Question
Show that m = 2 is the root of the equation 9m – 4 = 14.
Hint:
root of equation is value of m at which the equation becomes 0 find value of the m which satisfies the given equation.
The correct answer is: m = 2
Ans :- m = 2 is root of equation 9m- 4 = 14
Explanation :-
Let F(m) = 9m - 4 - 14
We know that m=2 is a root if only if F(2) = 0
F(2) = 9(2) - 4 - 14 = 18 - 18 = 0
![therefore m equals 2 text is the root of the equation end text F left parenthesis m right parenthesis](data:image/png;base64,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)
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x2 + 20x + y2 + 16y = -20
The equation above defines a circle in the xy-plane. What are the coordinates of the center of the circle?
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)
The graph of the linear function f is shown in the xy-plane above. The slope of the graph of the linear function g is 4 times the slope of the graph of f. If the graph of g passes through the point ( 0, −4), what is the value of g(9 ) ?
![](data:image/png;base64,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)
The graph of the linear function f is shown in the xy-plane above. The slope of the graph of the linear function g is 4 times the slope of the graph of f. If the graph of g passes through the point ( 0, −4), what is the value of g(9 ) ?
The mean score of 8 players in a basketball game was 14.5 points. If the highest individual score is removed, the mean score of the remaining 7 players becomes 12 points. What was the highest score?
The mean score of 8 players in a basketball game was 14.5 points. If the highest individual score is removed, the mean score of the remaining 7 players becomes 12 points. What was the highest score?
If a2 + b2 = z and ab = y, which of the following is equivalent to 4z + 8y ?
If a2 + b2 = z and ab = y, which of the following is equivalent to 4z + 8y ?
Intersecting lines r, s and t are shown below .
