What to do do I subtract the corridnates or add them

A theater has 56 rows of seats. If there are 13 seats in the first row, 18 in the 2nd row, 23 in the 3rd row. How many seats are

Anna35 [415]

Answer:

8428

Step-by-step explanation:

According to the Question,

Given, A theater has 56 rows of seats. If there are 13 seats in the first row, 18 in the 2nd row, 23 in the 3rd row.

We have a number sequence 13, 18, 23, ...

We can say that this is an arithmetic sequence because of the common difference 'd', is equal to 5, and the first term 'a1' is equal to 13.

The formula for the sum of an arithmetic sequence with n terms is given is $S_n= \frac{n}{2} [2a_1+(n-1)d]S$ .

Substitute the given values into the equation to solve for the sum of the 56 rows of seats.

$S_56= \frac{56}{2}[2(13)+(56-1)(5)]\\S_{56}=28\left[26+275\right]\\S_{56}=28\left[301\right]\\S_{56}=8428$

Therefore, there are 8428 seats in all.

4 0

3 years ago

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. At a historical la

Alborosie

Answer:

The number of candles will hold 2 candles

And large candle holder will hold 6 candles.

Step-by-step explanation:

Let the number of candles small candle holder have x

And the number of candles large candle holder have y

So, according to the information given in the question:

17 small candle holders means 17 x

and 2 large candle holders means 2y

using a total of 46 candles means $17x+2y=46$ (1)

Similarly, 8 small candle holders and 2 large candle holders, for a total of 28 candles gives:

$8x+2y=28$ (2)

We will solve equation (1) and (2) by elimination method:

Subtractijng the two equations we get:

$9x=18$

$\Rightarrow x=2$

Substitute x=2 in equation(2) we get: $8(2)+2y=28$

$2y=12$

$\Rightarrow y=6$

So, the number of candles will hold 2 candles

And large candle holder will hold 6 candles.

7 0

3 years ago

Find the area of 14 nine and eight

Reptile [31]

Answer:

Can u add the pic and I’ll answer it

Step-by-step explanation:

3 0

3 years ago

You have just opened a new nightclub, Russ' Techno Pitstop, but are unsure of how high to set the cover charge (entrance fee). O

Neko [114]

Answer:

a)q(p)=-15p+ +300

b)R(p)=-15p²+300p

c)C(p)=-30p+1600

d.1)P(p)=-15p²+330p-1600

d.2)p=$11

Step-by-step explanation:

(a).Before getting started, we are going to consider the cartesian plane, where x-axis corresponds to the cover charge and y-axis corresponds to number of guests per night . There, we will locate the following coordinates according to the previous information:

(9,165) (10,150).

Remember that the slope-intercept form of the linear equation is y=mx+b where m is the slope and b is te intercept.

The slope can be calculated by the next formula:

$m=\frac{y2-y1}{x2-x1}$

In this case we will assign (9,165) as the first coordinate and (10,150) as the second one. The order does not matter. At the end we get the same value for m.

Therefore:

$m=\frac{150-165}{10-9} = -15$

Now, we have the slope and two poitns. According to this, and taking into account that point-slope form of the equation of a line is y-y1=m(x-x1), find a linear demand equation.

Any of two coordintates can be selected. In this case we will select the second one.

y-150=-15(x-10) equation 1

Solve equation 1 for y

y=-15x+150+150

y=-15x+300

Above we had defined x as cover charge (p) and y as number of guests (q). Thus, rewrite equation 1.

q(p)=-15p+ +300.

it equation shows the number of guests per night as a function of the cover charge,

(b). The nightly revenue can be calculated multplying the price of the cover charge by the number of guests. So, we just have to multiply the equation 1 by p.

p*q(p)=p*(-15p +300)

R(p)=-15p²+300p equation 2

(c) To get the cost function of the nightclub we just have to multiply the cost of the two non-alcoholic drinks by the number of the guests ( equation 1) and add to it nightly overheads.

C(p)=2*(-15p+300)+1000

C(p)= -30p+600+1000

C(p)=-30p+1600 equation 3

(d) In order to find the profit in terms of the cover charge we will subtract nightly costs ( equation 3) from nightly revenue (equation 2)

P(p)=R(p)-C(p)

P(p)=-15p²+300p - (-30p+1600)

P(p)=-15p²+300p+30p-1600

P(p)=-15p²+330p-1600

To determine that the entrance fee we should charge for a maximum profit we are going to use the first derivative test (y'(x)=0) in order to find an extremum point.

Compute the first derivative of P(p)

P'(p)=-30p+330=0

30p=330

p=330/30

p= $11

The entrance fee that we should charge for a maximum profit is p=$11 per guest.

5 0

3 years ago

Can someone help me out how to work on this.

enyata [817]

Answer:

I don't think any are a correct graph of the function. But here are the ordered pairs. (1,0),(0,-2),(-1,-4)

Step-by-step explanation:

Take three values for x and plug them in for your y's. For instance x values of 1,0,-1. Plug each in to find the y value. 2(1) - 2 =y so (1,0)

3 0

3 years ago

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