A theater has 30 rows of seats. There are 22 seats in the first row, 26 in the second row, 30 in the third row, etc. How many people will the theater hold ?

Answers

Answer 1

Arithmetic Sequence

rows ---------32-n

first term ------------26-----------a

d---------------------------4

Sn = n/2( 2a+(n-1)d)

=32/2 (2*26+(31)4)

=16(52+124)

=16(176)

=2816 seats

Answer 2

If theater has 30 rows of seats, then the number of people that the theater will hold is 2400 people.

To find out how many people the theater will hold, we need to calculate the total number of seats across all 30 rows. Since the number of seats increases by 4 for each successive row, we can treat this as an arithmetic sequence.

The formula to find the sum of an arithmetic sequence is = (n/2) × (first term + last term),

where n = number of terms and the first and last terms are given,

In this case : First term = 22,

Last term = 22 + (30 - 1) × 4 = 22 + 116 = 138,

Number of terms (rows) = 30,

Sum = (30/2) × (22 + 138) = 15 × 160 = 2400;

Therefore, The theater will hold 2400 people.

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Related Questions

If a hole is 7 feet deep and 4 feet wide how much dirt is in the hole?

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Answer:

3 is the correct answer tbyvcrdgevzc

find gcf

18x^2-3x+24x-4

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Answer:

1,128 sorry I'm not sure but thank you

How do you turn a whole number into a fraction

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Answer: To convert a fraction into a whole number: Divide the numerator by the denominator, only if the numerator is a multiple of the denominator. Let us see an example of this conversion.

this is for algrebra so it might not be what you are looking for

hELPPP pls quick thanks <3

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Answer: can you show the selections?

Step-by-step explanation:

What are the values of w and x ? For brainily

Answers

Answer:

w would be like 33 and x would be 45

Answer:

x=66, w=48

Step-by-step explanation:

since this is an isocsles triangle, x and angle j would have to have the same measure, 66 degrees. When you add 66 and 66 together, you can get the sum of angle j and x which is 132. You can subtract 132 from 180 (since all angles of the triangle add up to 180) to get w

180-132=48

so x=66 and w=48

Solve the equation. 2p + 15 − 11p = 3(5 − 3p)

Answers

0=0

For the full explanation simply copy and paste your equation to your device browser.

Answer:

2p+15-11p=3(5-3p)

2p-11p+15=15-9p

-9p+9p=15-15

p£R

one will get the brainliest,Help me! to do this..i have been confused of this..please help

Simplify: (5/7-1/2 ) ×2 4/5 .


Simplify : 7/12 ÷( 1 1/3-3/4 )



Simplify∶ 2/3 ÷(1/2 ×4/5)


Simplify : (1/2+1/3) ÷ 1 2/3



Simplify : 2 1/3 ×2/7+1/4


Simplify : 3/4 of ( 3/5 + 1/3 )

Simplify : 3 1/3 of ( 3/5 -1/2 )

Simplify : ( 1 3/4 -1/2 ) ×2 1/5

Simplify : ( 5/9 –1/3 ) ÷2

Simplify : 1/4 +( 2 1/3 ×2/7 )

Simplify : 1/7 of ( 6 3/8 -1/4 )

Simplify : 5/11 of ( 1/2 + 3/5 ) ( 12 ×5 marks)


(13)From the books presented to a school library, 1/3 are educational publications

1/5 are literary publications, 3/7 of the remaining are translations. The

remaining books are children’s stories.

(i) What fraction of the total number of books is the educational and lite

Answers

1) 0.6

2) 1

3)1.66666666667

4)0.5

5)0.91666666666

6)0.7

7)0.333333333

8)2.75

9)0.111111111111

10)0.91666666666

11)0.875

13) i think this is it

8/15

Find the value of each variable. Please help! 25 points!

Answers

Answer:

what are the choices so I could help

Answer:

see explanation

Step-by-step explanation:

∠ L = 180° - (60 + 60)° = 180° - 120° = 60° [ sum of angles in Δ = 180° ]

Since the 3 angles are 60° , then the triangle is equilateral with the 3 sides being congruent.

Then

5x - 3 = 4 ( add 3 to both sides )

5x = 7 ( divide both sides by 5 )

x = [tex]\frac{7}{5}[/tex] = 1.4

and

2y + 6 = 4 ( subtract 6 from both sides )

2y = - 2 ( divide both sides by 2 )

y = - 1

Find the value of y that will make these two triangles congruent:

Answers

Answer:

5

Step-by-step explanation:

if the triangles are congruent then the side lengths must be equal:

JL=PM

PN=LK

NM=JK and

4y + 12 = 32 subtract 12 from both sides

4y = 20 divide both sides by 4

y = 5

What is the rotation of point A (-2, 3). 90 degrees?
A. (2,3)
B. (-2,-3)
C. (3,-2)
D. (3,-2)

Answers

Step-by-step explanation:

Let's pretend our point is actually a complex number. That would make the point -2–3i. Why would we do this? Well, rotation of complex numbers is simply a matter of multiplication, in this case by 1∠−90° , or -i.