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARkAAACQCAYAAAA82B+zAAAgAElEQVR4nO3dd3zb1b3/8Ze2rS1L3nuv2BnO3ssZ7AJtobfQ3UIXBcqlvbf8yu24t6X0Fkops6xCWSm30Ox4ZA+HJE4cZznb2bEkS15a369+f0gZlJWEOHLk83w89LDiOPKxne/b53zO+Z6jCIfDYQRBEPqJMtYNEAQhvomQEQShX6lj3YArInCSrfXv8u7yQxiHX8vnrxlDtlkV61YJwqAQ/z0ZfzurFtaxtTOVESUaDrRu4+Dp3li3ShAGjbjvyfS0NbFo6SpMc+7n326fxXinjwSTIdbNEoRBI+57MnprEkldLbz1x6d4q7kLi92GXhv3X7YgDBhxf7UpsiZzx73fZYaugd/c9yte33iSUKwbJQiDSNyHDKhIHfFv/Mev7mOSag+rVm3nhBTrNgnC4BHXNRln62LmLWzBMesubqmooHrseIL5qVjExJIgXDFxHTJanZrOlvd4bt4iXq8cydQbb+fzc4ZginXDBGEQUcT9bQU+D6ec3ShMySSbtbFujSAMOvEfMoIgxNQgKPxCV1cXnZ2dyLIc66YIwqAzKELm+Wef41e/+CVutzvWTRGEQSfuQ6bL62X//n3s37sXT2dnrJsjCINO3IeMJMvIskxCYgIarSj8CsKVFvchEwoGCQQCaDRa1GqxQEYQrrT4DxkpRDAYRKPRoFbF9bIgQRiQ4j9kQhLBQBCNVoNaLUJGEK60QRAykZ6MVqNFJUJGEK64uA8ZKRQiGAxEhksiZAThiov7kIn0ZEIiZAQhRgZByEgEAwFRkxGEGBkEIRMiEAyiUWtQKuP+yxWEASfurzopFCIUDKIVC/EEISbiPmTO9GTUGjFUEoRYiP+QkUKRmoxG9GQEIRbiPmSCwSDhcBiNRhPrpgjCoBT3IRMKhQiHw2JmSRBiZFCEDCB6MoIQI3EfMsFgEACtVoSMIMRC3IeMFAoRJizuWxKEGIn7kAmGQhAWwyVBiJW4D5lQdLgkprAFITbiP2RCUmQKWwyXBCEmBkHIRHoyajFcEoSYiPtf78FgCJVKheYSbisIh0GhuKCPRJbDKBRKFIoA3S43nj4wJNkxJ6rjP8kF4RPEfcgEAv4P7iUTDtHn7cTt8eA93UdiQRGZtoTzvhEyPScOcOBEJ76QkgRbGvn56Rg+KimCfbhPn+SU00mPMom83AxCbXW8t2wDB90yxsLJ3HrTFAodOi4oqwQhDsV9yASDIdRq9Xkh4+Fw83IW/uN1Xn+vlxuef5ofTcvFGP34wPHV/OWRl2mz1VBtPc7mTV4qvv4g352SwflnHQS72mlZ3cCK9/fjDunJHTOXDE0jzzz2Bt01t/H1OzW8/pM/8Gedg599cQRJou4sDFJx35MPBPxotNrzprB1OEpqGFOSglanQaFQnNfL6GTdM//DayfH8+OHvsu37v4p3x5zilf/+2nWec69ZtC9m2Uv/J4/vrkVw8Sv8uB/Pcg3rqnG0bGLreEsho8eRXn5LOYO6+Xg3iN094njxoXBq99Cpre3t79e+oKFQqHISQWa83oySiP29HxGVRVg02sIn3/9u9byj4UHKJ4yiRwFoNGQP24M2UfqmL86esSt/wRNbz/Js41Bpv/wF3x7Wj6G6D9XF1QzyuJm06pl1C9/k0V7k6gsz8ecKAZLwuDVLyHz/saN/M+vf82rr/yVjU1NuFzO/vg0n0qSJILBIGr1h7feDMky4XD4A7WSwM5mWjwmMrNSou9RoknJJDnRy86dbQC4967mH+9uhpIxZPVsYMG7i1i9vR1PAEibwte/UkuBdIA1y7aimXw3d8wtwSqGSsIg1i81Gb/fz5ZNW5j35ltYrDZGjBzB8OHDqRwyhJLSUhwOR3982g+RQhL+QPSkgguYwu7rOI0zbMRoOlN9UaBQmTAaJDwuN0G6Ob59NVvaFRRMCnNk80o2rt/C/t4Upn/9h3ztumpSR97C94b10itp0WnUqOJ+QCoIn6xfQmbCxIk8+of/ZeeOVrZu3UrzlmaWNzRiNBqpHjqU6mFDGTp0KJVDhvRr4JzbsEpzYYvxZDkyfPpACUXBme5OWOrDuf8oLkMuN4+fxY3DE5k5aSlP//J3vPrUqxQW/4ybKsyg1qOP+5K6IFyYfrsUysrLKCsv48bPfY79+/axZ/dutm1r4f2NTTzz56dISNRRUTmEqqoqRowYwfCaGux2+2Vtw7nhkvqCbpBMsNkwK7rp7pai7wkTlnro61VhSUpCGw4R9PnBmEV2fjoWE1hGXMMNN61i+RM7aN1/gmsrzIhlf4JwTr//vlUqlRQVF1NUXMysOXNoP3yY/fv209LSwvp1a3nlpZf422uvUVJSSlVVFSNHjWLMuLEkJSV95s8thUIEAoHI7JL6g5e+QqGIrLQ7ryijKymnNPFN2g+fQMaKCpmg8xgdvSZKy4tBHcSQaiXBe5ITp2XIVgJGLFYrVrsOrUYT/2sCBOEiXdFrQq1Wk19QQH5BAZOnTuGWz9/K4UOHaGlpYfXKVbz1xhvMe/tt8vPzGTJkCGPGjmP8pPHY7Zc2pApJ0TOX1OoPbSSuQEYRllAozyv+Zkzh2klJPLxmDUfvKiNHCnFi82YOpk3lO+OtQIDs4eMp+dsrrFmzkS+PGEMiHRw55MGaXUNNRbZYdCcI/0L18MMPPxyTT6xSYbFYyMnJYeiwYUyYOJGZtbXkFxRw6tQpGhvqaWhooG5ZHc1bttDT3YMj2YHeYLjgC9nj6WTpkqVotVpmz51DYmIiSCfYsuQdnn/+Neq37OTo6S48IRulxWkY1GZyCqycXPEOy9oC9B6q5+9L3Iy5615uq7KiRIXRnkGq7iRNSxfTdKQXZ+tqNhzWM+7WL1FbnSSGSoLwLxThcHhArRQLBoO43W5OnTzJ1q1bWd7QyPp16wiHIS09jfKKCiZNnszkyZNIS0//xNc6dOgQDz7wAEm2JB559HcYTSYI9+E+fpzjp1z0BmUU6kQM9nTyMu0kqBRAENfB7bTu66AvrMacUkhFZQ7ms8t9w4T6XLS37eHgKR9qg43UrEwy0pIxioQRhA8ZcCFzvlAohMfjweVysXVLM4319axevZpgKERycjIlpaVMnzGdyVOmkJmZ+aF/v3//fh64736ysrL47aO/IyEh4cI/uRTAF1KRoFN9zAeEkSSJcFiJWi3mqQXh4wzoOqVarcZut2O32ynIz6d2Vi0er5fmzVuoW7aMVStXsmrFCpKSkiguLWHWrFlMmTaNrKws4LzZpfNX/F4olZaEj8sXABSoVAP62ycIA8JVc5Wo1GosVisWq5XMzEymz5xBd3c3zVuaWbJ4EatWrmTdmrVY/vAYJcXFXHfjDTgcDkKhEFqtVhyJIggxMqCHSxdClmUCgQA93d00b93KogULWLVyJS6ni4SEBLxeL9NnTOfhX/yC3Ly8WDdXEAadqz5kzieHw8iSRE9PDy0tLbz8wgssXLAQg8GAVqejrKyMOXPmMPuauWRnZ8e6uYIwKMRVyPyrjU1N3HvPj8jPz6esvJyF8+dz+vRpVCoVFRUVzJozhzlz55CZlYVKpYos0BME4bKK65Bp2rCB7911N1+47Ys88OCDBPx+Nm/axIIFC1je0Iizo4OQJFFRWUntrFnMnTuXjKzMD25yJQjCZxLXV1IwGEKW5bPHoWh1OsaOH8/Y8eMJSSE2Nb3PksWLaaiv5+k//5k//P73lJeXUzt7FrWzZ5OdnY1OpxNnNgnCZxDXPZmVK1bwox/ewze++U2+94Pvf+zHhYGNG5pYtmQJyxsbOXXqFL29vZH7rWbPYvqMmeTm5pKQmHBxa20EQYjvkGmor+f+H93L3d//Ht/+zncu+N+937SRuro6Vq5YzonjJ+ju7iYvL4/a2ZF1OPn5+RgMBhL1enGvkiB8irgeLkmhEITDaLUXtzXdyNGjGDl6FP/+kwfZuqWZ+ob66A2cb/L8s8+SlZXNjJkzmTx1CvkFBVgtVvQGvSgcC8JHiOuQCYUk5LB8yadHKpVKhteMYHjNCH50773saG2lsaGBdWvX8t677/LySy+RkZnB1GnTmDhxMgWF+TgcDowmkwgcQYiK85AJEZbDl6Vwq1arI7v6DR3Kd7//ffbs2sWKFStoampi2dKl/O3V10hLS2fi5ElMmDiBwsJCUtPSsFgsInCEQS2uQyYYCiKFz80uXS4ajYbKqioqq6r4VjBI2549rF61mk3vv8/aNWuY99ZbpKSmMnbcOMaOG0tRUTHZOdnYbDYROMKgE9chI13GnszH0Wg0VFRWUlFZSUj6Bm172mhav57NmzazrbmZ9/7xDxwOB6PGjGb06DGUlJaSl593xTZTF4RYi+uQCYUklErVRRd+L5Vapaa8vJzy8nK+8tWvsnv3HjZv2sSWLZvZ0bqDJYsWY7ZYqBlZQ83IkZSXV1BUXERKSsqnv7ggXKXiOmQCgUDsVu8qFJSWlVJaVsrt//Yl2va00bJtG83NW2jZ1sKjj/wOg97A8BHDGTp0GEOGVlFeXk5qauqVb6sg9KO4DxmNRn1BZy71t+KSYopLirn51lvYt3cvO3fsZNu2yHExTz/9FFqNhiHVVVRXVzN02DCqhw4VgSPEhbgOmWAwgFqjGXC3BRQWFVFYVMQ1113L4UOHaNvbxvZt29m4sYmXX3oJpUJJWXk5Q6qqqKkZQc2oUSJwhKtW3IaMLMv4/TEcLl0ApVJJXn4+efn5TJ8+g2PHjnFg/35aW1tZt3Yt8956k7fffJPCoiKGDBlCzciRjB