezvFxcUMDg6OEOhYjhm3i8NisXD16lWOHj3KvHnzyMrK0lvsuMIBlySJmzdv8p//+Z+cOXMGSZKora3l448/pqOjY9Iu7cQgczgcVFZW8sknn/Do0SNUVaW6uprf/va3ejsdq9Xqsvu0adMmEhISnEK744XbfY7Ozk4OHDjAnTt3+P73v09YWJhLE36SJPHo0SNqamq4desWFouFGzducOLECbfvJ3AnYnJSVZVr165RU1NDd3c3AF9++SWnT5+mp6fHpee5q6pKeHg4u3fvBuDzzz+nr6/PqR/WWD4vl4pjeF8iSZJobGzk+PHjbNy4kVWrVukRCld2wBPneIhD5kUJi3n4zXN8fHyw2Wxomobdbtf7EQMu63Mr9nYsX76clJQULly4QHV1tVO/Mq9eVjkcDj2n0dzcTHFxMYDef0rsDnPlfg1jJ0V47nSaB2yiN7cQz0PkpMSeGsBlOSghAD8/P3bu3ElQUBAHDx7k/v37unDGEpc+eZHUkWUZRVE4ffo0dXV15OXlsXz5crfN0t/0vpN1SfVtvKjo05UWXnzFxMSQn5/PzZs3qaqq0q3/WOK2afHevXscOHCA6OhoUlNT8ff3d9el6MiGEpXJbjFehLHTi1Ekru40KZbAW7duZd68eRw5coSLFy+OebW2W0aAw+GgrKyMu3fvkp6ezvz5892yR1iPj6saEmB9Jg4xC5mW49nAF2t6QFVUFIcytAKQXDt8jM9D1F3t3r2b1tZWysrK9IDBWOU93CKOy5cvU1VVRWJiIhkZGVitVhRFcelsrQcHFBXF4UBTNWRR06OoSNrQn5MG7QVfgKooOBwOZCQkhhxeh8OBrBksiQa4ao+FYdKyWCwkJSWxZs0aamtrOX/+vJ5zEX+ORiAuFYcsy3R1dVFQUEBfXx/Z2dlERUWhqqrb9gljMA6S9myZICyYpumDxJUYZz63N8c2CAWGbpcEIMN+8NoAAAhlSURBVElO90fCtVZWRKZCQkLIysrC19eX0tJSWltbnUreR2P9XSoOSZL0+qnk5GTWrFmjR0Dc2ThY35MuS+JCn1+LB4RyPSGcLOG8Z3/4Hn53XaPYUpuens7Fixc5e/Ysdrt9TPZ9uHS6FmtDi8VCbm4ugYGB+t5gV29m0mdlVXthnNypmbGLn/vwNbNLrMc3/Hr9faXnHQqNUUeN5/dPlsf/+Q2/Dw6HAz8/P9avX8/Jkyf5n//5HxITE5k1a9aoLYekjeNdFwNebH393e9+x29/+1s0TWPOnDn4+Pjor3WX5dBUje6uLh4+fEhERATh4eE0NzfT29tLdHQ0Vpt1aAnhYiRJor29nebmZqKioggNDR3f9xs2CoyCfPDgAf39/URHRwPw6NEj+vv7mTlzpt7lHgAXiGM4YiPc4OAgDx48oKOjgx//+Md88MEH+Pj4jKpLzbhaDjHzyrJMb28vHR0dzJs3T28B6RHRIOm5MG02GxaLRc/i22w2rDYbiuqe4sPw8HDCw8NdcrTCcHEAIyypsYJA/NxoYTU3PE6xLPfz82PevHkoikJrays9PT1MnTp1VL7suFoOu92u3zxFUXj69CnAuKX7XwdN1ThcVsZvfvMbfvSjH5GTm8tHH35IQ0MDH374IZHTp6Nq7olaGdfN4z2RvMhyyLLMkydP+Md//EdaW1v5m7/5GwKnTOH/fvgh3d3d/NVf/RUzZsx4vkR1gziG9zoTS78pU6boBawusxzf9qCeD3QNkJx62kqSRHBw8LhkMkeDqqkEBAQgyzLBwcEEBQdhkWWsVithYWEEhwS7+xLdw7NH6XA4sNls+Pr6EjJ1KlOmTMFisWCz2QgNDSUoJFg8bo9ApATGopTklcUhlDn0jWaY/SUUVR1KDGmArDnV34h/625LMRxN1YaWTRK6b6E9i1wpqupRD96lPPvMiqbiUBxDWpFAY+h+qZrqdF+Ek+5uxLJYFI2OxuKOwufQcDjsdPf0PrtHEr5+fvjYfJEkGU1RsFqsI3xZT7iBw3EoCg5F0R+2qqkoqor27D9Xx/A9DUV9LgRN03AoilP6Q8P95/cZMZa5jIbXFockSVy9dpWf/eznREZGomkab765hPfe3cPs2bPRNM8TwbdhrMB1R+tJb2C4g26c6CbivXrtESxJ0NbWRmvrQ37605/w/vvvc/XqVUpLD2G3O7BYZK9YjogHboyeibIDs75qCOP9AOemawJPWy6PBaMO5QYHB7N06VJ8ff04c+YsHU/asdsHsVltQwrygrHl5+dHVFQUAQEBwFArmGnTpukh1PFeCr5oYAnBDheoqwMakiQxdepU/Pz8nFrleEujPeEf9/f3093drUdQg4ODCQwMHNEwQoSrYZTikCWZjo4OysrKaGt7xBdXrrDnvR/i4+M7lDnVwOLhM68kSSQnJxMbG0tUVBSapvHOO+/Q29uLv7+/W2bEF1kyI8ZQ+HhfR1BQEO+//z6yLBMYGAjAn/7pnwJDzZ6NOQ9PRdM0Tpw4QWFhIX5+fqiqSkhICBs3bmTDhg16rkQEm4ToR205unu6aWy8iKqoWC0W7t29S1dXF+HhYe5ILL8W06ZNY9q0afqut9mzZyPLMg6Hw20PXQhieBWBq8r6jYnQhQsXOl3T/Pnz9e/dWRP3MghL29TUxOPHj9mzZw+KolBXV8e///u/4+/vz5o1a0YsHWFU4hgKdc6aOYs///P/TVhoBIfKyvjkN//F0qXLCAtb/ax6c9Sfb9xRFMXpxhjrh9yzltb0kOStW7doaWkhMDCQmJgYfH19XWI1jD1rh4vAm5p6G/2k6Oho1q9fT0hICJs3b+aXv/wln332GUuXLsXHx0ffDiwYRRJQwiJb0RTw9/XHz9eXoMBA0BTQFGSZZxWtnn0TjU2LAbeto58dKo2kaciSRm9vL//28X9QUlKKr68f/f19rFmzhr/9278ddeb3ZRn+Hsblh8fiNORUvbJ+SOCSfjBSUFAQy5cv59NPP+XBgwfExsaOePavlQQU+Pr40trayi9+8X+QJImHDx+ybds2Fi9ejDpMhZ7Mtzm4LhkIkjT0TDWQJA0kKC0tprb2GD/98//FmjVr6e3qorW1Vc9Yu8IhNuYLxip34BKeCUTTFDRNRZZtgISiqKjqyACI3W5/4a8Zlc+xaNEiPvroIwD8/f2ZNWuWXljoFbOMJyJJdDx+xKlTp9i6NZUd+TuwWG3ImsbixYv1l3nLxONOhsae7BT1M1ZtdHR0EBYW9o0Ny0cljrCwMLZv365/b4ywiN5PJq/KUKl6Z2cnM2bOwGq1DWXvce7eYk48L48sD+Wy+vv76erqxOEY5Nq1a1RVVZGWlqYfxDrm0aoXVY56YomINyFLoKrPemlJEg6GNhIZezOZE8/LoTG07TkoKIivvrrORx/9Ch8fCz09PSQkJPDWW2857V0xTjijy3M8E4E5g40lGlNDQwkJDuL6V9fpHxjAx9cXmaG1satyHBMFTVXRNFizZg0SMp1dnQQE+BEfH09iYqLuv73onrqpq4HJN6KpTA0NJ2XDRv7j//2agMAQVievpfPxI1pbW8nNzWXq1KnmsuolGbpHGjExc5k/f8EzB/25FR5ehTBmlsNk7NE0kGSJ1LRU+gcd1J0+S8OFRiJCp7Jy5Up9pnNbtxYvZGgiEY08VBwOzclB/6ZI3LjuBDR5OfTyb01F0hTQNDTA7lB43PGE7u4egqZMISQkRN8XbawBMjHglOdQUFXtWa7juQsgrK4x6feie2mKw+MQnei1EbOa0XE0gx4vgxjarzeJmOLwAl70iEyrMf6Y048XYArBPZhenYcy3FqYAnE9pjg8FFMM7sdcVpmYfAOmOExMvoH/D+cznvYbu1p/AAAAAElFTkSuQmCC)
Maths-General
Maths-
Express the following recurring decimals as vulgar fraction
a) 0.444444444
Express the following recurring decimals as vulgar fraction
a) 0.444444444
Maths-General
Maths-
(32)3 + (2/3)0 + 35 × (1/3)4
(32)3 + (2/3)0 + 35 × (1/3)4
Maths-General
Maths-
Express 0.5248 in the lowest form.
Express 0.5248 in the lowest form.
Maths-General
Maths-
Write the following numbers in the scientific notation : 0.00000000065
Write the following numbers in the scientific notation : 0.00000000065
Maths-General
Maths-
Write the following numbers in the scientific notation : a) 5,07,460000000
Write the following numbers in the scientific notation : a) 5,07,460000000
Maths-General