11. ) Given f(x) = 2x² - 12x + 22, write the function in standard form, that is f(x) = a(x - h)² + k.

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A: Region and necessary definition:

Q: Use the following function to find f(9) and f(0). f(x) = 4x - 3 f(9) = f(0) =

A: To find f(9) and f(0) , we need to replace x by 9 and 0 in given function.

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A: The solution is given by

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A: Given that, f(1)=5 & f(2)=1 limx→-∞f(x)=4  & limx→1f(x)=2 f is continuous at x=2 but not…

Q: 5y

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A: Given: sin2x - 12 = 0 To find: The values of x.

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A: Please refer to the solution in next step.

Q: 7.27. Theorem. Let p be a prime and let i and j be natural numbers with i ‡ j satisfying 1<i,j<.…

A: Suppose, i2≡j2 (mod p)⇒i2-j2 ≡0 (mod p)⇒(i+j)(i-j)≡0 (mod p)⇒p|i+j or p|i-j⇒p≤i+j or p≤i-j

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A: g is continuous every where except x=-4,x=1 &amp; x=6 g has vertical asymptotes at x=-4 &amp; x=6 g…

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A: Here, the equation is given by zmyx+yt=zyx2. Here the ranges are -1≤m&lt;3, 0≤t&lt;1. The minimum…

Q: 10. Given f(x) a. b. C. d. 4(x-2)(x-5) 3(x-2)(x-6)' = determine: the x-intercept(s), if any (give x…

A: The give function is f(x)=4(x-2)(x-5)3(x-2)(x-6) To determine the a) x-intercepts b) Vertical…

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Q: 1. Determine the order and degree of the differential equation (A) order: 2, degree:4 (B) order: 4,…

A: Since you have posted a multiple question according to guildlines I will solve first(1)   question…

Q: why is 9.5 divided by 0.5 the same as 95 divided by 5?

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Q: Let V be a vector space, and let 0₁, 02, 03, 04 € V. Then Span {01, 02, 03, 04} = Span {0₁-02, V2…

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A: Stokes' theorem is a fundamental result in vector calculus that relates the circulation of a vector…

Q: beta

A: According to the question,        First,  define some of the terms for…

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A: The trajectory of several rockets is  shown as data matrix in 5×3 matrix 489517963248321

Q: 5-4 5 7 1 5. -1 -1 -4 -2-8

A: The given matrix is 15-4-1-45-2-87 To find the determinant of the matrix.

Q: Let U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }, A = {1, 3, 5, 7 }, B = { 3, 4, 5, 6, 8, 10 }, C = { 2, 4,…

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A: The curves are: r=2+2sinθ,   r=2-2sinθ. To Do:We have to find the area of entire region with both…

Q: 1. Consider f(x, y) = x − 2xy + y² and point P (1,1). Determine the following. (a) the directional…

A: Please refer to the solution in next step.

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Q: 14. One edge of a cube is 12 cm long if the edge is increased by 50% by how much percentage is the…

A: First  recall  the  formula  of volume  of a  cube :Let  a  be  the  side length  of  a  cube  then…

Q: 13. f(x) = x²e¯x, a=1

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Q: 3 A random sample of 1000 oranges showed that the mean amount of juice per orange was 8,4 fluid…

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Q: Problem 10 The transformation T : P3 → P3 given by T(ƒ(x)) = xƒ'(x) + x² ƒ"(x) is linear.

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Q: 5. Identify the direction of opening, coordinates of the vertex, the zeros, the y-intercept, the…

A: 1. The direction of the opening is downwards. 2. Co-ordinates of vertex is (1,9)

Q: + Y are invertible matrices of the same size, then X(X¹+Y-¹) Y(X+Y)-¹ = 1.

A: One has to show the said property.

Q: Find the vectors T, N, and B at the given point 16 r(c) = (1², 31², c), (4, 15, 2) T = N = B =

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