03jrT0tFg3XRAu2MC8+i4D6bzjUAZaT+ajqFQqsrOzyc7OZvyECdx00020H26ntbWV1atX8c933+P/3nmH3Lw8KirKGT12LBMmTCA9I0NMiwsDWlyHTODMEbXaq+vLVKvVpGdkkJ6RwYiRNVxz3bWcOH6c1tZWVq1YxbKldSxcsJCMzEzKysoYP2ECkyZPJjMrUwSOMOBcXVffRTgTMmqN+kOnR15N1Go1qamppKamMqSqitmz53C64zSt27ezvHE5a1ator6untTUFIpLSpg0ZQqTp0wmNzc31k0XBGAwhMwArslcLJVKhd1hx+6wU1xczPQZM/B0drK9pYX6+npWLl/ByhUreMbhoKCwkOkzZzB16lTy8vNj3XRhEIuPq+8jfHC4dGUW411JKpUKm82GzWYjJzeXKdOm4fV62b59O3VLlrFy5XI2rFvPU396kvyCfGbOmsX0GTMoKCiIddOFQSZu95Pp6DjNww/9nI6ODh774+OfetpkvJBlmb6+Pnp7eiKrjJcsYXljA6dOnsJisZBfUEDt7FpqZ8+hQPRwhCsgbkPm5MmTPPQf/0lvby+PPfHHQXmvUDgcJhAI0Nvby84dO1i0cCGNDQ2cOH4CvV5PQWEBs2bPYfacORQWFca6uUKcituQOXb0GP/xk5+AAh5/4gksFkusmxRT4XDkWF2fz8eOHa0snL+AhvoGjh87hkajobC4iNraWcy99hoKCwtRKsXRu8LlEbch0364nQcfeACDwcBjTzyBwaCPdZMGlHA4TMDvp7W1lQXzF9BQV8exY8cAKCoupra2lmuuu468/DzUarUIHeGSxW3IHDxwkAfuux9HsoPHn3gCrS7+ir+XkyRJbNu6lcULF1FXt4zjx48TDAQpLCpi1qxZzLlmLvn5BWi0mriZrROujLgNmX1793HvPfeQl5fH4396QixSu0jNW7awZPFi6pbVcfLECfr6+sjLz2fWrFnUzplNYWEhWq0WrVYrvrfCJ4rbkNmzew/3fP8HlFeU87+PPxbr5lzVtm7dSt2SpdTV1XHi+HF6enrIyspiZu1MZs6aRVFREQl6PYkJCSJwhA+J25DZuWMn37/7u9SMquGRRx+NdXPiRsvWbTQ2NNDQ0MCRI0fwejykpadTWzuTadOnU1xSgtFoJFGvF3UcAYjrxXghAgH/VX1LwUBUNbSaqqHVfP+eH7Jz506W19ezauUq5s9fwKuvvkpycjLTp89gyrRpFJcUY7PaMBgNInAGsfgNGVkiJIVEkbKfKJVKKisrqays5K7vfY+2tjaWNzaybs0a6uvreOuNN7E77NF7qaZQXFxEcnIKZotZBM4gE7dXoBSSkCXpiu3vO5ipVCrKysooKyvjW9/+Nvv37YscF7OhiQ3r1vGPd97BZrMxYcIEJkyaRHFJCRkZGVhtVhE4g0D8howUQpbluLxvaSBTqVQUl5RQXFLC17/xDQ4cOMCa1avY2LSRbdu2MX/+fCwWK2PGjmX8hPGUlJaQnZODw+EQReM4FbchEwpJyHIYrVbUZGJFqVRSWFhIYWEhd975Ffbv38+GDRvY9P4mdu3YwdIlizGZTIwcNZIx48ZRWlpKfkEBaWli5794EtchI8mX/2A34RIpFBQUFlJQWMjtX/oSB/bvZ/OmzWzZsoXW7dt55De/JTExkWHDh1MzsobKykqKi4vJyMyMdcuFzyhuQ0aSQoRlWdRkBqj8ggLyCwq45fO3cvDAAba3bKe5uZmWbdt46k9PolKrqK6uZtiw4VRVV1M+pJIsEThXpTgOGQlJktGI4dKAd2Yz9etuuJ7Dhw6xa9cutre0sHnTZl5++WXCskxFZSVV1dUMGz6MocOGkZWVFetmCxcofkMmJCHLYnbpapOTm0tObi61s2Zx9MhR9u5tY+eOHTQ1NTHv7bd4/bXXKCktZciQIQwfMZyRo0aTlZ0lisYDWNyGTCg6u6S9Ck4qGNT6DrK2bi17u2wMq51FVbIKBaBQKMjKziIrO4vJU6bwuZtv5sCBA+zcsZMN69ezYMF8/j7vbfLzC6gYUknNyFGMGzuOrJwsMS3+GYQlJ9vrG9ilqeGmkSEa/m81XUUzuWF8Dpf66zp+QyYUAhBT2P0qTKBzF4tfeIF3mw7iNxUx+abbuWVuNfaz13mIk1uX8PZr77B6bxfmkqnc9vXbmVhiQ9u3g1ceepIdqdWU63fy5E9auP1X9zE1/YP/LZVKJWnp6aSlpzN6zBiuv+F62tvb2bVrF2tXr6G+rp5