Question
Identify the equation of a line perpendicular to the line x/2 + y = -1
- y = -
x - y = - x
- y - 2x = 0
- y + 2x = 0
The correct answer is: y - 2x = 0
Hint:-
1. The slope of a line can be defined as the change in y coordinates of any 2 points on that line corresponding to the change in the x coordinates of those 2 points. This is generally referred to as the rise to run ratio of the given line i.e. how much did the y-coordinates rise vis-a-vis how long a distance was covered by the x-coordinates. Slope = m = rise / run = y2-y1 / x2-x1
2. Slopes of perpendicular lines are negative reciprocals of each other.
Step-by-step solution:-
x/2 + y = -1
∴ y = -1 - x/2
i.e. Y = -1/2 x - 1
Comparing the above equation with standard form of a line i.e. y = mx + c, we get-
m = -
…...................................................................... (Equation i)
Now, we know that slopes of perpendicular lines are negative reciprocals of each other.
∴ Slope of line perpendicular to the given line = - 1/ slope of given line
∴ Slope of line perpendicular to the given line = - 1/ - ![1 half](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAJFJREFUeNpjYMAP1IC4FogvMFAIFgNxGhD/Z6ASGDVo1KBBYdB/LHgUDCbwn0w8CgYLsAbiNUD8CYh/QaujaHIMOgjEkUDMA+VrAfFRqBjFQB6IL1HLyz+oYYgl1HsUAQ4gPgmNBLKBIBBvAGI3SgxRghqiQokhGkA8G4i5KDFEHIhXATELpYG7BeoimhZyWAEAI3M1I31CbrEAAABidEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtbj4xPC9tbj48bW4+MjwvbW4+PC9tZnJhYz48L21hdGg+ND6jrQAAAABJRU5ErkJggg==)
∴ Slope of line perpendicular to the given line = 2
∴ We need to find the line from the given options, whose slope = 2.
a. y = -
x
∴ y = -
x + 0
Comparing the above equation with standard form of a line i.e. y = mx + c, we get-
m = -
≠ 2
b. y = -x
∴ y = - x + 0
Comparing the above equation with standard form of a line i.e. y = mx + c, we get-
m = - 1 ≠ 2
c. y - 2x = 0
∴ y = 2x + 0
Comparing the above equation with standard form of a line i.e. y = mx + c, we get-
m = 2
d. y + 2x = 0
∴ y = - 2x + 0
Comparing the above equation with standard form of a line i.e. y = mx + c, we get-
m = - 2 ≠ 2
Final Answer:-
∴ Option c i.e. y - 2x = 0 is the correct option.
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(i) the shaded portion and (ii) the unshaded portion.
![](data:image/png;base64,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)
In the figure given below, find the area of:
(i) the shaded portion and (ii) the unshaded portion.
![](data:image/png;base64,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)
The shape of the top surface of a table is a trapezium. Find its area if its parallel sides are 1m and 1.2m and perpendicular distance between them is 0.8m .
The shape of the top surface of a table is a trapezium. Find its area if its parallel sides are 1m and 1.2m and perpendicular distance between them is 0.8m .
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)
The figure above is the floor plan drawn by an architect for a small concert hall. The stage has depth 8 meters (m) and two walls each of
length 10 m. If the seating portion of the hall has an area of 180 square meters, what is the value of x ?
Note:
There are different concepts used to solve this problem. Another concept used which is not mentioned in the hint is that the perpendicular drawn from the vertex of an isosceles triangle to the
base cuts the base in half. This property is also applicable in equilateral triangles as they are a special case of isosceles triangle.
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)
The figure above is the floor plan drawn by an architect for a small concert hall. The stage has depth 8 meters (m) and two walls each of
length 10 m. If the seating portion of the hall has an area of 180 square meters, what is the value of x ?
Note:
There are different concepts used to solve this problem. Another concept used which is not mentioned in the hint is that the perpendicular drawn from the vertex of an isosceles triangle to the
base cuts the base in half. This property is also applicable in equilateral triangles as they are a special case of isosceles triangle.
The area of a trapezium is 34cm2 and the length of one of the parallel sides is 10cm and its height is 4cm. Find the length of the other parallel side.
The area of a trapezium is 34cm2 and the length of one of the parallel sides is 10cm and its height is 4cm. Find the length of the other parallel side.
In the figure, ABCD is a rectangle and PQRS is a square. Find the area of the shaded portion.
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)
In the figure, ABCD is a rectangle and PQRS is a square. Find the area of the shaded portion.
![](data:image/png;base64,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)
A cylinder is surmounted by cone at one end, a hemisphere at the other end. The common radius is 3.5 cm, the height of cylinder is 6.5 cm, and the total height of structure is 12.8 cm. Find the volume of the structure.
