Suppose that m and n are real numbers with m + 5n = 10. Find the least possible value of the expression m + n°. Enter exact values. (This means that numbers such as can be entered as a decimal but numbers 1 such as - need to be entered as fractions.) least possible value: when m = and n =

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A: We know that Ax=0 has infinite number of solution iff rank(A) &lt;3

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A: Note: According to Bartleby guidelines; for more than one question asked, only the first one is to…

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Q: (ii) Find the set of values of k for which |(x- 4)(x+2)|=k has four solutions.

A: Let's find.

Q: 16. The roots of the equation x+ 2px + q = Odiffer by 1. Show that p q - 4.

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A: Topic- Differential Equation

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A: Here, to prove this result we have to use Rolles theorem.

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Q: Solve for u. 2u-11u+31 (4-7)- If there is more than one solution, separate themn with commas. U =…

A: This problem is related to quadratic equations and we solve this using root formula.

Q: Find all solutions of the equatiion. m - - x² + e* 2.

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Q: of t/4 for x. (If an answer is undefined, enter UNDEFINED.)

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Q: n 10x + 11y = n has

A: The equation as, ax+by=S. The smallest positive integer S is expressed as, S=(k+1)*a*b

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A: Given-2sin (∝) = 1To find all the solution of the equation for 0 ≤ ∝ ≤ 2π

Q: 64q10.5+q20.25q30.4

A: Total utility=319.87

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Q: Solve for A if T (24T-5 [¹12]) = 41-9 [16 -1

A: Here we have to solve for A .

Q: Show that the equation x3 - 17x + c = 0 has at most one root in the interval [-2, 2].

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Q: how many integer solutions are there to the equation  X + y + z = 10 for which  a. x,y and z + 10…

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A: First of all, consider given equation and simplify.

Q: 7.For which value of k will the roots of 2x + kox+1 = 0 be real? .2 1) 1 2) 2 3) 3

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Q: 1. Find how many real solutions x2 + 6x + 24 has. What are those solutions (real or otherwise)?

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Q: If 18( – 4)² – 1 = 0 then find the solutions x in the form x = c±Vk, where c is an integer and k is…

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Q: Find the solution to an = -3an 1- 3a, 2– an 3 ,n > 3 with ag — 5, а, — —-9 and az 3 15.

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Q: For which values of a does ax = 1 have a solution inZ6?

A: Z5=0,1,2,3,4,5ax=1If a=0, then 0x=1⇒ No solution.If a=1, then 1x=1⇒One solution,x=1

Q: 5. Find all the values of the argument a with which the equation tg(2n (x +)· lg(4x + a + 3) = lg(4x…

A: We will use basic knowledge of sets and functions to answer this question as follows.

Q: The value of x such that 8x + 4, 6x – 2, 2x + 7 will be consecutive terms in an AP is A. 2 В. 15 С.…

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Q: Which of the following is the solution set of In(5x – 7) < In(2x + 8) (5, 00) (-00, 5] (-00, 5) [5,…

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Q: Given that the equation z2 + (p + iq)z + r + is = 0, where p, q, r, s are real and non-zero has a…

A: Introduction :--