/vvdPsrOzKSsrY8zYMUyYNJGcnFwROBch3NvGkhdfY/7qFewvuofUnct4YekxHHOHcv34nEt+3bgNmUAgiFqjFlPY/SjYfYBlz77A+5oypszMYOeKhbz4yBG8yl9y/9w8FIBr21IWNO4iYeSNfKF4A/NeeZHf9hlI+8VXKGx+kxf3J/HTb97EhAwP3atu46/1n2fyl/P5uGhQqVQkp6SQnJLC0GHDmD1nDieOH2fXrl2sWrmKtatWsWzZMtLS0igpKWbchAlMmjSJgoICFCJwPplSS0rFeLJXvkWbcze7K7/AQ79JIcGSfcm9GIjjkAn6/ahVatTi3qX+EQ7hP7WPzqyb+c4NI8k0womaTPp+/Bsal2zglrl55CMTthYxdk4ZmUUFWNRj0R3czM+27eJkV4iiQC8eyYE9yYzBnIhN4aWv78KDQKVSYbfbsdvtlFdUMH3GDJxOJ7t27mRF9OSGlStW8hfHc+QXFjJl8mQmTZ1CSUlJP35jrl4KXSaVw9t592QQf3oO026aQlHCZ3/duA0Zf8CP+io5PfKqpFChzxzL9TcZMesjRVd7ejGluUns8PkIAqDEllWMDQVKJSCd5oQ/ixkzp1KUpEY76U6+N/9h/vvBn1GsO8TW8B3cf236x/ZiPolSqTx7ekNBQQGTJk/G672H3Tt30dDQwPKGBtavXcvzzz1HTm4uU6dPY9q0aZSVl1++78nVTqFEOt5KmzOP6Tdec1kCBuI0ZMKyHD1zSSMW4/UbBUqdCfN57/H1OukIQuaIcs4cLadUKiDcw5FNdbz+zCtsUo3mztljSNcDVPLlX/yR8XsP4QwY+FZBATmpn/3npVQqsVgsWCwWsrKyGDthHD+85x7a9uxh2bJlNNbX8/tHfscLzz1PVk4OM2bOYGZtLWVlZZ/5cw80kiTh9XpxOp24nS6cTicuVwdOpxtnRwcdzg4kSeKhn/+cjPRUunbs5KC+mq+Munx7YsdlyEiyTMAfRK1WodHE5Zc48MhuDm1ZS1tgLF+6ZTS68/6q79BOtu48hiItHWn5G/zX/W58v3uA6yvs6CyZlI9IR0aJsh9moRUKBUaDEaPBSGpaKiNHj+Kee39EW1sbSxYtprGhnj88+nuef+ZZsrOzmTGrltlz5lA+gHs44XAYl9uFy+nC1dGB0+WKBoYTV4eTjmh4ODs66O7uQZak6Lqxc49QKIRSqcRsMpGVk01YlgmH/ezYvp2+ki9Rabx87b2qrsC+QyuZ93YDe33pjL/1NmaXfXTaSpJ83nBJ9GT6XwjnjhW8t+Q44370a+b8yxFXCdnDqP1CFbO1ak4t/R0/+OlfeWP+tYzPm0SaHlAoL2mIdLEUCgWJiYkkJiZit9sZMWIE9953L3v37mXRwoXU19Xxp8f/yPPPPEtObg4zamuZe801lJWV9fsslSRJeDweOk530NHRgcsZDYrTTpzOaHB0dOB0OvF6vYRlGfnMIywTlsJIsoRCocBkMmG320lJSaGs3I7d7sDhiDzsDjsOuwNHsgOL1YpKpUKlUqHX6wn3tbJ163Eyx1SScRm/tqsnZI7P5z+/9Rf0X76bmYYm/nzX/bj+8jS3F374S5DlM+dga8Ts0hXgO7mdhndXo/38f3LXuKQP/b1CpUarivycMkaNYkjqPFq6eglKV7qlH3Rmj+IRNTUMHTaM+378Y9ra2li4YAF1S5fyzJ+f4rmnnyE3N5cZtbVce911lJaVfuIeRedvNCnJMp3uyLDk9OkOOjpO43I6I72ODufZ3kbH6Q68Xi+yLBMOh889CEP05UwmEw6Hg8zMTKqqq0hOTsFut+NIdkTeOhw4kpOxWq1oNRoUAAoFKJUoFQoU//L4SImZ3PzbRXwtP/uyhv5VEzKuVe9RnzqHd26eRqFhJMcXTWD+8qPcXvjhg+XlM+dgq1RidqmfBTy7qf/bW+yvvpv7a7NQyF0cP3yI070pVFekRLrhKCK1GYBOF+5wAZXVWZgMsW37+VQqFYmJiVRVVTFkyBDuve9+du/axaKFC1iyaDHPPvM0zz79NLm5uYwaPZox48Zis9lwu1x0OJ04T5/raTidHTg7nHR2diLL8rlPolCgOPtUgcFgwOFwkF+Qj93hONfjSI72OuzRXkiy42ywnR8QH/f8UikUNnKKbZ/5df7VgAuZsBQiEJJRaTSolQqQgwQkNSqLA6P7BO2dvaRLhznekUiq3fSRryHJMgExu9TvQt59LHvq17xwcDi3F7bwz3ea8Z/aweY9HrKu/