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
Stolb23 [73]
3 years ago
10

WILL GIVE 100 POINTS

Mathematics
1 answer:
padilas [110]3 years ago
6 0

(a) The explicit rule to model the sequence formed by the number of seats in each row is a_{n}=15+3n

(b) The 35th row has 120 seats

Step-by-step explanation:

The rule of the nth term of an arithmetic sequence is

a_{n}=a+(n-1)d , where

  • a is the the first term
  • d is the common difference between each two consecutive terms

∵ There are 18 seats in the 1st row

∵ There are 21 seats in the 2nd row

∵ 21 - 18 = 3

∵ The number of seats is increased by 3 with each additional row

- The number of seats in each row represents an arithmetic

   sequence because there is a common difference between

   each two consecutive rows

∴ The number of seats in each row formed an arithmetic sequence

∵ The number of seats in the first row = 18 seats

∴ a = 18

∵ The number of seats in a row continues to increase by 3 with each

   additional row

∴ d = 3

- Substitute the values of a and d in the rule of nth term

∴ a_{n}=18+(n-1)3

- Simplify the right hand side

∴ a_{n}=18+3n-3

- Add like terms

∴ a_{n}=15+3n

(a) The explicit rule to model the sequence formed by the number of seats in each row is a_{n}=15+3n

∵ There are 120 seat in a row

- Substitute a_{n} by 120 in the rule above

∴ 120 = 15 + 3n

- Subtract 15 from both sides

∴ 105 = 3n

- Divide both sides by 3

∴ n = 35

∴ The number of the row is 35

(b) The 35th row has 120 seats

Learn more:

You can learn more about the sequences in brainly.com/question/7221312

#LearnwithBrainly

You might be interested in
Are 6:5 And 17:5 equivalent
Andrews [41]

Answer:

no

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Express 80 miles per hour in kilometers per hour
Anna [14]
80 miles per hour is 128.74752 kilometers per hour
8 0
3 years ago
Read 2 more answers
If AC is parallel to DE, find X
UNO [17]

Answer: x = 50

Concept:

Here, we need to know the idea of alternative interior angles and the angle sum theorem.

<u>Alternative interior angles</u> are angles that are formed inside the two parallel lines, and the values are equal.

The <u>angle sum theorem</u> implies that the sum of interior angles of a triangle is 180°

If you are still confused, please refer to the attachment below or let me know.

Step-by-step explanation:

<u>Given information:</u>

AC ║ DE

∠ABC = 85°

∠A = 135°

<u>Find the value of ∠BAC</u>

∠A + ∠BAC = 180° (Supplementary angle)

(135°) + ∠BAC = 180°

∠BAC = 45°

<u>Find the value of ∠BCA</u>

∠ABC + ∠BAC + ∠BCA = 180° (Angle sum theorem)

(85°) + (45°) + ∠BCA = 180°

∠BCA = 50°

<u>Find the value of x (∠EBC)</u>

∠EBC ≅ ∠BCA (Alternative interior angles)

Since, ∠BCA = 50°

Therefore, ∠EBC = 50°

\Large\boxed{x=50}

Hope this helps!! :)

Please let me know if you have any questions

8 0
1 year ago
Beth is making fruit salad. She adds 3 grapes for every 2 strawberries. If she uses 12 strawberries, how many grapes will she us
Diano4ka-milaya [45]
The answer is 18. she will use 18 grapes.
5 0
3 years ago
Read 2 more answers
Of all rectangles with area 324324​, which one has the minimum​ perimeter? Let P and w be the perimeter and​ width, respectively
ra1l [238]

Answer:

For w = 18 units perimeter is minimum

P = 2(18 + w)

Step-by-step explanation:

Given;

Area of the rectangle = 324 units²

P is the perimeter

w is the width

Let L be the length of the rectangle

therefore,

P = 2(L + w)  ............(1)

also,

Lw = 324

or

L = \frac{324}{w} ..........(2)

substituting 2 in 1

P = 2(\frac{324}{w} + w)

now,

for minimizing the perimeter

\frac{dp}{dw}=\frac{d(2(\frac{324}{w} + w))}{dw} = 0

or

2((-1)\frac{324}{w^2}+1) = 0

or

(-1)\frac{324}{w^2}+1 = 0

or

(-1)\frac{324}{w^2} = -1

or

w² = 324

or

w = 18 units

For w = 18 units perimeter is minimum

therefore,

from 2

L = \frac{324}{18}

or

L = 18 units

objective function for P is:

P = 2(18 + w)

8 0
3 years ago
Other questions:
  • What is the value of x? <br><br> x=
    15·1 answer
  • Write a quadratic equation with the given roots write the equation in the form ax^2+bx+c=0 where a,b,and c are integers -5/4 and
    9·1 answer
  • Can someone answer this question please answer it correctly if it’s corect I will mark you brainliest
    8·2 answers
  • HELPPPP PLEASE<br>60 POINTS​
    10·2 answers
  • HELLER HELLPPPP MEHHHH
    8·2 answers
  • A garage door is 16 feet wide; the scale is 2 inches = 1 foot. How wide is the door on the scale drawing? Door = ________ inches
    13·2 answers
  • What is the degree measure of the angle –15π÷2​
    5·1 answer
  • Find the Perimeter of the parallelogram with endpoints A(0, 2), B(2,5), C(5,0), and D(3,<br> -3).
    10·1 answer
  • Help plzz<br> How does robby respond to keith confessing his fear of chickens
    10·1 answer
  • Send help lol confused
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!