A cylinder is surmounted by cone at one end, a hemisphere at the other end. The common radius is 3.5 cm, the height of cylinder is 6.5 cm, and the total height of structure is 12.8 cm. Find the volume of the structure.
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hvQpbEVNZHwY32G9xov0E0GqW7v4/uru57qgu/eu0a77/7Lj3dPRiNRgqKCqmsrKK4uBiHw45xgS0qcb9oEnZ/yXK2lhuwWa1M9Ayw4qmnyc8KIZHi4J6jxKejWryN8IA9tmIF6zds4MPde6isqmTp8mWYv0Dre7yujn0f7mV8YhyHw8Hi2hqqqxcRyY5gs9nQ60WJ01zS5NM1u718NDa6YV0NJw68y/aOfoYGe+hPhtBbHFq8jfCA5eTm8Ju//Vus27CeYChEZUXFrANm09PT7Nm1i/oT9aTSKQKBAGsXr6W6pga/z4fFYhGzHe8TzS+lmUUVFAyNE0tK2F0Bnl62loygb9bX3Zzu/Kn/CUgQm4pitokJM/NBcUkJ+QUF6HS6Ow6a9fb18d4773KlpQWDXk8kEqGsvJyKygqcLteCrSl/kDQI+81EfkQyUbFkJYWVtSjIWCxWDPrZr9ySFOe9n/2c1r5h4tj5yq98i9KwhxN7P0Cx2OjsnuDJLevx2e88OUeYW7IsYzQaP/ffm5ubeO+dd+nv68dmt1NZVUllZSUFBYUzj86M4tHZg6JB2CWu1X3AkL2YsuI8nGYdBqMJg/ELDrIkO+mPWSmuzMGgN+C2WZnqPMXes+0888zjJOv3sf9UJptXL8Jh/NTFQ2Xeb6r3qDt44AD79+5jKhrF5/OyctVKqqqrCWdmiqms84Qm3fihG9cYKSrEbtZx7WorhUX5t/5temwQg9V5q1rt86Q7rjM8HSfdNcCydY8Tcpo4tXMXKXs14ewiLMU+flB/iRWVRTgCn2zdTSYTdocYF7jf4tMx9uzZTcPZs6gqRCIRSsvKqaiqwOVyfeEBt3feeptTJ+sJZ2by/V/7NeyiF6cpTcJesnYrFy838eO/28nRujOEMkIzNeWkae5J8ed/9s8pyo/c8RhpazarHvMTH77B2z/+f0j8xh/Rdq0DW85KjEYd/qCfvg97ScTjgJ2R0VGuXrlCKpmksbGRWCyG2+MBVCxm87zfUfNhoioqsm7mlsxqszI1NcmJ4/WcPH6cvv5+QqEg5RUVhMOZyLLE1StXUVQF9S7rFQx6A23tbfzkRz+mpaUFi8WCoqhUL1qEXj+//46qOlORlxXJIisr6xM7Gs83mpyZO6uAkmQCVdXTNxSltKKcjJAfHSmkIxcw3sUfzBgq4TGfgqSWcfXg65xtaseqSDMLDigzs7cMJgPSzZFbnSxj0BtAVVFVhenp6MwFRiffLDfUg9iJ5t6pM5+eTq/D5XKRTCQ4cfw4+/buw2g0khWJUFFVyfrA40SyIzjsTnQ6GZipH5eRQTf756+qYLXZaG9to729nenpaTo7Oujq7KR60SIMBiPz9+8ooaoKsizPnOc8L8jR7DLkzy7CnVnAosVVnNi/hz3vHUWxZrB200Z8gdnLYAY62zAFC3Ca9GANk5fhJs+5nL/de410eiNN5xspr9qA3THTtbPZbJSWlqKi0tzUzKKaxWRlZiLJMiaTSVRCfUl6vR6TycRUdIr9e/ex98O9JOIxyisqqKisoKy8nGAwOPNZy/LMRVdR7imWBoMBi+Ulrl67xv59+ygtKWHzls3U1tag0+nn//ZhNxdSme/jEpKqcXX/+f1vUd/ciWS0YzUbiOs9PPf0WvyeO68R13n+MPsbbuDPjGA2GFm8pAa3foJfvPo+7lCI/s5ulmx8lor8DPSfyvEbr29jxaqVRCJ3vlUQ7t7ExATvvvUWZxvOYdDryM7JobS0jMrKStxeN0aj9hfUSxcvcu3qVYKhDBYtWoRVPG7VlOY3GNcGkqzZ+Ay5OVlYzCb2bHsdKREF7hx2X04x1QkzOqubvNxsHDYzYOGZLU/SNzpJUVkNuZHAZ4L+EdGOa6OjvZ3t27fT1to2sxpQVSUV5eUUlZTgcDjmtOqsvKKCktJSZFme963kw0jzsLv1US5eamQ6Okli8Dr7zlynePkaZptWY3aFqFrsQ5VkDB+7x3eHsrH700iyDt3nbBChzv+O3rx3+tQpdry3g+GhIUKhEGvWrqG8opLsnGxsVut9GXiSZVnMpptDmv8Fa1as5XjdMT7ccYZYWqZixVrcXs+sr5MkCf3tWg1JEnOm50haSbPz/Z0cOXiIVCpJJJLNsuXLqKysnLkfN5tF+B4hmqfIk1XAyrUGMnJLUIwOCgrycDtEqeJ8MjI6yvZtb3Dx/HlMFjMFRYWUlpZSXl6O2+O54ww54eE1B02mhCeUjdOfCZJ883GMMB9cv36d7dveoL29DZ/Px7LlyymrKKewcGYqq+hBPdrm5q97cy13YX6oO3aMD97fycjICJFIhI0bN1FeWUFWVpZYBWYB0TyRl+r2kPBVkS3f4Ce/2ImlcDXfenYdPqfoyt9PyWSSd995l6NHjoCqkpefz5p1aymvqCAQCIi5CAuQ5mFv7YuzpkThh//bP6IUrMStTCInpwER9vthaHCQN15/nfMXLuBwzDw6Ky0tm1mV1e3GKBZsXLA0D3uGI8VP/vtf05QM8/3qbI4ePMP4xHI8vi++wuxHxbPRiSmsjoW7++bdaL58mbfeeIMbN24Qzgizbt06yioqyM/Px2qzoRdd9QVP87BXLluDLZDLi5lF5PhtOC1O3G7XXb8+0X+eV/b38MxTawh47Rx49010LhetbcNs+dpmgi5R3fZxBw8eYNfOnYyPT5CfV8Czzz5HWVkZ4axMzOLRmfAxmoddio9Qf3gfVztfJZ1OcGPCxl/86e/jct/NlsrTHN61i131Eo8/vprp9mMcbh7kxecX03fuMB+eyOe59bU4zQu7nj0ej/Hm9jc5dvQYBoOO4uISSktLKS0rx+/3YzSJR2fCZ2ke9m2/eJO0LciqdZWYDVB/vh3zXezPDnD64DEsZiOyEWSdjgtH94KzlmBmHqaSIP/36UbW1pTgNH+ydTcYDNgestrns2fO8PabbxEIBXnppRfJCM++/vrgwABvbt/OpYuX8Pp8rF27htKyUgoKi7Db7bcG3OqOHmPHjh3k5eXy1a99jWAoNNe/jvAQ0H66rDeTqqeeIS80M0G2rPgaXvfsXe/BlpNM2nNYGkjibOzGZDLR29WNNbwavV7G4/Uy0N9NMpEAIBqN0tvbi5JO09Fxgz2799y6XYhEIhgMhvuyg+cXoTKz0EZnRwc/+od/4NjRY5jNZkaGhnnhpRcxmc0zSzOrKjqdDrvdjizLXL16lQP799F4qRGLxUJhURHl5RXk5OVitdro6+2lR1Uxm0y0tLTw03/6Kcfr6rCYTExMTPDU5qcxmUyoyvz6PB4JqgqyjM/nw+PxzOvbJs3Dro5d5b/+x3+HzmDFKCW4OmLmr/78jynJv3MFU92hw7QmXXQk2ulo7GP34UWY0ippRUVRIJ1KYrb88h40kUgwMDBAMpFgdHSM/v5+bLaZiSGyLGOxWOZf2FUVu93O1StXOHvmLFNTU4wMD3P69ClWr11za5NCl8vF6Mgo27Zt41zDOWxWK5lZWdQuWUI4I4OMzDAmk5loNEp0amqm5l9VcblcXLxwgUsXLxKPxejt6ubC+QssWrwYq9V6T2u8C7OTJAmL2Yzb7X7Qp3JHmofdn1fBU9nLcHu8GKUUh042YTHN9jYqizZspTCth7b9bDuXJj8rQK5nDXveaUFJb+RiwyWqFj2NwznTS7DZbBQXF6OqKldarlBYVEgoGELSybhdrnk7UcRgMGC327lw4SIv/+xnBEJBtj77LDW1tXi9Xrq6unhz2zYOHzqC3WFn3fp1VFVVkZ2Tg91uR6fTIQGKqn5mnMJgNLJ5yxauXr3G66++Sl5hAU9u2khlZSVGo3HeXfweGZKE9SFYElvzevZYIoUcG6SppR29J5eI34zD4UCW7xw+VQVJmaJuxza21XXy3Ne/xdpyD++/vRPJ6mB4aJyVm7ZQnB34zN5xb7y+jZWrVpKZlfXLX0zLX0pL0sxKLu1t7Vy+fBm/30ftkiX09vbxxmuvceHCBcLhMBWVlZSWllJQWIDd4fjkxUv9ZZWfdJtjX7t6jStXWnC6XFRUVOB2u2e+iCLsc0KFh2KCkuZhH205zA9e3ctkEgwohBY9wUubV+Fz3MU64WqS