1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
romanna [79]
3 years ago
10

. Using the Binomial Theorem explicitly, give the 15th term in the expansion of (-2x + 1)^19

Mathematics
1 answer:
timofeeve [1]3 years ago
3 0
Let's rewrite the binomial as:
(1 - 2x)^{19}

\text{Binomial expansion:} (1 + x)^{n} = \sum_{r = 0}^n\left(\begin{array}{ccc}n\\r\end{array}\right) (x)^{r}

Using the binomial expansion, we get:
\text{Binomial expansion: } (1 - 2x)^{19} = \sum_{r = 0}^{19}\left(\begin{array}{ccc}19\\r\end{array}\right) (-2x)^{r}

For the 15th term, we want the term where r is equal to 14, because of the fact that the first term starts when r = 0. Thus, for the 15th term, we need to include the 0th or the first term of the binomial expansion.

Thus, the fifteenth term is:
\text{Binomial expansion (15th term):} \left(\begin{array}{ccc}19\\14\end{array}\right) (-2x)^{14}
You might be interested in
Tracy has a cell phone plan that provides 250 free minutes each month for a flat rate of 29$. For any minutes over 250 tracy us
iVinArrow [24]

Answer:

Since Tracy is charged $29 for 250 free minutes so:

For x ≤ 250, f(x) = $29

tracy is charged an extra $0.35 per minute for calls over 250 minutes, so:

For x ≥ 250, f(x) = 29 + 0.35(x - 250)

7 0
2 years ago
34.15 round to the nearest hundred
I am Lyosha [343]
It’s zero, I think. Because
3 doesn’t round up. It’s stays the same. But since there is nothing in the hundred place. It is 0.
4 0
3 years ago
A lighthouse has a shadow that is 36 feet long. Zara is 4 feet tall, and she is standing next to the lighthouse. Zara has a shad
pychu [463]

Answer:

48 feet

Step-by-step explanation:

At a particular time, objects and their shadows are proportionate.

Therefore, in figure,

AB/FD = BC/DE --- (1)

where AB is the height of the lighthouse, BC, its shadow and FD is the height of Zara and DE is her shadow.

From the given information,

BC = 36 feet

FD = 4 feet and DE = 3 feet

(1) becomes

AB/4 = 36/3

AB = 12

AB = 48

Hence, the height of the lighthouse is 48 feet.

7 0
3 years ago
Kerry’s grandmother, Mrs. Reynoso, is helping Kerry pay for guitar lessons. She has set up a special savings account to pay for
s2008m [1.1K]

Answer:

Month 5 is when it will be at $100

I hope this helps!

Step-by-step explanation:

x---0-----1-----2-----3----4-----5

y-300-260-220-180-140-100

y=40x+300

5 0
3 years ago
Simplify this expression: cos t(sec t − cos t)
Nostrana [21]
\cos t \, (\sec t - \cos t)
= \cos t \, (\frac{1}{\cos t} - \cos t)
= 1 - \cos^2 t
= \bf sin^2 t
5 0
3 years ago
Read 2 more answers
Other questions:
  • Geometry - Will give 5 stars + Thanks!
    13·1 answer
  • A recipe calls for 16 fluid ounces for light whipping cream. If Anthony has 1 pint of whipping cream in his refrigerator, does h
    5·2 answers
  • Math help picture below
    13·1 answer
  • How many solutions does 25 + 3A + 9 = 34 + 3A have?
    13·1 answer
  • How many 4 inch long pieces of wood could be cut from a board that is 2 yards long?
    8·1 answer
  • Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the trian
    12·2 answers
  • How to graph lines with positive slopes
    5·1 answer
  • Find the missing value and please show how
    13·2 answers
  • 1. Employees of a landscaping company built a retaining wall with area 23(3/8) sq ft. They used brick to make the top portion of
    7·1 answer
  • Use the substitution method to solve the system of equations: y = 2x + 7; x = 9
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!