Classrooms on one side of the drama building are all numbered with consecutive even integers. If the first room, the room with the smallest classroom number, on this side of the building is numbered y, write an expression in y for the sum of the
first four classroom numbers in a row. Then simplify this expression
The sum of the first four classroom numbers in a row is

Answers

Answer 1

Consecutive odd numbers are two apart (5, 7, 9, 11...). So given an odd integer, we can add 2 to get the next odd integer.

If the first odd integer is y, then the first 4 odd integers are

y

y+2

y+4

y+6

These add up to 4y+12

Answer 2

The sum of the first four classroom numbers in a row is 4y+12.

It is required to find the sum of the first four classroom numbers in a row.

What is arithmetic?

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

Since the smallest classroom​ number on the side of the building is numbered y ​ and each consecutive even integers is separated by a difference of  2.

y is the first class room.

y +  2  is the second class room.

y +  4  is the third class room.

y + 6 is the third class room.

The sum of the five consecutive class rooms are given as:

y + (y + 2) + (y+ 4) + (y + 6)

collecting alike terms we get

= y + y+ y+ y + 2 + 4 + 6

= 4y + 12

Therefore, the sum of the first four classroom numbers in a row is 4y+12.

Learn more about arithmetic here:

https://brainly.com/question/11559160

#SPJ2


Related Questions

The ratio of dogs to cats is 3:8 there are a total of 99 dogs and cats in the shelter. How many are cats.

Answers

Answer:

72 cats

Step-by-step explanation:

sum the parts of the ratio, 3 + 8 = 11 parts

Divide the total by 11 to find the value of one part of the ratio.

99 ÷ 11 = 9 ← value of 1 part of the ratio, then

8 parts = 8 × 9 = 72 ← number of cats

if segment ac has a midpoint of b, and ab=32 and bc=5x+7, what is the length of segemnt bc

Answers

Answer:

             BC = 32

Step-by-step explanation:

B being midpoint of AC means:

BC = AB = 32

True or false: To determine the absolute value of a number, you can count how many units it is from zero.

Answers

Answer:

True the absolute value is how many digits away the number is from zero.

Step-by-step explanation:

A dolphin is at the surface of rhe water and then descends to a depth of 4 1/2 feet then the dolphin swims down another 2 3/4 feet what is the location of the dolphin relative to the surface of the water

Answers

Answer:

   down 7 1/4 feet

Step-by-step explanation:

4 1/2 + 2 3/4 = 4 2/4 + 2 3/4 = (4+2) +(2/4 +3/4) = 6 +5/4 = 7 1/4

The dolphin is 7 1/4 feet below the surface.

Answer:

Step-by-step explanation:

A) The sum of 5 and 2 times p is at least 11.

Answers

5 + 2p is at least 11.

Subtract 5 from both sides.

2p is at least 11.

p > 5

If mZA = (8x + 6)° and m
ZB = (7x + 24)', then find the measure of ZB

Answers

i got x=18 i think u mistaken za for zb

Kesha drives 26 miles in 48 minutes. Keeping the same rate, how many miles does she drive in 12 minutes

Answers

about 6.5 miles

this is because there will be about .54 miles in one minutes so then you multiply that by 12 and get about 6.5

hope that’s correct

Once you are finished with your practice problems respond to the discussion prompt:
Classify each of the following rational numbers as repeating or terminating decimals.
3/5
1/9
7/10
5/12

Answers

Answer:

terminating

repeating

terminating

repeating

Step-by-step explanation:

3/5 = 0.6 ; terminating

1/9 = 0.1111... ; repeating

7/10 = 0.7 ; terminating

5/12 = 0.41666666... ; repeating

Please help me to prove this!​

Answers

Answer:  see proof below

Step-by-step explanation:

Given: A + B + C = π                     →  A = π - (B + C)

                                                     → B + C = π - A

Use the Pythagorean Identity: cos² A + sin² A = 1   →  sin² A = 1 - cos² A

Use Double Angle Identities: cos 2A = 2 cos² A - 1 → cos² A = (cos 2A + 1)/2

                                             → cos A = 1 - 2 sin² (A/2)    

Use Sum to Product Identity: cos A + cos B = 2 cos [(A + B)/2] · cos [(A - B)/2]

Use Cofunction Identities:  cos (π/2 - A) = sin (A)

                                             sin (π/2 - A) = cos A

                                             cos (-A) = cos (A)

Proof LHS → RHS:

[tex]\text{LHS:}\qquad \qquad \sin^2\bigg(\dfrac{B}{2}\bigg)+\sin^2 \bigg(\dfrac{C}{2}\bigg)-\sin^2\bigg(\dfrac{A}{2}\bigg)[/tex]

[tex]\text{Pythagorean:}\qquad 1-\cos^2 \bigg(\dfrac{B}{2}\bigg)+1-\cos^2 \bigg(\dfrac{C}{2}\bigg)-\bigg[1-\cos^2 \bigg(\dfrac{A}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =1-\cos^2 \bigg(\dfrac{B}{2}\bigg)-\cos^2 \bigg(\dfrac{C}{2}\bigg)+\cos^2 \bigg(\dfrac{A}{2}\bigg)[/tex]

