Find the vertex of the parabola Y= 6X^2.+24X + 18 O (6, 2) O (2, 6) O (2,-6) O (2, 6)

Q: Determine the equation of a quartic function that has zeros of-7,5, and point (2, 9).

A: Quartic function is a function of the form f(x) = ax4  + bx3  + cx2  + dx , where a is non zero,…

Q: Find two positive integers whose sum is 16 and the sum of whose squares is minimum

A: Given sum of two numbers are 16. Let first number be x and second number=16-x. Now, sum of squares…

Q: Find the rectangle whose vertices with one is on side x-axis. on

A:

Q: Find the area of the quadrangle with vertices (6, 1), (-6,4), (-2, -4), and (5,-3)- Area = 1.0 4.0

A: To find the area of quadrangle with given vertices.

Q: Find an equation of the line through the point ( 3, 5 ) thatcuts off the least area from the first…

A:

Q: Use polynomial interpolation to find a cubic curve that goes through the points {(0,-3), (1,0),…

A:

Q: Write an equation for a quadratic function in vertex form with vertex (21, 6) that passes through…

A: Given that Quadratic function whose vertex is 21,6 and passes through point 23,4 To find : equation…

Q: Find the positive integer that maximizes the sum of the numbers and its reciprocals?

A: First make equation and then differentiate

Q: Find the equation of a straight line passing through the point (2,3) and making non-zero intercepts…

A:

Q: Find two positive numbers whose sum is 15 so that the sum of their square is minimum,

A:

Q: х + 2х, 3x, = 5 -2х, — 3х, + 6х, —D —7 Зх, + бх, : -7 Зх, + 6х, — 7х, %3D15 -

A:

Q: Find two positive numbers whose sum is 14 and the sum of whose squares is minimum

A:

Q: Find the equation for a quadratic with vertex at (-4, 4) and y-intercept at (0, 1) y =

A:

Q: Find the dimensions of the rectangle of maximum area which can be laid out within a right triangle…

A:

Q: A farmer has 600m of fence to enclose a rectangular divided pasture adjacent to an existing wall. He…

A: In question given that  farmer has 600m of fence to enclose a rectangular divided pasture adjacent…

Q: There is a line through the origin that divides the region bounded by the parabola y and the x-axis…

A:

Q: A rectangular bird sanctuary is being created with one side along a straight riverbank. The…

A: Let us assume the side of bird sanctuary along the river side is x km and other side is y km. Since,…

Q: 2. Find two numbers whose sum is 50 and whose product is a maximum.

A:

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

A:

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 an equation of the line through the point (3,5) thatcuts off the least area from the first…

A: The line with slope m (where m < 0 through (3, 5)).

Q: What is the image of the point (2,-3) after the transformationr.

A:

Q: Find the equation of the plane through the points (0, 1, 1), (1, 0, 1), (1, 1, 0) Thank you.

A:

Q: Find the maximum/minimum value of y = 10-4x - 3x² and where it occurs using completing the square.

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: = (T-) (प॰,,५) %3D -1 = )7-6 (4-7) 11 Find the fcilowing: 3D3x+8 9={-7,-6),(0, -7),(2,8), (5, 6)3

A: Given : g = {(-7,-6),(0,-7),(2,8),(5,6)} h(x) = 3x + 8   g-1(-7) = ? g(0) = -7 g-1(-7) = 0   h-1(x)…

Q: A rectangle is constructed with its base on the​ x-axis and its upper two vertices on the parabola y…

A: Given informationRectangle base is on x axisTop on parabola

Q: The life expectancy for females born during 1980-1985 was approximately 80.6 years. This grew to 81…

A:

Q: There is a line through the origin that divides the region bounded by the parabola y = 5x into two…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Write the equation of the sphere centered at (5, – 2, 4) with radius 3.

A:

Q: Find the coordinates of the maximum point. 4 In x +4 y=

A:

Q: By using the method of least squares, find the best parabola through the points: (0, 3), (-1,–1),…

A: According to the given information, it is required to find the equation of parabola using the method…

Q: By using the method of least squares, find the best parabola through the points: (-1,–2), (1,0),…

A: Given data: x -1 1 2 0 y -2 0 3 0 The general equation of the parabola is y=c0+c1x+c2x2…

Q: Find the point on the line y = 2x + 3 that is closest to theorigin.

A: Given equation of line,  y = 2x + 3 To find the point on line that is closest to the origin.

Q: A farmer wishes to build a rectangular fence and has 800 meters of fencing material with which to…

A:

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

A:

Q: :Find the equation of the plane through (-1, 6, 2) and perpendi cular to the jain of (1, 2, 3) and…

A: Given,           The equation of the pane through -1,6,1 and perpendicular to the join            of…

Q: the area of the largest rectangle that can be drawn with one side along the x-axis and the two…

A: Given curve is y=e-x2. Here the curve is symmetric about origin. Consider the vertices of rectangle…

Q: There is a line through the origin that divides the region bounded by the parabola y = 5x – into two…

A: SOLUTION-

Q: Find the points on the curve y = 19x² closest to the point (0, 2). (0.395 2.973) and (-0.395, 2.973)

A:

Q: 8. Find the best parabola to fit the data points: (-1, –1), (0, 1), (1,0), (2, 3).

A:

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: Find the rectangle whose vertices with one is on side X-axis. on

A:

Q: Find the distance between the two given point (-5,-3) and ( -2,3)

A: To Determine: Find the distance between the two given point Given: we have two points (-5,-3) and (…

Q: Find the point on the line 2x + y = 9 that is closest to the point (−4, 3

A:

Q: Write the standard form of the quadratic function whose graph is a parabola with the given vertex…

A: Given : Vertex : -3,-11Point : 0,7

Q: Find the cxhreme Point and extreme direcbion region of the て-う + X2u5 2 (メメ): - 3X、 → X2c-2 -Xit…

A: We are given the following system of 2d Linear equations : -3x1 + x2 ≤ -2 -x1 + x2 ≤ 2 -x1 + 2x2 ≤ 8…

Q: Determine the ordinate of the third vertex (2,y) of a triangle with an area of 27 and two other…

A: Area of the triangle is 27 and the vertices are -4, 6,  2, -6  &  2, y.