Answer:
Step-by-step explanation:
A term is a combination of letters and/or numbers separated by a + or a - sign. Our polynomial has 5 terms.
A coefficient is a number stuck to a letter...it HAS to be stuck to a letter to be a coefficient. Our coefficients are 1, -198, 5, and -2 (notice I let out the 4).
That's because a constant is a number NOT stuck to a letter. The 4, then, is the only constant in this polynomial.
The leading coefficient is the number that is stuck to the highest-degree variable. Our highest degree variable is a 12 in 5x^12. So the leading coefficient is 5. In order to have a polynomial in standard form, we always list the terms in order of descending powers (highest power to lowest).
The degree is also the same as the highest power in our polynomial. Ours is a 12th degree.
You run 0.5 miles every 3 minutes => 1 mile every 6 minutes. Your friend runs 2 miles every 14 minutes => 1 mile every 7 minutes. You run a whole number of miles every number of minutes that is a multiple of 6. Your freind runs a whole number of miles every number of minutes that is a multiple of 7 Then the least possible number of miles that you both run to end at the same time is the least common factor of 7 and 6 minutes. This is 7 * 6 = 42 minutes. You will have run 42 min / (6 miles/min) = 7 miles, and your friend will have run 42 min / (7 miles/min) = 6 miles
Answer:
x(x - 7)(x^3 + 2)
Step-by-step explanation:
Note that x is a common factor here:
3x^5-7x^4+6x^2-14x = x(3x^4 - 7x^3 + 6x - 14), or:
x(3x^4 - 7x^3 + 6x - 14) Note that 6x - 14 can be rewritten as 2[x - 7]
and that 3x^4 - 7x^3 can be rewritten as x^3[x - 7]
Therefore, x(3x^4 - 7x^3 + 6x - 14 becomes:
x(x - 7)(x^3 + 2)
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
.
<span>Visually impaired students averaged 8.14 hours of sleep with a standard deviation of 1.78 hours. Average sleep of the students will be 6.36.</span>