2. (a) Factorize the following expression completely. 12n - Amn (1 mark) (i) Show that - 4x = X(4x -3) 1-x (b) (ii) Hence, solve the equation - 4x - 0. (c) Make v the subject of the formula p = V5 + vt . The distance needed to stop a car, d, varies directly as the square of the speed, s, at which it is travelling. A car travelling at a speed of 70 km/h requires a distance of 40 m to make a stop. What distance is required to stop a car travelling at 80 km/h? (d)

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A: Given:

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Q: Solve  radical equation. (√3x + √18) = x

A: We first simplify √18

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Q: What are the roots of the equation -90 = x(x - 18) ? %3D A. 9 and -9 B. 9 + 3i and 9 - 3i C. 9 + V3…

A: We can make it easier for you.

Q: 49 14(a). Solve the following equation: x + X+1 13.

A:

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A:

Q: Solve for x: 3+(5x-1)2=11 Write a simplified, exact answer,( not a decimal approximation)

A: Equation given in the question: Subtract 3 on both sides: Take square root on both sides: Add 1…

Q: 1? - 6х + 20- 62

A: Our Aim is to solve the equation given below:-x2-6x+20=6x-(i) by factorization method.

Q: (3х- 13x + 1) Bx - 1)(3x + 1) = (Simplify your answer.)

A: Our Aim is to multiply the expression given below:-(3x-1)(3x+1) -(i)

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A:

Q: find fG25 and g (6)

A: Solution:-     Given:             fx=4x2-x             gx=-2x-1

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A:

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A:

Q: use the equation y=x² - 17x + 72. For what values of x is yis greater than and equal to 0?

A: Given query is to find the values of x for which y is greater than equal to zero

Q: if px2+qx+r=0 is one root then find the square of the other a=p , b=q, c=r

A: The quadratic equation of the form ax2+bx+c=0 can be solved using the formula x=-b±b2-4ac2a This…

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A:

Q: Solve the Equation: x²-12x+39=0 1. (-5, 4) ○ 2. (-7,8} O 3. (8,-4) ○ 4. (6, -5}

A:

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A:

Q: -3 2/3 . (-2 1/4)   How do you solve this?

A:

Q: Modify the following equation so that it is in quadratic form Determine the values for a, b, and c.

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A:

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A: We have to simplify and solve the given problem

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A: Given: -4x+6-7=-2x+4 for finding value of x, we simplify given expression and find value of x

Q: (&*+12)+5-8x+12 Based on the equation above, what is the value of 5x+1?

A:

Q: (15x - 8) 226

A: Given,

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A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.