3s4uxqJxXP4wQZ+T6FAvg2NTYHaRFfTedlnqN17fxsrVq8j6WNgfFucaGnhr+3Y6O7spLCyksrqK0tJSItkRLGYL0ueU9d7JR916YN63NsL9o3k3/mRjD4uWryKUEcYgw7UrbTcXr7iLsEsGQpFcPho7lgC7LwObRwFZ/tzWWkV96Lqo7+/YwZ49u0kl05SVlrJm3TpKSksJhTIwGg1fqqWQJOmhaGmE+0vzsA8MR1n/lc1EAjMj4ycPHiI6MYn3LmfQ3e5LKj0irdPk5CSvv/oax44exe12s2jRYsrKyiguKsbt9YiqM2FOaf7tWr+qjLf/4f+kua2H4YkYxY9txeCY36OUc629rY3XXn2NxkuXyMnLZfPWLZSUlpKXl3fr8ZogzDVNwq6q6q0WOVK+km86Q1xv6wCTE7PJhNO6MGd0nag7wVtvv8lAXz+lZWV86zvfobikmMzMmamsoqst3E+ahF2SJN78u78mtOHbTFzYxaH68wxPJjDpVS4Pmvlv/+l/pqw4R4u3eii889ZbfLBzJ7Ksp7K6ki1btlBUXEwwGJzTBRsF4U4068aXP7YeT6aPxmse1m3cgsXmwKhTOXWhDaf90d+xc2x0lNdu3o8Hg0FWr1lDWXk5+QUFuN3uefvcX1g4NAt72dKVAISee+kTO2OUlRRje4Qr1a5eucprr/6C5uZmCouKef6F5ykpLSUnNxer1Sq66sK8oUnYuxuP8M6uo3QPTvxydxBAR5Lrw0b+w7/5PQrz7m7xikQKjDfP6qN69smxCezz7IJx5PAR3npzO6Mjo1RUVfKrv/ZrFBUXEw6HMZm+4A62gnAfaBL21Ng4ztwSsiscWAzyra25DHoJ+9krmO6i6k0Za+fdD0/S3nSW6dBy/tk3NxNwWfjgtVcwBfxcaenluW98lUzv3dfGa01Jp3lz+3Y+2LkTs8XKosWLqawop6CoCL/fLx6dCfOaJt9OV04pi90J9Do9H3+KZNTruHq9m7tZYDaa1FFRu5xVi9z84X/aywub12AZOMHx9im+tXwt403H2F3XzPNPLsNt+dTFQ2VO9/4bGRnhtVdf5cihw2RGstj41NOUlZWRl5+H0+kUj86Eh4ImYR9ubWD7voukFBmTfmammwoYdCrHGwdZtW4t4VmOYXZnkG0eZdcrJ1n6+AbC4QDnX96Hwb2SQCgbS0mYvznexBPLynFbPrkQhqyTMRq1H+VuOHuW1199jfb2dgqLiviV732PkpISsiIRzGbRVRceLtq07KFinnuxHIMsYb65m6UMyDqJFe1dhAOz7wij1+uZmIzi8gdpefsdzq9aSkdXP5ZcMzodOF0uRoa6SCWTACiKQmw6hqqqTI5PcO3aNaamosiyhNvjRjdL4c1HVLhVP261WonFYhw5fJid7++kuamJ1tZWEskELreL2toa3B4PqVSSyYnEvX9gwiPlo3UKDIYvN815rmkSdm9hFWNXmnBm5RHtv0Fvby/xZBq9LHHh0nWKi4pwuWZflsrlC7H62e9y4eAurrT3YTaaSKZSKAqkkgksdhvyzUdYw0NDNDQ0EI/HaWlpoae392Z1nURGODzrKqofhdxkMmG1WhkcHGTPnj3caG8nNzcPFbh8+TKpVApJlmhubOLY0aPY7XZSqdSX/9CER4KqqsiyTFFJCfn5+fN63EabM5Nl2i6cImQNcXn/LtpHY+hNdsx6qD/TztNPPTHrITovX8SUVULALhG35rMk4iI/sI4/f/UySmoT585cZHHNczhvjso7nE6qFy1CURR6unuorK4iFAohAUaTadaSTrPFgsVipampkVd/8QrHj9ZRUlbKd7//PSorq25ugaTys3/6KTa7ja3PPcuSpUuxWCwoiqLJxyY8GiRJurXWwHymWYnrUE8nJneQ0b5OjBH4v0gAABZ7SURBVDY7ZpMVg16muamZopJiHI47Pzq7cXY/7x9twpedT25OLpUVJdj0MT548z2mZT1jk2nWbXqK/Ewvnx4O2/b6NlZ9wRLXCxcv8OrLr9De1k5lZSVLly2jsKiQrEjk5qMzlba2dhovXcJkNFK9eDGBQGBed9ME4U40r2dPT3Ty3rt7uNLRD2qay70p/uxf/haFeXdeUDE+OUJXzxA6i51wRgDjzW2bp8eHGB6fQjY5CXqdt907btvNxSsikcis57dn927eeH0biqKwuKaGxTU1FBQWEAqFbntlVhRFlIwKjwTNbzBe/vt/ZMoapLiiCrtJx1R9M4ZPLy1zGya7h4Lizw7kWZw+spyz7O5+myWaPm56epptr73OBzt3EggEWLduPeWV5eTl5eHxeu8YZPFYTXhUaB52oz3I8i3PUZYz05KXl5Xi9c/tRBiL1YLD+dkBwI6ODl75+cucPnWK4pISvvWd71BSUkx2Tg42m9hhRlhYNO/Gd554ix++fZzBsSgGOUnrpJ3//d//MSUFs3ex70Vfbx9//V/+C5lZmfz+H/wBVouF06dO88rLP6evt5fqRYtZvnw5BYWFZGZliqozYcHSvGXffeAMmUXlrCsowGHWc+xUIzbz3DyOSKfT/Oe//EsOHjiAwWigra2NsdExLBYLS5Yu5evf+Ab5+fkEgkHRHRcWPM1TGMkvp2jDVgpCM6vT5OVk4fTMTTd+ZHSUk/X1jI6MoNPrqTt6jH/xR3/I8uXLiWRnz/t1vAXhftI87PG+i/zln7wLegsmOcm1CSf//a/+DeVF2i9e4fV4qF2yhM6OTqbGx/nN3/4dnn/hBTye2WfsCcJCo/2WzeWr+PWqTVjtDox6mfrTl3A77rwbzL2SZZn/5X/9twRDQUpKStm4aZNozQXhc2gyQNd39RJysIiA00Q6kUD+2BzhVEpBr4/R2NJPTiSM3XrnApJYUsVsmHntR/Xs46OjOO8Q4tdffY2Vq1eRnZ39ZX8VQXhkadKyB3Kz+OCNn9MTt7F01WqqSrLRA6npUc7XH+Vwww0e27gFg/HzF55MDl7h1fcOcvX8aZLZ6/nj3/gaQbeVt3/2j9jDYRobO/jad75Ojv+zoZdlGVlMehGEO9Ik7LLBzcont3Lt8kVO7XqNN37Uy3QijdnupbCsinVPPklJYRZG/ecHsmc4zmNrNrBu3RL+6k//G81b16F2H+Z0j8L31y8mdvU4u45c4utPr8Bj/eRpq6hzWc4uCI8Eze7ZvcEwDqeTSH4x4xNTJNMqeqMZj9eP3+dCN0vLG4gUYrJYkCUFo8GA1SBz6dBhLN61eAMZLCrJYsehZp5eWYXH+qnR/TlevEIQHgWaDtAZzDbCEdusC1XcjsU6s0Zd+9Ft5D/1NXLDYQ73DWCMGJAlsNodjI903ba81GQyYbXNzSCgIDwq5lXxbWqwiVP9dl54bj0Bq4TDaSOeSKIokIjHsLmc6G7WC3d3d3P08GGmp6c5c+YsLS2XcTpdSDLo9QZxDy/cF+rNhU8WLV5MeUXFvJ6hqX3YE3288tMPqNy4hXJvku5pB0HvzYUo7yA1dIUfvXaQUF4pwy0Hab9eTNmSVWx7s4VUeiMNZy6xZMkLuG7Ws/t8PtasW4eqKMRicRbX1JARzkCSQEL6xHLWgjCXJEnC5XSin+f17JqHfeebu5joaqJzcAMVeXkc2fZPPPH0JiyRO5e4XjrXwOjIENH4Oa4notQ+XUVG5Vf4lYH3OLJrO1P+VWxdVYHbMnPRMJlMZGbOHNPv95OdnU1m1p3fQxAWMs3DPqlYWfNYIQN2H3omOXrwGDXLHyNzlrAX1D7Br5avQVFUFBXc/hAGo55VG59mbCKKZHbgdVpvu22zoiooqlg9RhDuRPOwb1pfzds/+X/Z87M/4m+GesiqfQZnMDTr6xweP7dby8ZodRKwzr5+nSAId6Z52D1Zpbz4+/+e1T29JNEjGS343aJ2XBAeNM3DfubDbRw5c4Xx6SR6nURTd5x//69/n6L8u18fThAE7Wke9s6eEbLzC7G6vBiVYWLnJjAaFub+7IIwn2h/z/7S97Baf7mJY9PZ/wMSk0BA67cSBOEL0L4bv/Nn7DxygfEEpKcGaRn38MQ35tXcHUFYkDRPoWoJsOX5l7A7XUiqisOfSXbYr/XbCILwBWm+MNuap54ikuEjGZ8mlUpw+NAhRkZGtH4bQRC+IO0XnPzJ/8XR1imcHg92Axw6183qlY8RCs7Wuit0XWnibEsvq9atwOe0AzBw5QynLreBu4QnHyvDZBS3BIJwLzRPzo1JM1994WkKCvLRyxJP9g0QyQzexSslDNIAr7yyg4Lyspmwjzbzg7dO8+LzT3H23R9zwPw91tcW8+nt2QVBmJ3m3fiSsJXGy1c4fuIUZ0+f4v3dhxgZm7iLV0oEC7NRYgmUm2Ws5w7sIG71EcjMpabIw