Find the equation of the axis of symmetry and the vertex of its graph. f(x) = x2 + 8x − 1   (a)axis of symmetry=       (b)vertex (x, y) =

Q: Find the x- and y-intercepts of the graph of the equation. x²-16 X-4 y =

A: As we know that; To determine x-intercept, we need to solve for x after plugging y=0.   The given…

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Q: Solve. X+y +z = - 11 2x + y-z = - 13 X-y +z = 1

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A: General form of a quadratic equation isy = ax + bx + c1st point:   (0,7) ⇒ x = 0, y = 7…

Q: Find the general solution for: y'' - 4y' - 5y = -6xe(-x)

A: We need to find the general solution for y'' - 4y' - 5y = -6xe(-x). ---------(1)Idea: First, we will…

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A: value of P given below..

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Q: he general solution of y" +

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Q: Solve and identify the graph of the equation x2+y2+z2-2x+4y+6z+14=0

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Q: Approximate the solution(s) to x3-2x+2=0 using a graphing utility

A: x3-2x+2=0

Q: 7x+2y=8 x-2y=-8 Find x and y of linear equation using elimination method

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Q: Find the equation of the axis of symmetry and the vertex of its graph.   f(x) = −2x2 − 4x − 1…

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Q: Solve:  2x-y + z = 7 x + y - z = -4 x + 3y - 2z = -11

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Q: The profit from the sale of x units of radiators for automobiles and y units of radiators for…

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Q: Find a general solution of y" (-2-2 i3)y. y(x) =

A: The given differential equation is  y'' = (- 2 - 2i√3)y or, y'' - (- 2 - 2i√3) = 0 or, (D2 + 2 +…

Q: Find the number of units x that produces a maximum revenue R in the given equation. R = 24x2/3 − 2x

A: Given equation for revenue is, R = 24x23- x

Q: use Separation of Variables to find the general solution. y' + x2y = 0

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Q: Find the general solution and particular solution

A: We can solve this using substitution method of differential equation

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Q: Find axis of symmetry and vertex of y=x2+4x+3

A: given that y=(x^2)+4x+3 find axis of symmetry and vertex

Q: The equation of the axis of symmetry of y= 2x2 -7x+ 5

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Q: Solve 3x + 2y > 6 graphically.

A: Shaded area below is the graphical solution.

Q: Test the equation for symmetry. x = y4 - y2

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Q: Consider the linear equation 3(x+1) = 3x + 3 Is x = -3 a solution to this linear equation?

A: Given data,                   3  x + 1  = 3 x + 3

Q: The profit from the sale of x units of radiators for automobiles and y units of radiators for…

A: To find the value of x and y that leads to maximum profit, use lagrange multipliers function:…

Q: Explain the steps to find x- and y- intercepts of an equation of the form Ax + By = C

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Q: Find the solution of the equation which passes through the x-axis.

A: If it passes through the X-axis, then, y=0 & z=0 is satisfied. So, we get, 0 = (p²+q²)/2 +…

Q: Solve by graphing. x-y=-4  x+2y=17

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Q: The Maximum point of y = 9-x² x²-4

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Q: The equation x 2= 2 x has three solutions: x = 2, x = 4, and one other. Estimate the third solution…

A: Given:

Q: a. Solve x2 + 2x-y+1%30 and x + y-1=0 using Elimination Method

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Q: 3x2-y2=3 symmetric with respect to y-axis or x-axis

A: Given curve, 3x2 - y2 = 3 Or, 3x2 - y2 = 3Or, 3x2 - y2 - 3 = 0Let's call LHS as C(x, y). Hence, C(x,…

Q: (a) To find where the graphs of the functions y = m¡x + b1 and y = m2x + b2 intersect, we solve for…

A: a) To find where the graphs of the functions intersect, we solve for x in the equation:…

Q: An equation for the stretched y = x2 -1 vertically by a factor of 3.

A: If we have a function f(x) vertically stretched by a factor of 3 function is g(x): g(x) = 3f(x)

Q: Consider the linear equation: 3(x+1) = 3x + 3 Is x = -3 a solution to this linear equation?

A: Given equation is, 3(x+1) = 3x + 3

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Q: f (x) = x² . – 6x + 5 - Show the coordinates of at least FIVE points (including the vertex and all…

A: fx=x2-6x+5 It can be written as, ⇒fx=x2-6x+9-4⇒fx=x-32-4 Now comparing with fx=x-h2+k, we get h=3…

Q: Approximate the solution(s) to x3 = x2 - 5 using a graphing utility.

A: We have to approximate the solution(s) to x3=x2-5 using the graphing utility .

Q: y"-y-4e-x+3e2x; y(0) - 0.y(0) --1.y"(0)-2

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Q: Solve 4x - 12 = -x² by graphing. Select all solutions that apply. x= -9 x=-8 x = -7 x=-6 x=-4 x= -3…

A: we can write the equation as: f(x) = x2 + 4x - 12 = 0 a= 1, b= 4, c=-12 plotting the quadratic…

Q: Find the equation of the axis of symmetry and the vertex of its graph. f(x) = −2x2 − 4x − 1   (a)…

A: Given,           fx=-2x2-4x-1

Q: Find the x- and y-intercepts of the graph of the equation. 2x - y - 7 = 0 x-intercept (x, y) =…

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Q: Find the point on the line 2x+4y+1=0 which is closest to the point (-4,2).

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Q: the equation x2 = 2x has three solutions: x = 2, x = 4, and one other. Estimate the third solution…

A: To sketch the graph and find the solution of the equation.

Q: Draw the graph of the problem and comment the solution.                Max z = 10x1 +   20x2…

A: Problem isMAX Zx =  10 x1 + 20 x2subject to2 x1 + 6 x2 ≤ 102 x1 + 4 x2 ≤ 164 x2 ≤ 8x1    ≥ 5and…

Q: What points (x, y, z) satisfy the equations x2 + y2 = 4 and z = 3?

A: Given: x2+y2=4, z=3

Q: Find the solution such that y' = 2(2x – y) passes through the point (0, -1).

A: From the given differential equation: y'=22x-y So, we can also write as: dydx=4x-2y....(1) Now use…

Q: Find the general solution of (2x –y) = 2y – x

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Q: Find the general solution for y' = y – xy³e-2x

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Q: x  -   y  -  z  =  2 -x  +2y  - 3z  = -5 3x  - 2y  - 7z  =3 solve x, y and z

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.