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For what values of k does the line y=kx-1 have two distinct points of intersection with the circle (x-2)^2+(y-3)^2=2?

sub y=kx-1 into circle equation, get (k^2+1)x^2-(8k+4)x+18=0for 2 distinct solutions need b^2-4ac>0, ie -8k^2+64k-56>0iff k^2-8k+7<0complete the square: intersections of equation in k satisfy(k-4...

Answered by Christopher B. • Maths tutor

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Solve x^2 = 4(x – 3)^2

x² = 4(x-3)²x² = 4(x-3)(x-3) - showing that these are double bracketsx² = 4(x² - 6x + 9) - expanding the double bracketsx² = 4x²

Answered by Emily L. • Maths tutor

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Expand the following equations

a. x(x+4)b. 3x(x+4)c. (x+8)(x+3)d. (x+7)^2

Answered by Kane S. • Maths tutor

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There are 10 boys and 20 girls in a class. In a class test, the mean score of the boys is 77. The mean score of the girls is 80. What is the mean score of the whole class?

To calculate the mean of the whole class:1) Find the sum of the individual scores of the whole class. Boys: 10 x 77 = 770Girls: 20 x 80 = 1600Total of Boys and Girls: 770 + 1600 = 23702) Divide the sum of...

Answered by Anuj M. • Maths tutor

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Solve the simultaneous equations: 3x + y = -9, x^2 + 2x - 3 = y

Rearrange the first equation to equal 'y' so y = -9 - 3xSubstitute this into equation 2 so x^2 + 2x - 3 = -9 - 3xRearrange this to equal 0 so x^2 + 5x + 6 = 0Factorise this by utilising brackets so that t...

Answered by Maryum J. • Maths tutor

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