8FjDQyPTt32tYIg3JnmLfv05CgDw6NMjY1gMcD5xnaem47d3YslM0a9bqZqDWi9chVXuAadTiIYCtF5qJtYLA58ckaeXq/HYrHc5oCCIHxE87Cv+/pvUjk4gsnuwKCTWfPk5F12428vnZ5ZckpBRZKlW214d1cXR27Ws58+dYptr72GyWRCr9ezZOkSrFYrirab3QjCZ6iKgk6nY3FNzcKrZ+9s2McPfrqLx3/n3/JcjYu6M9143F4sZvNdvFoHknxrp9bikmKOXh9GSasM9HWTl1+C+WYL7vP72fDEE6hAKpmiuLQUf8CPJEk4HQ5kne6Omz0KgmYkCYfDgV4/vwePNT+75iEjLz1RwaTehGz0cXH/B5TnBQn4ZtsVJk3L0YO0XjnHzsNniGSHqXzqm3j+8w84ut/C+fpxnv52NQHPTNhNJhOh0Ew1ncfnpaS0hIyMDK1/HUF4ZGge9my3jraeMboazzN6+hccujLEM8rddG1ksiqf5O9/WoPdF8Cil8EY4Xf+4HcZj05TXVVDViQTw23G4hRFue3adIIg/JLmYV+6YTNWs46Oow00T8M//+PfJT/vbireJGzuAKXuT86h94ez8CqK2JhREL4kzcO+Z8cOMkuq+P4/ewwkHS63C7385R6NiaALwpenedhTiQkunTzMBYONvIqlLBV7rwnCvKB52Fdveg69Xqa3rZFXfvCX/A+1mP/wp79DQUSUuArCg6R52E/veZ3d++uYNPgprdzIv1i1ksygaN0F4UHTPOz9w9Os++p3KSoqJBgK43HczfN1QRDmmuYjX5u3PE5X82WmdXac8ihXOgaIxtNav40gCF+Q5mE/erQBQ7SLrqEo2DI49M52hvt6tH4bQRC+IM3DnjK4WF6bh042Exvv4sTxs4yNTd7z8TobT/D+e9t5d/8ZotOJz/kpSdS9CcIsNA/7048vpuHiNV7+2z/j29/6bWxlS3Fn3Mu+rqAMnueH756joHw50YY32XfuGlO3mSgXjU4Ri8dRNZ4Ln0wmaW1tZXh4GEXRdseZRCJBV2cn/X19pNPa3uYoikJHRwe9vb2aHxvgcnMzA/39mn8mAOfOnWN8fFzz4wI0NDQwNXW7EukvJ5lMcv7ceaLRqObH1pLmA3TWQD6bv/eHLB8ZRtXbGO3vx2W6t2tKw/6dKI4SAuFsFhcH+NGx89QU5WDzf7LEVVUUkonPa/XvXTqdprOjA0VRcLlmm9v/xSSTSXp7e7FaLHg8HnQabgqoKgrdnZ3YHA58Pp+mxwa4dvUaaiF4fT5NjwvQdOkSfp8Pp1P7XYAuXbhAJCsLm03bTUvSqRRNTY1kRbKwWufv1uHatexKjHPHD3HwxAWs3kxKKxbhS3fw8pt76B4cvadDtl2/jtPpRJbBHwzS09lDPHb72vh0Oo2qdUujKKRTKVKplOa9BvXmfP5UOq35sRVVnTl2KqX9Z8LMhSo9B+cNMz2eueiNAMTjcdJz8HmoqkoikZiTz0NLmrXsO3/4t+xvGSQ5Ncnl688i957l0KlW1n/91wllzL7X221PTq8jlVJm6tmVNHqjHunm1NmP789+qv4kr7/2OlarFYPRyPr167DZ7V+qmylLErHYNBfOXcDpdlFYWIher9ekRl4ny4yPjXO5pQWr1UJJSYmmx45Go7Q0X8bucHAu/yyyTqfZF9FoMHD65Cmam5o4dTIDWZbR5MiqitlsZu+eDxno7yd4s6JRi2NLzCxwsu31bYyPjxMIBDQLvSxJTE9Pc6WlhU2bNmlyzLmiUdjHGDQU8J3vPk92lp89P/kbLkb9/Paf/BlVxVk4zPf2NqXlFRxuGiSRSNLT1UlhYfWtDSh8Ph8bnngCWZZJpxW+/d1fwePxoAJut3um6/olvuCSJJFMJPD5/ITCYXJzctDp9ZrUyEuyzPRUlNyCfGxWKwWFhRgNBk0CKUkS6XSacDiM3eGgsKhIs2MDGI1GUskU+YWF5OXnfenP+eNMZjN9fX2s37CBjIwMTVtKk8lEV1c3GzdtIpSRgaJR70GSJOKJBCqgn8cLV4BmYY8BMpNjo4w5TcRNfpaUlOOzqmx7dTvPPbuZcPiLt+6lT36djJN/T/3hD7h4IcnT36nE756ZpGMymQgGZ1bAcblcFBcX32oNtJJMJPD5/WSEQmRmZSFJ2o35T0ejDA4PYbNaCYfDmi