Consider the triangular region in the plane given by the triangle (1, 6), (6, -1), and (1, -4). Sketch the region, and write a system of inequalities to describe the region bounded by the triangle.

Q: Sketch the region defined by the inequalities -1 ≤ r ≤ 2 and-π/2 ≤ u ≤ π/2.

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Q: A rectangular lot having an area of 5000 sq. meters is to be fenced on three sides. Find the minimum…

A: topic - application of derivatives

Q: Use lagrange multipliers to find three positive numbers whose sum is 51 and the sum of whose squares…

A: Given that, the sum of the positive number is 51. That is, Fx,y,z=x2+y2+z2 and gx,y,z=x+y+z=51.…

Q: Find the midpoint between the two points (3, 6) and (-4, 8).

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Q: Explain in word what are the possible consistent and inconsistent system for 2 lines planes?

A: The conditions for the consistent system of equations can be explained as follows:

Q: A rectangular field with one side along a river is to be fenced. Suppose that no fence is needed…

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Q: An open top rectangular tank with a square base is to have a volume of 10 cubic feet. The bottom is…

A: To find out the dimensions of minimum cost.

Q: Explain in word what are the possible consistent and inconsistent system for 3 planes?

A: To explain: the consistent and inconsistent system for 3 planes.

Q: Find a set of parametric equations of the line with the given characteristics.

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Q: Use Lagrange multipliers to find three positive numbers whose sum is 18 and the sum of whose squares…

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Q: Write the system of inequalities using the graph. 4. 3 -2V 1 2 Oy 2x + 1 Oy > -x – 2 y 2x + 1 Y <…

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Q: Solve the system graphically and indicate whether the solution region is bounded or unbounded. Find…

A: Solve the system graphically and indicate whether the solution region is bounded or unbounded. Find…

Q: Find the maximum area of a rectangle in the first quadrant where one side of the rectangle lies…

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Q: Find the area of the rectangle whose vertices are the points with coordinates (5, 2), (5, -6), (0,…

A: Explanation: Given that,  Vertices are : (5, 2), (5, -6), (0, -6), and (0, 2).     Firstly we will…

Q: Find a point on x axis which is equidistant from A(2,-5) and B(-2,9)

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Q: Find a plane through the points (2,1,-2), (5,-4,4), (6,7,-4)

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Q: Use slopes to show that the square with vertices at (-2, 5), (4, 5), (4, -1), and (-2, -1) has…

A: Given that the four vertices of the square are: A4, 5 ,B-2, 5 ,C-2, -1 and D4, -1   If a line passes…

Q: What value of b will make the system y=3x+2 and y=3.5x+b intersect at the point (2,8)?

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Q: write the system of inequalities that describe the finite shadrd region B) find the length of one of…

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Q: Choose the best selection for the quadrilateral with vertices at the following points. (-6,2),…

A: A(-6,2) B(-3,1) C(-4,-2) D(-7,-1)

Q: ) Find the equation of the plane through the points: (2,4,5), (1,5,7), (–1,6,8).

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Q: Find the three areas of the region bounded by y= 2x²+10 , y=4x+1 and the lines x=-2 and x=5.

A: We need to find the area between two curves. The area between two curves y=fx, y=gx for x∈a,b is…

Q: origin. 104 8- -10 -4 -2 2 4. 10 8- -4 H. -8- -10 F' = G'%3= H' = 6. 6, 4, 2. 6.

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Q: find the area of the parallelogram whose vertices are listed. (-2,0), (0,3), (1,3), (-1,0)

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Q: A rectangular poster is to contain 800 square inches of print. The margins at the top and bottom of…

A: Given data: Area of the poster which contains print is: A = 800 in2 Margin at top and bottom is: x0…

Q: The corners of a triangle are (2,1), (4,4), and (6,2). Give the system of inequalities which…

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Q: Find the system of inequalities that has the solution triangular region enclosed by the three lines…

A: The given question can be solved by using the given graph as shown below. The given graph shows a…

Q: Use slopes and the distance formula to show that the quadrilateral whose vertices are (0, 0), (1,…

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Q: Find the perimeter of the rectangle whose vertices are the points with coordinates (-1, 5), (3, 5),…

A: We have to find the perimeter of the rectangle whose vertices are the points with coordinates (-1,…

Q: Find the perimeter of a polygon whose vertices are (3, 5), (-1, -7), (-2, 4,) and (5, -6). Express…

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Q: Find the intersection of the planes 2x + 4y - 6z = -8 and 2x + 5y - 7z = -9.

A: We have to find the intersection of the given planes.

Q: Create a system of inequalities that results in a closed shape on the coordinate plane

A: We have to create a system of inequalities that results in a closed shape on the coordinate plane.

Q: A circle has center at the intersection of the two lines, 4x + y = 4 and x - y= 6.  If it passes…

A: two lines are system Ax=b is

Q: Draw a second line on the graph in order to demonstrate a system of equations with no solution .…

A: here we need to draw a second line such that the system has no solution  so the system has no…

Q: A rectangular field with one side along a river is to be fenced. Suppose that no fence is needed…

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Q: A rectangular poster is to contain 128 square inches of print. The margins at the top and bottom of…

A: Let the length of the rectangle be x Length after 1 inches of margin = x-2  inch The breadth of…

Q: Find a point on x-axis which is equidistance from A (2,-5) and B(- 2,9).

A: Topic:- geometry

Q: Determine the distanee between the point ( 2,-3,1) and the point of intersection of the following…

A: We have to find the distance between two points.

Q: the length of the line seyment joining the two Pointsof intersection with the two levels of two…

A: For xz level use y=0 and for xy level use z=0.   Then find two point . Then use the distance formula

Q: A rectangle with horizontal and vertical sides has one vertex at the origin, one on the positive x-…

A: consider an arbitrary point on line  2x+y=100 is   x , 100-2x which is the one of the vertex of the…

Q: A company manufactures bicycles and skateboards. The compan bicycles cannot exceed 10, and its daily…

A: Solution-

Q: Represent two planes that intersect at a line represented by 3 +2

A: There are so many pair of planes that represents the same line.

Q: A square has an area of 36 and one side that lies along the line y = 3. What could be the location…

A: To find the possible co-ordinates of square.

Q: Determine which of the points (-3, –4, -6), (– 3,4, 5) satisfy the linear system 2x1 8x2 2x3 -48…

A: In this question, the concept of matrix multiplication is applied. Matrix Multiplication Matrix…

Q: Which system of inequalities best matches the 10- purple shaded region? A. y 2 x2-5x+ 6, ys0,…

A: topic - inequality

Q: Find the area of a parallelogram whose vertices are (- 2, – 3, 2), (2, – 4, 2), (2, 2, 0), and (6,…

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Q: What is the area of the triangle formed by the lines y=-2x+6, y=-2, and x=0

A: Find the solution below

Q: Find the area of a rectangular garden with vertices at A(3,4), B(3,-2) C(8,4) and D(8,-2).

A: Given:  Vertices of rectangular garden:    A(3,4), B(3,-2) C(8,4) and D(8,-2)