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Andrei [34K]
3 years ago
12

The base ticket price for a football game is modeled by the function p(x) = 15x + 10, where x is the years since the team starte

d playing football. Not included in each base ticket price is a service charge modeled by the function c(x) = 5x + 2. To find the total cost of a ticket, a fan should use what operation on the polynomials?
Addition

Subtraction

Multiplication

It cannot be determined
Mathematics
2 answers:
lora16 [44]3 years ago
7 0

Answer:  First option is correct.

Step-by-step explanation:

Since we have given that

Price of base ticket for a football game is given by

p(x)=15x+10

Service charge modeled by the function is given by

c(x)=5x+2

We need to find the total cost of a ticket :

p(x) + c(x)

= 15x+10+5x+2

=20x+12

So, we have used Addition operation on the polynomials.

Hence, First option is correct.

Svetllana [295]3 years ago
6 0
The total cost of the ticket is the sum of the base ticket price, p(x) = 15x + 10, and the service charge, c(x) = 5x + 2. Therefore, from the word sum, the operation involved is Addition. This is the first among the choices given.
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Let f be defined by the function f(x) = 1/(x^2+9)
riadik2000 [5.3K]

(a)

\displaystyle\int_3^\infty \frac{\mathrm dx}{x^2+9}=\lim_{b\to\infty}\int_{x=3}^{x=b}\frac{\mathrm dx}{x^2+9}

Substitute <em>x</em> = 3 tan(<em>t</em> ) and d<em>x</em> = 3 sec²(<em>t </em>) d<em>t</em> :

\displaystyle\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\frac{3\sec^2(t)}{(3\tan(t))^2+9}\,\mathrm dt=\frac13\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\mathrm dt

=\displaystyle \frac13 \lim_{b\to\infty}\left(\arctan\left(\frac b3\right)-\arctan(1)\right)=\boxed{\dfrac\pi{12}}

(b) The series

\displaystyle \sum_{n=3}^\infty \frac1{n^2+9}

converges by comparison to the convergent <em>p</em>-series,

\displaystyle\sum_{n=3}^\infty\frac1{n^2}

(c) The series

\displaystyle \sum_{n=1}^\infty \frac{(-1)^n (n^2+9)}{e^n}

converges absolutely, since

\displaystyle \sum_{n=1}^\infty \left|\frac{(-1)^n (n^2+9)}{e^n}\right|=\sum_{n=1}^\infty \frac{n^2+9}{e^n} < \sum_{n=1}^\infty \frac{n^2}{e^n} < \sum_{n=1}^\infty \frac1{e^n}=\frac1{e-1}

That is, ∑ (-1)ⁿ (<em>n</em> ² + 9)/<em>e</em>ⁿ converges absolutely because ∑ |(-1)ⁿ (<em>n</em> ² + 9)/<em>e</em>ⁿ| = ∑ (<em>n</em> ² + 9)/<em>e</em>ⁿ in turn converges by comparison to a geometric series.

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3 years ago
6sqrt20 + 8sqrt5 - 5sqrt45
marta [7]

Answer:

11.1803398875

Step-by-step explanation:

4 0
3 years ago
Directed line segment AB has endpoints A(2,3) and B(8,15). Point P has coordinated P(6,11). What ratio does P partition AB into?
Vladimir79 [104]
Refer to the graph shown below. It confirms that points A, B and P are
 collinear.

Calculate the length of AP (as a).
a = √[(6 - 2)² + (11 - 3)²]
   = 8.9443

Calculate the length of BP (as b).
b = √[(8 - 6)² + (15 - 11)²]
   = 4.4721

Calculate ratio a/b.
a/b = 8.9443/4.4721 = 2
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Answer:  2:1 ratio.

7 0
2 years ago
Which of the following is the solution for 6x + 3 ≤ 27
postnew [5]

Answer:

x  ≤  4

Step-by-step explanation:

6x + 3 ≤ 27        subtract 3 both sides

6x ≤ 24              divide 6 both sides

x ≤ 4                   There's your answer

5 0
3 years ago
A price is decreased from £800 to £640. Calculate the percentage change.
Anni [7]
<span>There is a decrease of 20% from ÂŁ800 to ÂŁ640.

    A change from 800 to 640 represents a negative change (decrease) of -20% Using the formula :

   Percent change = [(800 - 640) / 800] x 100 = -20 % (decrease)

       800 is the old value and 640 is the new value. In this case we have a negative change (decrease) of -20 percent because the new value is smaller than the old value.</span>
6 0
3 years ago
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