Answer:
The coordinates of point E on CD are
.
Step-by-step explanation:
Let be
,
and
. The given ratio can be translated vectorially into this:
![\overrightarrow {CE} = \frac{5}{3} \cdot \overrightarrow{ED}](https://tex.z-dn.net/?f=%5Coverrightarrow%20%7BCE%7D%20%3D%20%5Cfrac%7B5%7D%7B3%7D%20%5Ccdot%20%5Coverrightarrow%7BED%7D)
And let consider that each point is a vector with respect to origin:
and ![\vec {D} = (-7,11)](https://tex.z-dn.net/?f=%5Cvec%20%7BD%7D%20%3D%20%28-7%2C11%29)
Then,
![\vec E -\vec C = \frac{5}{3}\cdot (\vec D -\vec E)](https://tex.z-dn.net/?f=%5Cvec%20E%20-%5Cvec%20C%20%3D%20%5Cfrac%7B5%7D%7B3%7D%5Ccdot%20%28%5Cvec%20D%20-%5Cvec%20E%29)
![\vec E +\frac{5}{3}\cdot \vec E = \frac{5}{3}\cdot \vec D + \vec C](https://tex.z-dn.net/?f=%5Cvec%20E%20%2B%5Cfrac%7B5%7D%7B3%7D%5Ccdot%20%5Cvec%20E%20%3D%20%5Cfrac%7B5%7D%7B3%7D%5Ccdot%20%5Cvec%20D%20%2B%20%5Cvec%20C)
![\frac{8}{3}\cdot \vec E = \frac{5}{3}\cdot \vec D + \vec C](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B3%7D%5Ccdot%20%5Cvec%20E%20%3D%20%5Cfrac%7B5%7D%7B3%7D%5Ccdot%20%5Cvec%20D%20%2B%20%5Cvec%20C)
![\vec E = \frac{5}{8}\cdot \vec D + \frac{3}{8}\cdot \vec C](https://tex.z-dn.net/?f=%5Cvec%20E%20%3D%20%5Cfrac%7B5%7D%7B8%7D%5Ccdot%20%5Cvec%20D%20%2B%20%5Cfrac%7B3%7D%7B8%7D%5Ccdot%20%5Cvec%20C)
![\vec E = \frac{5}{8}\cdot (-7,11)+\frac{3}{8}\cdot (-1,-5)](https://tex.z-dn.net/?f=%5Cvec%20E%20%3D%20%5Cfrac%7B5%7D%7B8%7D%5Ccdot%20%28-7%2C11%29%2B%5Cfrac%7B3%7D%7B8%7D%5Ccdot%20%28-1%2C-5%29)
![\vec E = \left(-\frac{35}{8},\frac{55}{8} \right)+\left(-\frac{3}{8},-\frac{15}{8} \right)](https://tex.z-dn.net/?f=%5Cvec%20E%20%3D%20%5Cleft%28-%5Cfrac%7B35%7D%7B8%7D%2C%5Cfrac%7B55%7D%7B8%7D%20%20%5Cright%29%2B%5Cleft%28-%5Cfrac%7B3%7D%7B8%7D%2C-%5Cfrac%7B15%7D%7B8%7D%20%20%5Cright%29)
![\vec E = \left(-\frac{35}{8}-\frac{3}{8},\frac{55}{8}-\frac{15}{8} \right)](https://tex.z-dn.net/?f=%5Cvec%20E%20%3D%20%5Cleft%28-%5Cfrac%7B35%7D%7B8%7D-%5Cfrac%7B3%7D%7B8%7D%2C%5Cfrac%7B55%7D%7B8%7D-%5Cfrac%7B15%7D%7B8%7D%20%20%20%20%5Cright%29)
![\vec{E} = \left(-\frac{19}{4}, 5\right)](https://tex.z-dn.net/?f=%5Cvec%7BE%7D%20%3D%20%5Cleft%28-%5Cfrac%7B19%7D%7B4%7D%2C%205%5Cright%29)
The coordinates of point E on CD are
.
Answer:
t=d/v
Step-by-step explanation:
v=d/t
vt=d
t=d/v
Answer:
Step-by-step explanation:
this question is like greater or smaller so if you had the numbers 2 and 8 of course you know that the 8 would be more.
Answer:
The population in 4 years will be 33,000.
Step-by-step explanation:
I got this because 8% of 25,000 is 2,000 so what this mean is that in one year the population increase by 2,000 since the question ask for 4 years, 4x 2,000 = 8,000, so in 4 year the population increase by 8,000 making the population 33,000 because before the 4 years the population was already 25,000 and in the 4 years the 8,000 more people come making the population then 33,000.
9514 1404 393
Answer:
4.1
Step-by-step explanation:
x is the short leg of a right triangle with hypotenuse 8.8 cm and longer leg 7.8 cm. Its measure is found using the Pythagorean theorem:
x^2 +7.8^2 = 8.8^2
x^2 = 77.44 -60.84 = 16.60
x = √16.6
x ≈ 4.1