2
Remember in basic Algebra we learned that all variables can be substituted as 1's If needed. So lets do that: -k - 4k = -1 - 4(1) = -5 So now we can rewrite this removing the 1's we put in: -k - 4k = -5k
k=-2
Tangent line equation: y = x+k Circle equation: x^2 +y^2 = 25 If: y = x+k then y^2 = (x+k)^2 => y^2 = x^2 +2kx+k^2 So: x^2 +x^2 +2kx +k^2 = 25 Transposing terms and collecting like terms: 2x^2 +2kx +(k^2 -25) = 0 Using the discriminant: 4k^2 -4*2*(k^2 -25) = 0 Which is the same as: 4k^2 -8k^2 +200 = 0 Collecting like terms and subtracting 200 from both sides: -4k^2 = -200 Divide both sides by -4: k^2 = 50 Square root both sides: k = + or - the square root of 50 Therefore it follows that the possible values of k are plus or minus the square root of 50
-4k + 10 - k + 2 = 2k + 4k + 18Combine all the 'k' terms on the left side:-5k + 10 + 2 = 2k + 4k + 18Combine all the 'k' terms on the right side:-5k + 10 + 2 = 6k + 18Combine the numerical terms on the left side:-5k + 12 = 6k + 18Add 5k to each side:12 = 11k + 18Subtract 18 from each side:-6 = 11kDivide each side by 11:k = -6/11
x =√k+√k+√k…… ectx² = k + xx² - x = kx² - x + (1/2)² = k + (1/2)² factorise x² - x + (1/2)²(x + 1/2)² = k + 1/4(x + 1/2)² = (4k + 1)/4x + 1/2 = ± √(4k + 1)/2x = 1/2 ± √(4k + 1)/2it obviously has to be positivex = 1/2 + √(4k + 1)/2x = (1 + √(4k + 1))/2
4k-7 = 7 4k = 14 k = 3.5 or k = 7/2
31 = 3-4k 31-3 = -4k 28 = -4k Divide both sides of the equation by -4 to find the value of k: k = -7
8-4k = 40 (4k-8) - 8 = 40-8 4k = 32 4k/4 = 32/4 k =8
4k-64 = -60
q=4k+4uImproved Answer:-If: Q = 4k+4uThen: k = (4u-Q)/-4
2
-4k-2=10 -4k=10+2 -4k=12 k=-3
wait is that algerbra? then what equaiton
There are infinitely many of them.Take any positive integer k and let 0
Remember in basic Algebra we learned that all variables can be substituted as 1's If needed. So lets do that: -k - 4k = -1 - 4(1) = -5 So now we can rewrite this removing the 1's we put in: -k - 4k = -5k
J = K+6 K + J = 4K Replace J in the second equation K + (K + 6) = 4K K + K + 6 = 4K 2K + 6 = 4K Subtract 2K from each side 6 = 2K divide both sides by 2 3 = K So, Keisha is 3 and therefore John is 9