U+qK5w0L1rMNm8mE2eNp8DiYe3CJlTTbuWL04qxXqFlKx/qIcjhyBAj+lySJbq7u+k4fTrycEaGKM7THbicTtIzMuj0ePB0dtLe3s6hQ4d48403AD7QO9BqtZhMJlJTUykpLSHJfq6XYXdE30aDJMmeNGhueRlgIdPNvhUv86c3jjPqa9/hC+OycTW9zuN/WkziLXfz45pneezHD5KhPMLpkp/ym2s/3DWHyPg2MlwSi/H6jdTLoWXP8NjftuFStfA/6yLd+1BQRfa425g7xAacIuDczv89+SjP/iWP0tJyhk69hR/PGUmm6bP915PPr0l8zCMSHB04ndE6h8sV+XNHBy6XE5crUjz1er3R2cjIIXZKpRKVSoVSqUShVKJPTCQnOxtHzQiSbEkcOXKEQwcPEgwFCQVD+P1+wrLMLbfeyo2fu4nyigp0Op3Y+jVqQJ1W4GxexLKmVbz36np01z3IfdN8NNQfRpuoImv67cyutBF2H+GUZCc7JfHjX8fp5L9+/jDHjh7hyaeeIlVsghRTAW8Hrl4lpqQkDJ/wy1uW5Q/MgMiSHNmrORSKvC8k0dfXi7PDidMVKYa6OqKFUacTl9NJp9uNu9ONp9NDKBRCpVKhVqtRq9WRIqdajVqlQqvTYU9Kig5NkrHb7SQ5Igv7kpKSsEd7IbYk2yf2hnft2kX9smXU19Vz+NAhvF4vjuTkyHExtbVUVlaSEC02D9ZbHAZQyMh4vT3ozWGan7qPX64Ikpk9iTvvuYWRWbaL6nKdOnWK//ezn+F2ufnzM09jt9v7rdXCJ5NlmZAkIUkhQsEgwWAIKRQidN7D1+fD5XJGp2IjNQ2Xyx0ZsnR04PF46PJ68Xg8+P1+NFoNGo0GjVqDWhN5rtaoSdDpsNmsOBzJJNkdkbBwREIj8rCTZI88749exp7de2isr6ehvp6DBw/S2dmJLSmJ6TOmM23GDCoqKjCbTBiMxkEVOAOoP6fEbI7UWCqHVqJ8/j00N46jNPPiAgYihd9gIIBGox40494rSZZlgtHACAYDkfAIhQgGgwQCAULBED5fH263OzIkcblwdThxOV043S5cLidej5furi66uroiwaHRoNXp0Go0aLVaNNGZH51OR2pqKhUVFWd7GbZoUNhsNpJskd6G1WaNef2tpLSEktISvn33Xezft5/GxnpWNK5geeNy3pn3d8xmE1OmTWP69OmUlZdjS0rCZDKhUqli2u7+NoBC5owejvWqMel6cR0/TV8f2PQX9wqSLOP3B0Th9yLI0VXSwUCAQDQsAn4/gUCQQMCPPxDA5/Pjcbtxu12RAHG6cLnduF0u3K5IbaOnp5eenm780TOvdDodCQkJ6HQ6dDod2oQEErRacnNzo70KO0lJtrO3BFhtSdhsVqw2G1Zr7IPjUigUCgqLCiksKuTr3/gmhw4dYkVjI2vWrKFpwwbmv/tPjGYjEydOYsrUqZSWlZGSmoI1um4l3gyYkAn5+wjKAU41L6XxdBYTRqfyzpa17DlaSFCrJik9BZP2wn4AkiTh9/vR6cyDuvgWDofx+/0f+fD5fPh9Pvr6fHR1eSNB4XbT6e7E7XZHHy66urrp7e2lr6+PgN+PVqslISGBhIQEEhMTIwGSkIDJbCY9M4MkWxK2aC/DarNitZ55nPvzYFCXkLQAAAliSURBVPqZKJVK8vPzyc/P586vfY0j7e2sXLGC9evW09LSwuLFizDoDYwdO5ZJU6ZQWlZKRmYmDocjboZUA+Sn3cO+1X9nfsMWjqgquP7O2xhVcZLGH8zjxecClJVM4vYvJGHUqriQ1QCyJJ/d6iHe/kPLsvyBkPBFg8Ln8+Hz9dHb24uvz4e3y4un00NnZyedbnfkbWcnnZ1uurxd+KJhExlWatDr9SQmJkbe6vXo9YlkpGdgKDVhiwaFzWbDYrFgtliwWq2YzRYsVgtms1kMSy+AUqEgJyeHL99xB1++4w7a29tZu2YNTes3sHPnThoaGkhMTGTkqFGMnzCBsrIycnJzSEtLu6q3qRggV6BEsKeDIycUlH9pGiOLTJjka/jazYdZcjKNibPHkG3WXVDAQOT0yDPrZK4G4XA4GhZ99EV7DX19Pnp7e6OPHnp7e+nu6sbj8UQenZ0feN7V1UUgGCQYDBIKBlFrNBgNBvR6AwajPvLWYCA5ORmjyYjFYsFqsWCxWjFbIkFhNpsxmc1YLGbMJrPY8KufZWdn88XbbuOLt93GkSNH2LihiY0bN7KztZVHfvMbtFotw0eMYPSYMVRUVlJYWEDmVbi38cCZXZKDSChQKNXnljSHZVBcfIK37dnDXd/6NkOqq3j8iScuazMvVBjw9fnOBkRPTw99vb30dPfQ09tDT09PtPDZQ1eXF483MoPi9Xjwer14PF66u7oJBoPIcmS/Yo1Gi8FgwGA0YjQaMRoNGI0mDAYDRpMJs9mMxWzGZDFjMpkwmcyYzSaMRiMmsxmT0YhWp/vUtguxdaS9nebmZjZv2kzr9hZ27tiJQqGgeuhQampqGFJdRUlJCTm5H17tPhANnF/1Sg0fqrhcQsBApPAbCoXQXOaeTKTH4aenu4uenmhQdPfQ09NNd3c3XV1eurzddHdHZk283q5IkHi9dHV30eWNvF+SZMLhyHJztUaNyWjGZDZiMpkwGk0UFCRjMkeem0xGzCYTJrMZo8mEwXAmXIwYjEYRHHEoKzubrOxsrrv+eo4cOUrr9ha2bd3Ktq3beOnFlwiFggypqmLosGFUV1dTWTWEvLy8WDf7Yw2ckLmMZElGDofRXODF19fno7s7Ggjd3XR3ddHd3Y3X6430Lrxeurq66Orqpqe7m66urkiwdEU/tqfn7MKvM8vLz/QszGYzdoeDvIJ8LGZLtFcRCQuTyYjeaMSgN2Aw6KPP9RgMBnQiOAQgKyuTrKxMZs+Zw7GjR9m9ezet21vZsnkz8956i1dfeYXSsjKqqqsZOmwow4cPJy8/f0Cd3hCXIePz9dHR0UFPdzenT5/mSPuRSC+jqwuvx4OnM1LL6PR46D3bI+k+O6zp6emhNxockWlwNVqtDpPJhNkSKXZm5+RgtUTqGRZLJDz0hkhA6PWGs0VUvT6y2lNv0KPTXaatxoRBKSMzk4zMTKZOm8apU6fYt3cvO3bs4P2mjSxasIC33niDoqIiKs8cFzN6NHl5eTGfFh84NZkL4PP5ovWKaN2isxOvtwuvJzLt2hktgLYfbqdpwwaSkpLIyMzA6+2KFFB7epAk6ewt/jqdDrPZjNVmxWK1YbVasFis2GyR8DCZTGf3Hzkz+6LTJZCoTzw7havVagfUbw1hcJFlGafTyaGDB9m9axcb1q9nw4YNeD1ecnJzKS8vp2bkSMaNH09eft4lTYZIoSD+vhCJpsQLnnw5X8xDJhgIRAIiOkvS6Y7Mmrg73ZGp1+i6je7ubvr6+vD5+s7Ovvj6Is+DwSAJiZGL3qA3IEkSe/fupbS0lGkzZ2A0GLHaIlOwRqPxbHDooovEzl8sdua5IFxt5Oj+NUeOHmXP7t2sW7uWtavX4Ha7ycjIoKS0lNFjRjNh4iSKiopQqT+thxPG59zO8nfr8FTfzRdHXlpPvF9CJuD34+6MhIMn+tbtcuPpdONyuc9uHXhmSbn/zJqP6PoPn89HKBQiITEBg96A3mDAYrFgs1kjy8mTkrBabSTZI4u+zGZzJCQSEjCZTDRv3sxP/v1B7rjzTn760M/OrgWJl8VNgvBpZFnG6/Fw6uQp9rS1sWb1KlYuX4HT6SQ5JYWCggLGjx/PpCmTKSsv/+hrI9xDe/2TPPTYcW54/g/cfIn3GV/Wmsxrf/0r896eR29vDwF/gEAggN/vjyxRDwTO9jhMxsi0qsViITU15ezNa2fuSbHb7ZjNFhISdJF7WDSRDcE10Z3uztwU93HBcfzYMTRaDUkOO0qFQvRMhEFHqVRGbs2w2SguLWHylMl856672NvWxsqVK2lsaGTdunW89NKL5ObmMWly5BaHIVVVAIT8J9n8ziv8Y1EdzUcNpLzzKrqRU5g9OvuiQ+Oyhow+UY9BryctLZWkJPvZ2+fPBIfVakWXkIBGrT5392z0NvwzD41G85lrHGc2StaK/X0FAYVCcXamMzc/j7HjxvOdu77L/n1tNDYup6G+nsf+9w+8/OJLFJWU8NQzT2M2JWLNLEAT8pI2/SvcMXsSDnvaJQXGZQ2Zudddy9Tp01Cp1aiUysjb6EbFV3KocmYvErHUXRA+SIECo8mI0WQkMyuDmlGjuOu7d3PowAHqltVx8tRJtFodCqWGlOwEpB4NlRNqqSpMueTPeVlD5syNc7EmSRKyLEJGED5NZJmFnpSUFKqGDo3UQhMSAB++jjbaT2cwsfTSAwbidJ1MMBhErRJbbwrCxfhAByEYoLN1P+2Gcko/46m+cTnd4vP5UKlV4swlQbhEcqCb/fsPIhWXU/IZf1fHZcgEAgFUajUa0ZMRhEsSCnVx6OgRFKpOtr75HG+t77jk14q7kDmzUZNapboqd1UThAFBoUARDODd3czB9Gu4dazjkl8q7moysiwTiG69KQq/gnBpNMZC7vj9Um4xZpD88QeDXJD4DJmAH5VKhVb0ZAThkiiUKgzJGVyOQz7jbrh0ZntKlVqNWqz0FYSYi8OQkc6eVKATPRlBiLm4CxlJOjdcEoVfQYi9uAuZsCj8CsKAEnchI8ky/kAgOoUtQkYQYi3uQiYyhe0Xi/EEYYCIv5CRZHz+yJlLYqsHQYi9uAsZSZbw+3yi8CsIA0TchQxAKBRCDsskGj7jUkVBED6zuFvxazFbuPOrX8Hv86G8xMPhBEG4fGJ+WoEgCPFN/KoXBKFfiZARBKFfiZARBKFfiZARBKFfiZARBKFf/X/zIeaNz4EHGAAAAABJRU5ErkJggg==)
Intersecting lines r, s and t are shown below .
![](data:image/png;base64,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)
The surface area of a cube is 6(a/4)2,where a is a positive constant. Which of the following gives the perimeter of one face of the cube?
The surface area of a cube is 6(a/4)2,where a is a positive constant. Which of the following gives the perimeter of one face of the cube?
![table attributes columnspacing 1em end attributes row cell y equals x squared end cell row cell 2 y plus 6 equals 2 left parenthesis x plus 3 right parenthesis end cell end table](data:image/png;base64,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)
If (x, y) is a solution of the system of equations above and x > 0, what is the value of xy ?
![table attributes columnspacing 1em end attributes row cell y equals x squared end cell row cell 2 y plus 6 equals 2 left parenthesis x plus 3 right parenthesis end cell end table](data:image/png;base64,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)
If (x, y) is a solution of the system of equations above and x > 0, what is the value of xy ?
![](data:image/png;base64,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)
In triangle ABC above, side AC is extended to
point D. What is the value of y-x?
Note:
It is important to know the basic properties of a triangle to solve such problems. The most important property to remember is; the sum the interior angles of a triangle is 180°. This is often used in solving problems in geometry.
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)
In triangle ABC above, side AC is extended to
point D. What is the value of y-x?
Note:
It is important to know the basic properties of a triangle to solve such problems. The most important property to remember is; the sum the interior angles of a triangle is 180°. This is often used in solving problems in geometry.