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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}
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kicyunya [14]

Answer:

Senior citizen tickets = $9

Student tickets = $11

Step-by-step explanation:

We begin by converting these into simultaneous linear equation;

Senior citizen tickets = a

Student tickets = b

5a + 9b = 144

14a + 6b = 192

5a = 144 - 9b

a = 144/5 - 9b/5

a = 28.8 - 1.8b

We now substitute this into the first equation

14(28.8 - 1.8b) + 6b = 192

403.2 - 25.2b +6b = 192

-19.2b = 192 - 403.2

b = -211.2/-19.2

b = 11

Put the value of b into either equation

5a + 9b = 144

5a + 9(11) = 144

5a +99 = 144

5a = 144-99

5a = 45

a = 9

6 0
3 years ago
Help please!!!!!:( Solve the equation for x. Round your answer to two decimal places. Do not include "x =" in your answer.
svet-max [94.6K]
The solution to the problem is as follows:

If you use Ln you can get rid of e. 

ln(e^0.4x) = ln(0.4) 

0.4x = ln(0.4) 

x = (ln(0.4))/0.4 

<span>x = -2.29
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I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
4 0
3 years ago
Read 2 more answers
Need Help PLZ!!!!!!!!!!!!
d1i1m1o1n [39]

The answer is A. Because you can’t lose the amount of steps you took.

4 0
3 years ago
What is the area of the figure?<br> Enter your answer in the box.
nordsb [41]

Answer:

The area of the figure = 112 in²

Step-by-step explanation:

The figure consist of:

1) A square of side length of 10 in.

2) A right triangle with a base of (10 - 6 = 4 in) and a height of (16 - 10 = 6 in)

So,

The area of the square = (side length)² = 10² = 100 in²

The area of the triangle = 0.5 * height * base = 0.5 * 6 * 4 = 12 in²

So,

The total area = 100 + 12 = 112 in²

<u>The area of the figure = 112 in²</u>

6 0
2 years ago
Find the value of x.
Paul [167]

Hello!

As we are looking for the opposite side and hypotenuse, we will use the sine.

sin30=1/2

This gives us the equation below.

1/2= 5/x

1/2x=5

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Therefore, x=10.

I hope this helps!

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2 years ago
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