So to start, you shift the point of rotation to 0+0i, rotate it by multiplying, then shift it back to the axis of rotation.

z=−i[(−2−x0)+(−3−y0)i]+(x0+iy0)

=−3−y0+x0+(2+x0+y0)i

x=Rz

y=Iz

Thus the new point is at (−3+x0−y0,2+x0+y0)

hence (-3,2)

Multi step problem 4/7w = 4.2

Answers

Answer:

7.35

Step-by-step explanation:

4/7w=4.2

multiply both sides by 7

24/7w=29.4

simplify

4w=29.4

divide both sides by 4

w=7.35

Answer:

w equals 7.35

Step-by-step explanation:

7 times 4/7w = 4.2 times 7

4w = 29.4

Divide: 4w/4 = 29.4/4

w = 7.35

Please help me solve 9 and 10 ASAP please

Answers

Answer:

[tex] \sqrt{ |?| } [/tex]

Beckett went to two different stores at the mall. He purchased a $36 hat at the first store and a $52 pair of shoes at the second. Beckett estimates that he spent a little less than $80 in total. Is Beckett's estimate reasonable? Explain your thinking.

Answers

Beckett’s estimate was incorrect by almost 10 percent; if he was thinking clearly, he would have known that he spent at LEAST $80 in total

Beckett spent $88 in total his estimate of $80 is wrong.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Beckett went to two different stores at the mall. He purchased a $36 hat at the first store and a $52 pair of shoes at the second. Beckett estimates that he spent a little less than $80 in total.

The total spending will be calculated as,

Total = 52 + 36

Total = $88

The estimated spending is $80. Therefore, Beckett spent $88 in total his estimate of $80 is wrong.

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Which of the following best describes the algebraic expression 10x +2?
A. The sum of ten times a number and two.
B. Ten times the sum of a number and two.
C. The product of ten plus a number and two.
D. Ten times the quantity of a number plus two.

Answers

Step-by-step explanation:

option A describes the algebraic expression 10x + 2.

hope this answer helps you dear!

What is the coefficient in the expression 8−x7? Question 7 options: −7 7 17 −17

Answers

Answer:

7

Step-by-step explanation:

Complete the equation. ( − 4 ) 2 =

Answers

Answer:

-16

Step-by-step explanation:

multiply 4x4 and then determine if its negative or positive

-8 This is what I believe it is hopefully this helps

If the slope of a line and a point on the line are​ known, the equation of the line can be found using the​ slope-intercept form, y = mx + b. To do​ so, substitute the value of the slope and the values of x and y using the coordinates of the given​ point, then determine the value of b. Using the above​ technique, find the equation of the line containing the points (-4,7) and (2,-2).
What is the equation of the line?

(Simplify your answer. Type your answer in​ slope-intercept form. Use integers or fractions for any numbers in the​ equation.)

Answers

Answer:

y=-3/2x+1

Step-by-step explanation:

NOTE: Doing graphs by hand is a lot easier, it saves a lot more time as well.

Step 1: plot your 2 known points.

Step 2: draw a line that goes between both points

Step 3: find the distance of the points in RISE/RUN format.

-9/6. The slope is negative because the line goes down to the right.

Step 4: find your y-intercept.

1.

Step 5: simplify your equation

-9/6 = -3/2

A 10 kg bag of potatoes costs $5. Write a formula for the cost of potatoes.

Answers

Answer:

10/5

Step-by-step explanation:

10 bags =5$

therefore one kg equals 10/5

Which equation represents a line which is parallel to the y-axis?

Answers

Answer:

x= 3

Step-by-step explanation:

I hope this helps but if there are options lmk

Answer:x= -2

Step-by-step explanation:

Please help me solve this

Answers

The answer is x = -18

Solve the simultaneous equations
x-6y=5
xy - 2y2 = 6
-
Show clear algebraic working.

Answers

Answer:

(- 7, - 2 ) , (9.5, 0.75 )

Step-by-step explanation:

Given the equations

x - 6y = 5 ( add 6y to both sides )

x = 5 + 6y → (1)

xy - 2y² = 6 → (2)

Substitute x = 5 + 6y into (2)

(5 + 6y)y - 2y² = 6 ← distribute and rearrange left side

5y + 6y² - 2y² = 6

4y² + 5y = 6 ( subtract 6 from both sides )

4y² + 5y - 6 = 0 ← in standard form

(y + 2)(4y - 3) = 0 ← in factored form

Equate each factor to zero and solve for y

y + 2 = 0 ⇒ y = - 2

4y - 3 = 0 ⇒ 4y = 3 ⇒ y = [tex]\frac{3}{4}[/tex] = 0.75

Substitute these values into (1) for corresponding values of x

y = - 2 : x = 5 + 6(- 2) = 5 - 12 = - 7 ⇒ (- 7, - 2 )

y = 0.75 : x = 5 + 6(0.75) = 5 + 4.5 = 9.5 ⇒ (9.5, 0.75 )

(- 7, - 2 ) and  (9.5, 0.75 ) are the solutions.

