Complementary is 90 degrees and supplementary 180 degrees
9514 1404 393
Answer:
1.67 m, 8.33 m
Step-by-step explanation:
If the ratio of lengths is 1 : 5, then the ratio of the shortest length to the total is ...
1 : (1+5) = 1 : 6
The shortest length is (10 m)×(1/6) = 1.67 m. The longer length is 10 -1.67 = 8.33 m.
The lengths of the pieces are 8.33 m and 1.67 m.
the real solutions for the equation
are -
![x=4,2+-2\sqrt{3i}](https://tex.z-dn.net/?f=x%3D4%2C2%2B-2%5Csqrt%7B3i%7D)
Step-by-step explanation:
= ![- 64](https://tex.z-dn.net/?f=-%2064)
= 0
We can write 64 as
+
= 0
using the identity (
)
we get,
= ![(x+4) (x^{2} -x*4+4^{2} )](https://tex.z-dn.net/?f=%28x%2B4%29%20%28x%5E%7B2%7D%20-x%2A4%2B4%5E%7B2%7D%20%29)
=
....................(1)
solving the quadratic equation ,
=0
solutions of this quadratic equation can be obtained by
![x=-b +- \sqrt{b^{2}-4ac } /2a](https://tex.z-dn.net/?f=x%3D-b%20%2B-%20%5Csqrt%7Bb%5E%7B2%7D-4ac%20%7D%20%2F2a)
let use y for factors
![x=-(-4x)+-\sqrt{(-4x^{2} )-4*x^{2} *16} / 2*x^{2}](https://tex.z-dn.net/?f=x%3D-%28-4x%29%2B-%5Csqrt%7B%28-4x%5E%7B2%7D%20%29-4%2Ax%5E%7B2%7D%20%2A16%7D%20%20%2F%202%2Ax%5E%7B2%7D)
![x=4x+-\sqrt{16x^{2} -64x^{2} } /2x^{2}](https://tex.z-dn.net/?f=x%3D4x%2B-%5Csqrt%7B16x%5E%7B2%7D%20-64x%5E%7B2%7D%20%7D%20%2F2x%5E%7B2%7D)
![x=4+-\sqrt{16-64}/2](https://tex.z-dn.net/?f=x%3D4%2B-%5Csqrt%7B16-64%7D%2F2)
![x=4+-4\sqrt{3i} /2](https://tex.z-dn.net/?f=x%3D4%2B-4%5Csqrt%7B3i%7D%20%2F2)
<u />
..................(2)
from the equation 1 we have,
![x-4=0](https://tex.z-dn.net/?f=x-4%3D0)
which gives solution
and from equation 2 we got ![x=2+-2\sqrt{3i}](https://tex.z-dn.net/?f=x%3D2%2B-2%5Csqrt%7B3i%7D)
so the real solutions for the equation
are -
![x=4,2+-2\sqrt{3i}](https://tex.z-dn.net/?f=x%3D4%2C2%2B-2%5Csqrt%7B3i%7D)
Answer:
Step-by-step explanation:
![2a(5a^7)\\ \\ 2(5)a(a^7)\\ \\ 10a^{(1+7)}\\ \\ 10a^8](https://tex.z-dn.net/?f=2a%285a%5E7%29%5C%5C%20%5C%5C%202%285%29a%28a%5E7%29%5C%5C%20%5C%5C%2010a%5E%7B%281%2B7%29%7D%5C%5C%20%5C%5C%2010a%5E8)
Answer:
6000
Step-by-step explanation:
Each mp3 sells at $120 per mp3 player multiply that by 100 its $12000
It cost them $45 per mp3 to be made multiply that by 100 its $4500 then add the $1500 for the week and its $6000
$12000-$6000=$6000
They make a profit of $6000 in a week