Find all solutions to the following quadratic congruences by first making the lead coefficient 1, then g the linear coefficient even, and finally by completing the square. a) 4x² + x + 1 = 0 (mod 7) (b) 2x² + 3x + 1 = 0 (mod 11) (c) 3x² + 5x + 1 = 0 (mod 13)

Q: 4. Show steps and find -9x²-9x-4 x³ - x 3 √⁹x² - dx. 3

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Q: If m<1 = 6(3x+1)-2, m<2= 3(x+2)+9, and m<ABC= 5(3x+5)+6, find x and m<ABC.

A: Given,           ∠1=63x+1-2           ∠2=3x+2+9            ∠ABC=53x+5+6

Q: Three rational expressions have the following characteristics: a) Rational Expression 1 i. NPV's=…

A: Given that  a) NPV's are 52 and -5 and numerator is a difference of squares polynomial. b) NPV's are…

Q: The positive value of k for which x2+kx+64=0 & x2-8x+k=0 will have real roots

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Q: Solve the polynomial congruence: x³ - 3x² +27= 0 (mod 225).

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Q: Suppose f : X → Y , g : Y → Z. (Thus g ◦ f : X → Z.) Show that if f and g are surjective then so is…

A: f :X→Y  , g :Y→Z    so , g∘f :X→Z Given f and g are surjective , we have to prove that g∘f is…

Q: S 2 xdx 24-1

A: To evaluate the following integral.

Q: 2 Express ( √5 - √5₂) in 2 simplest a + bi form.

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Q: the number of nonnegative integer solutions to (x₁ + x2 + x3 + x4 + X5) (X6 + X7 + x8 + x9 + x10) =…

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Q: શે-2 – 7) 4x(3-2x) 1$'+107 d) (12x – 6x) + (3x) f) -8y* +24y 4y

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Q: 2√72 py, without using a calculator: 2n+1 a) (2n)n-1 4"+1 (2n-1)+1 32k+132k-1 b) 2/18-√32…

A: Step 1: Step 2: Step 3: Step 4: