Answer:
cos ∠CBD = - 4√41 / 41
Step-by-step explanation:
AB = 4 ΔABC = (4 x AC) / 2 = 10
AC = 5
BC = √5² + 4² = √41
cos ∠CBD = cos (180° - ∠CBA) = cos 180° cos ∠CBA + sin 180° sin ∠CBA
(cos 180° = - 1 sin 180° = 0 cos ∠CBA = 4 / √41 )
cos ∠CBD = (-1) x cos ∠CBA = - 4 / √41 = - 4√41 / 41
let's recall the remainder theorem.
we know that (x-1) is a factor, that means x -1 = 0 or x = 1.
since we know that (x-1) is a factor, then dividing the polynomial by it will give us a remainder of 0, which correlates with saying that f(1) = 0, in this case, so we can simply plug in "1" as the argument, knowing it gives 0.
![f(x)=3x^3+kx-11\\\\[-0.35em]~\dotfill\\\\\stackrel{0}{f(1)}=3(1)^3+k(1)-11\implies \stackrel{f(1)}{0}=3+k-11\implies 0=-8+k\implies 8=k](https://tex.z-dn.net/?f=f%28x%29%3D3x%5E3%2Bkx-11%5C%5C%5C%5C%5B-0.35em%5D~%5Cdotfill%5C%5C%5C%5C%5Cstackrel%7B0%7D%7Bf%281%29%7D%3D3%281%29%5E3%2Bk%281%29-11%5Cimplies%20%5Cstackrel%7Bf%281%29%7D%7B0%7D%3D3%2Bk-11%5Cimplies%200%3D-8%2Bk%5Cimplies%208%3Dk)
Answer:
He must win 11 more matches to qualify for the bonus.
Step-by-step explanation:
24/36 * 100 = 67% (to the nearest %) - This is the current percentage of what the Tennis player has won.
If we add 14 more matches on to the 36 the player has already played, we know that the Tennis player plays 50 matches in total.
Let's say the Tennis player was playing 100 matches, they would need to win 70 or more to qualify for the bonus. Because the player is playing half this amount of matches, we half the amount of games they have to win...
35/50 games or more must be won to qualify for the bonus. The Tennis player has already won 24 matches, so must win 11 more matches to qualify for the bonus.
Hope that helps!