58oCoKfr8fu8Oh+bEBXG43fp+PzMxMTT8TAI/Xiz8QIDQHaxMEAn7CmZn4/druY5CIx7HZbJp/FlrT6FtgpufyKc7UH8LitJFIJDB2DXL++AHqmsdYs2494XsZkDdn8Ou/91tMRmPUVC8lIzN02xP2+rxzUhmnqCpOpxOj0Yhyc/khLdmsNkwmk/bjAYDdbsdssczJfaTX58VkNs3JZxIMBudsaadgRobm5wsz9+xzed5akVRNvg1jnD11A7vDisk8c1+tKiqyLHH16nVqamtwu+99NFtVZtaf+zzRaBSTyaT5H/KjgRedTqd566iqKslkEkmS0Ov1mrcKiURi5l7VYND82NFoFIPBMCdf7qmpKcxm85yEcnJyEqvVOicNQ3RqCrPFMq/LsTUKe5pUWkav++yXSkklkXQ6JGnuPgQVFVSJed6L+gxFVZAkWfMJQaqqoKoS8pdcR+C+u/lVVFQVSZLmpFusKgpofGxFUZAkCVUFSWLeduc1CvuDM3DtLPVNnUynbWx8ciUeh1bPOVVGuq9x/mIzlkgNi4qzMN9uTax7kqT14il27T2BLauUzZs3ENTsvBM01h9h75EGcqpXsmHNUtxWk0bHnqGOt1F3eZyc3FwyA05kTb7cKkc/eJvLbd2MR+HxF16kMi/jtsuQ3auhG43Un7tCVvkKyvNDGG7TOH0xCr3Np9h55ByxWBJJr8ebu4itG2pxaPyZa2H+9jnuRqyTv/vJbnKLKglFz/PGvnMMTyU1OriEkozRXL+X89d7iae0uyb2dt6gvS9OzaJi+ptPsO3944xOxjU5dldrOzp3FssrQjQ3HKf+4g1iSW2fLR9863Xe3LGPnpEpVFWrNHbS2hfHl5FL9eLFhD02vnQWP+bUjp/w6r5miquWUpzt+9KrJwGoqRQ3rrVg8IQoLi0my6UwlZRJKfOzZZ/fa9/OouvMIfpkD+5gmLzqAn744xM8sbQEr02bmV02lx+f08Swomq6Br03kMkSVxinYZzBnm7ODI4STySBL98a+MMRMkwWrgxcIysDQn73raW5tXDt0nkm41Ekc+hmr1tFkx15ujtwRorJzvCQGwnidlo1a4lGmnbzSt0gz39lCeFwCItJm7EGSWegYs1WygxWdEqCozsHWFObg8Nm1OT4WnuoW/auG22YnU5kWcbu8TPS300yfpe7z9wFWafHaDRo1E39JaPJgtNhZWJwlFQaltRWYbdp0403mS0M32hk9+4PqT9/jbHxCc2eg091NNAxruIOhHFaDDfHBjQ5NGnJCVNd1O95mX/9J/+Oww3XSWh07IM73iGlpLl8Zj9/8of/iv0NbSQ1ma0jYXf7cNospMfaGDRm43M60c/Phv3hDrveYCCdSM90JZUUOr3x1gw7LaiSBEgzTwK0HnRJT3C9sxspUMnK6hxs91g/cDvujHy+/4d/QJYNGk6cZGpKmwKNXfvqudp4nvaOTjqvXKKppZXxqDa3H7pgCY9vWMc3f/X3WBEc4mxDEyPj2hy7tfUGNaufYOs3foNNpTp2HTjJ4Oi0JscGSMYmObj3OOWL83A65+/c+Ie6G19QWslkXTPT0xN03egkt6QEi1W7Igc1lSIRTxCPJ25OvdUokKlJGhsaaB2SWFSZjTI5xJgxiMNk+NLvkE4mUdHj8QcIZ0dQLU5kTZ6EpFm27kliikzf6UFMHRIOhx2TUZtHZGlVwmKxYTAaCAUjxLOCGA3afD0zMzPoHpvE7nRQlJ/FxUEL2m0GmqK7+RhX4gGWuTyaDihq7aEOu7tiA+szGzh1oo7BK+187ZlvEvRrVy010Hmdi1c6GB8/y/CKcrw2tyZfkWsXTvHjH/yIoZSRd94wUFS9gt/+9ZeQNbiXPHtkF0frG3EEAoTySqiursRm12JpMJmcgiJQYnTUpRkdGiAWi5HWaDDq6pE3eb+hj2AoiLlwI+uWlOK2anMh2frd3+K//nA3Bz6M0d9j4bnNi2/NxPyy4lNj7N5xmNqv/ipej12TY86Vh/7R2+RwP6OT00iyHn9GBia9dpMx4tEJBgcHUfRWAn4fZqM218bpyTH6+vpJI5FMqVjtLjJDPvQanPvE6BDDo5PojCZcLhc2m0XjezWV8aF+hifiOD1eXA4bOg1GtqdHB+gbGsdstWF2uHHZTBo+r07R291PSgGdTo8/6MOg0aSddDpOT8cA3swQVuOCmEH3gH00m0EQhM/1UA/Q3SKCLgizejTCLgjCrETYBWGBeKhH44XZqYqCoqqo6swGmZKkoqoq6bSKLMuazq4T5jcR9kdcKjZOS9MlWrsnKaiqJi9ko7XpEh1DScoqysnJDDx81XHCPRGX9UecweqG8U4OHDhA4/V+jGYH16+0Mjw6id1uveM6AcKjRbTsC0DF2mcoPXmZjquXaXRNYw1FKC6swmHV09vZAUYLXrcTCRjp6yGpM+ML+DGqcQZGJklOjiJb3Xi9PswmndiQ4yH1aDxnF2Y1cOkAP995jN4pGy++8CwVQai/2M5U/3Uu9qmseayKdCJJavgqe88OsOXFr5Mdv8jPdjUwNTpCTs0Gtm7eSH6GC9EZeDiJbvwCEah8nKAUwyCpZOZkcvLgAerrjjEtG0glUySiUYLhCNUrlpGaHKGvu4/MoIekZGXJxhf56ub1RPx2EfSHmOjGLyB2i5WA0YbDaqKzcxCTM8iyDVvZZLVhVYb5cN9J+oI20ooKioLRZMbuchPMyCIz5EcvmoaHmvjzLSApJU0sFmNsKkZFeSaj/Z2cPHWR1q5B+lsbuXD5OmOTKWwGldGJcfpGJkglEsRi0yRTYtvth51o2ReI8f4O7OE8vMNJejv7qVr/PKr1CKcutjDg8lBSs5J1S2L0xPUsXV6LLeykfThBvt+GXkoSS6SwaFTOKjwYYoBugUglYsRicZIpBaPZgs1qJpWYZmxsEoPFjtNuITE9STShopdVJL0eNaWQTiWRjSYsZjN6MQHnoSbCLggLhLhUC8ICIcIuCAuECLsgLBAi7IKwQIiwC8ICIcIuCAuECLsgLBD/Py6i3Jvkif4JAAAAAElFTkSuQmCC)
The scatterplot above shows the revenue, in millions of dollars, that a company carned over several years and a line of best fit for the data. In Year 4 , the difference between the actual revenue and the predicted revenue is n million dollars, where is a posative integer. What is the value of n ? Round your answer to the nearest whole number. (Disregard the 5 sign when gridding your answer.)
Note:
As we are not certain if the point of the actual revenue is exactly at the midpoint of 50 and 60, so instead of taking the midpoint 55, we can also take it to be 54 or 56.
Then the value of n can be 4 or 6 too.
![](data:image/png;base64,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)
The scatterplot above shows the revenue, in millions of dollars, that a company carned over several years and a line of best fit for the data. In Year 4 , the difference between the actual revenue and the predicted revenue is n million dollars, where is a posative integer. What is the value of n ? Round your answer to the nearest whole number. (Disregard the 5 sign when gridding your answer.)
Note:
As we are not certain if the point of the actual revenue is exactly at the midpoint of 50 and 60, so instead of taking the midpoint 55, we can also take it to be 54 or 56.
Then the value of n can be 4 or 6 too.