What is equation?

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.

Here, we have,

Given the equations

x - 6y = 5 ( add 6y to both sides )

x = 5 + 6y → (1)

xy - 2y² = 6 → (2)

Substitute x = 5 + 6y into (2)

(5 + 6y)y - 2y² = 6 ← distribute and rearrange left side

5y + 6y² - 2y² = 6

4y² + 5y = 6 ( subtract 6 from both sides )

4y² + 5y - 6 = 0 ← in standard form

(y + 2)(4y - 3) = 0 ← in factored form

Equate each factor to zero and solve for y

y + 2 = 0 ⇒ y = - 2

4y - 3 = 0 ⇒ 4y = 3 ⇒ y =  = 0.75

Substitute these values into (1) for corresponding values of x

y = - 2 : x = 5 + 6(- 2) = 5 - 12 = - 7 ⇒ (- 7, - 2 )

y = 0.75 : x = 5 + 6(0.75) = 5 + 4.5 = 9.5 ⇒ (9.5, 0.75 )

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Please I actually need this done

Answers

Answer:

AC = 19

Step-by-step explanation:

A__C__S

AS = AC + CS

6x -4 = (4x-1) + 7

6x - 4 = 4x + 6

6x - 4x = 6+ 4

2x = 10

x = 10/2

x = 5

AC = 4x -1 = 4(5) - 1 = 20 - 1 = 19

I hope I helped you^_^

Answer:

19

Step-by-step explanation:

AS = AC + CS

6x - 4 = 4x -1  +7

6x - 4 = 4x + 6

Add 4 to both sides,

6x = 4x + 6 + 4

6x = 4x + 10

Subtract 4x from both sides

6x- 4x = 10

2x = 10

Divide both sides by 2

x = 10/2

x = 5

AC= 4x - 1

    = 4*5 - 1

     = 20 - 1

     = 19

1. Line a passes through points (-2, 1) and (2, 9). Write an equation in slope intercept form that is parallel to line a. Show your work.​

Answers

Answer:

The answer is y=ax+9−2a i think

what is the height of the prism?

Answers

Answer:

6m

Step-by-step explanation:

Hope this helps!!!

Answer:

Step-by-step explanation:

l = 3 m

w = 2 m

Volume = 36 cubic meter

l * w * h = 36

3 * 2 * h = 36

6 * h = 36

      h = 36/6

h = 6 m

Please solve this law of indices question
and don't give studip ans
i will mark as brainlisted ​

Answers

Answer:

hope you understand .............

Perimetre of rectangle is 256cm.it length is 3times as long as its breadth.find breadth or length.

Answers

length = 3 breadth

which means 256 = 8 breadth

breadth = 32

length = 96

pls mark me as brainliest!

State if the triangle are similar amd if they are, give the reasons AA SSS SAS

Answers

which triangles?

i see no triangles

try again bro

guys pls help me!!!!!!!

Answers

Answer:

x = 131

Step-by-step explanation:

the angle adjacent to x on line l corresponds to 49° and are congruent, then

49 and x are adjacent and sum to 180° , that is

x + 49 = 180 ( subtract 49 from both sides )

x = 131

please help with solving systtems of equation by graphing I'm lost

Answers

Answer:

Solution is (3, -3)

Step-by-step explanation:

To solve by graphing, you literally have to graph both lines to see where they intersect. That point of intersection is the solution to the given system.

Given the following linear equations:

y = - x   where the slope (m) = -1, and the y-intercept (b) = 0.

y = x - 6 where the slope (m) = 1, and the y-intercept (b) = -6.

Plot the intercepts (0, 0) for the first line, and (0, -6) for the second line, as a starting point, then use the given slopes (rise over run) of each line to plot the next points. Repeat the process until you have enough points to connect with and create a line.

Attached is a screenshot of the graphed systems of linear equations. It shows that the solution is (3, -3).

Please mark my answers as the Brainliest, if you find this helpful :)

The length of a rectangle measures 5/8 of a foot. The width of the rectangle measures 2 1/2 feet. What is the area of the rectangle?

Answers

Answer:

1 9/16 square feet  or 1.5625 square feet

Step-by-step explanation:

Area of a rectangle is Length x Width

First convert 2 1/2 into a number that is just a fraction.

2 = 4/2  so 4/2 + 1/2 = 5/2

Now you can multiply the two fractions to find the area.

area = 5     5       25

          --  x  --   = -----

          8      2       16

To simplify this, you know 16/16 = 1  so subtract 16 from the numerator which leaves 9/16

Your answer will be 1 and 9/16

2 1/2 multiplied by 5/8 = 1.5625
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