Ask question

Ask question

All categories

3 years ago

15

In a section of a baseball stadium, there are 11 seats in the first row. There are 15 seats in the second row, 19 seats in the t

hird row, and
23 seats in the fourth row.
If the number of seats in each row follows the pattern described above, which recursive function defines the number of seats in the nth row?
A. f(1) = 11
f(n) = 4.f(n - 1), for n > 2
B. f(1) = 4
f(n) = f(n - 1) + 11, for n > 2
C. f(1) = 11
f(n) = f(n − 1) + 4, for n > 2
D.
f(1) = 4
f(n) = 11. f(n − 1), for n > 2

1 answer:

jok3333 [9.3K]3 years ago

3 0

Answer:

A

Step-by-step explanation:

You might be interested in

The first three terms of an arithmetic series are 6p+2, 4p²-10 and 4p+3 respectively. Find the possible values of p. Calculate t

Doss [256]

Answer:

First Case:

$\displaystyle p=\frac{5}{2}\text{ and } d=-2$

Second Case:

$\displaystyle p=-\frac{5}{4}\text{ and } d=\frac{7}{4}$

Step-by-step explanation:

We know that the first three terms of an arithmetic series are:

$6p+2, 4p^2-10, \text{ and } 4p+3$

Since this is an arithmetic sequence, each subsequent term is <em>d</em> more than the previous term, where <em>d</em> is our common difference.

Therefore, we can write the second term as;

$4p^2-10=(6p+2)+d$

And, likewise, for the third term:

$4p+3=(6p+2)+2d$

Let's solve for <em>d</em> for each of the equations.

Subtracting in the first equation yields:

$d=4p^2-6p-12$

And for the second equation:

$2d=-2p+1$

To avoid fractions, let's multiply the first equation by 2. Hence:

$2d=8p^2-12p-24$

Therefore:

$8p^2-12p-24=-2p+1$

Simplifying yields:

$8p^2-10p-25=0$

Solve for <em>p</em>. We can factor:

$8p^2+10p-20p-25=0$

Factor:

$2p(4p+5)-5(4p+5)=0$

Grouping:

$(2p-5)(4p+5)=0$

Zero Product Property:

$\displaystyle p_1=\frac{5}{2} \text{ or } p_2=-\frac{5}{4}$

Then, we can use the second equation to solve for <em>d</em>. So:

$2d_1=-2p_1+1$

Substituting:

$\begin{aligned} 2d_1&=-2(\frac{5}{2})+1 \\ 2d_1&=-5+1 \\ 2d_1&=-4 \\ d_1&=-2\end{aligned}$

So, for the first case, <em>p</em> is 5/2 and <em>d</em> is -2.

Likewise, for the second case:

$\begin{aligned} 2d_2&=-2(-\frac{5}{4})+1 \\ 2d_2&=\frac{5}{2}+1 \\ 2d_2&=\frac{7}{2} \\ d_2&=\frac{7}{4}\end{aligned}$

So, for the second case, <em>p </em>is -5/4, and <em>d</em> is 7/4.

By using the values, we can determine our series.

For Case 1, we will have:

17, 15, 13.

For Case 2, we will have:

-11/2, -15/4, -2.

8 0

3 years ago

Simplify: (3x^2 + 4x - 3) - (4x^2 - 3x + 2)

Snowcat [4.5K]

$(3x^2 + 4x - 3) - (4x^2 - 3x + 2)\\\\=3x^2 + 4x - 3 -4x^2+3x-2\\\\=(3x^2-4x^2)+(4x+3x)+(-3-2)\\\\=-x^2+7x-5\to D)$

3 0

3 years ago

oee [108]

Answer:

x=7+ the square root of 85 /2 , x = 7- the square root of 85/2

Step-by-step explanation: hope I helped

7 0

3 years ago

Read 2 more answers

Alex is standing 60 feet from the base of a flagpole. He measures the angle of elevation to the top of the pole as 35º. Vera is

ivanzaharov [21]

Answer:

49.4 degrees

Step-by-step explanation:

In Triangle AXY,

$Tan 35^0=\frac{|XY|}{60} \\|XY|=60*Tan 35^0=42.01\:feet\\$Therefore, Height of the pole=42.01 \:feet$

We want to determine the angle of elevation from the point Vera is standing to the top of the flagpole, which is the angle at V in the diagram.

In Triangle XVY

|VY|=36 feet

$Tan \theta=\frac{|XY|}{|VY|} \\Tan \theta=\frac{42.01}{36}\\ \theta=arctan(\frac{42.01}{36})\\ \theta=49.4^0$

Therefore, the angle of elevation from the point Vera is standing to the top of the flagpole is 49.4 degree to the nearest tenth of a degree.

4 0

4 years ago

Your quiz must include at least one word problem the requires multiplication or division of decimal by a power for ten. Example:

butalik [34]

Answer:

Total cost= $235

Step-by-step explanation:

Giving the following information:

Dontae wants to buy 100 tiles for his kitchen floor. The tiles cost $2.35.

<u>To calculate the total cost, we need to use the following formula:</u>

Total cost= 2.35*x

x= number of tiles

<u>For 100 tiles:</u>

Total cost= 2.35*100

Total cost= $235

5 0

3 years ago