[tex]\text{Double Angle:}\quad 1-\bigg(\dfrac{\cos(2\cdot \frac{B}{2})+1}{2}\bigg)-\bigg(\dfrac{\cos (2\cdot \frac{C}{2})+1}{2}\bigg)+\bigg(\dfrac{\cos (2\cdot \frac{A}{2})+1}{2}\bigg)\\\\\\.\qquad \qquad \qquad =1-\dfrac{\cos B}{2}-\dfrac{1}{2}-\dfrac{\cos C}{2}-\dfrac{1}{2}+\dfrac{\cos A}{2}+\dfrac{1}{2}\\\\\\.\qquad \qquad \qquad =\dfrac{1}{2}[1-(\cos B+\cos C)+\cos A][/tex]

[tex]\text{Sum to Product:}\qquad \dfrac{1}{2}\bigg(1-\bigg[2\cos \bigg(\dfrac{B+C}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)\bigg]+\cos A\bigg)[/tex]

[tex]\text{Given:}\qquad \dfrac{1}{2}\bigg(1-\bigg[2\cos \bigg(\dfrac{\pi -A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)\bigg]+\cos A\bigg)[/tex]

[tex]\text{Cofunction:}\qquad \dfrac{1}{2}\bigg(1-\bigg[2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)\bigg]+\cos A\bigg)[/tex]    

[tex]\text{Double Angle:}\qquad \dfrac{1}{2}\bigg[1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)+1-2\sin^2 \bigg(\dfrac{A}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =\dfrac{1}{2}\bigg[2-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)-2\sin^2 \bigg(\dfrac{A}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =1-\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)-\sin^2 \bigg(\dfrac{A}{2}\bigg)[/tex]

[tex]\text{Factor:}\qquad \qquad 1-\sin \bigg(\dfrac{A}{2}\bigg)\bigg[ \cos \bigg(\dfrac{B-C}{2}\bigg)-\sin \bigg(\dfrac{A}{2}\bigg)\bigg][/tex]

[tex]\text{Given:}\qquad \qquad 1-\sin \bigg(\dfrac{A}{2}\bigg)\bigg[ \cos \bigg(\dfrac{B-C}{2}\bigg)-\sin \bigg(\dfrac{\pi -(B+C)}{2}\bigg)\bigg][/tex]

[tex]\text{Cofunction:}\qquad 1-\sin \bigg(\dfrac{A}{2}\bigg)\bigg[ \cos \bigg(\dfrac{B-C}{2}\bigg)+\cos \bigg(\dfrac{B+C}{2}\bigg)\bigg][/tex]

[tex]\text{Sum to Product:}\ 1-\sin \bigg(\dfrac{A}{2}\bigg)\cdot 2 \cos \bigg(\dfrac{(B-C)+(B-C)}{2\cdot 2}\bigg)\cdot \cos \bigg(\dfrac{(B-C)-(B+C)}{2\cdot 2}\bigg)\\\\\\.\qquad \qquad \qquad =1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(-\dfrac{C}{2}\bigg)[/tex][tex]\text{Cofunction:}\qquad =1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(\dfrac{C}{2}\bigg)[/tex]

[tex]\text{LHS = RHS:}\quad \checkmark\\\\\quad 1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(\dfrac{C}{2}\bigg)=1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(\dfrac{C}{2}\bigg)\quad[/tex]

                   

Which of the following options represents the graph of the function show above? f(x) = (x+3) ^3- 1
f(x) = (x-3) ^311
f(x) = (x-3)^3+ 1
f(x) = ( x + 3)^3+1

Answers

Answer:

C

Step-by-step explanation:

First, notice that this is a cubic function.

The standard form for a cubic function is:

[tex]f(x)=a(x-b)^3+c[/tex]

Where a is the vertical stretch, b is the horizontal shift, and c is the vertical shift.

From our graph, we can see that unlike the parent function, x³, this cubic is 3 units to the right and 1 unit up from the standard position.

Therefore, our b is +3 and c is +1. Let's substitute these values. Also, let's assume a is 1. So:

[tex]f(x)=(x-3)^3+1[/tex]

Therefore, our answer is C.

And we're done!

1- Find the slope of the line: y = -4/3 X-1*
m= -1 m= -4 m= -4/3 m= 4 v

Answers

Slope-intercept form: y = mx + b

m = the slope

y = the y-intercept

In our problem,

y = -4/3x - 1

m = -4/3

The slope is -4/3

NEED HELP ASAP!!!
TEN POINTS!

Answers

The answer it’s letter D

A very large book has pages numbered from 1 to 11521. How many times is the digit 3 printed? Helppp

Answers

Answer:

The total number of pages from page X to page Y is Y minus X plus 1.

So from 1 to 9, there are 9 minus 1 is 8 plus 1 is 9.

Step-by-step explanation:

Whenringingupacustomer,acashierneeds15secondstoprocesspaymentaswellas3secondstoscaneachitembeingpurchased.Ifittakes21secondstoringupacustomer,howmanyitemsarebeingpurchased?

Answers

Answer:

um, can you make that a bit clearer thanks! (:

Step-by-step explanation:

9) What two operations are needed to solve 2x - 4 = 16?
a. Addition & division
b. Addition & subtraction
c.Multiplication & subtraction

Answers

Answer:

a. Addition & division

Step-by-step explanation:

2x - 4 = 16   (adding 4 to both sides)

2x  = 16 + 4

2x = 20  (dividing both sides by 2)

x = 20/2 = 10

Hence we can see that the two operations are addition and then division

A pound is approximately 0.45 kilogram. A person weighs 87 kilograms. What is the person's weight, in pounds, when rounded to the nearest
whole number?
ОА
39 lb
OB. 52 lb
OC 193 lb
OD. 180 lb

Answers

Answer:

OC 193 lb is correcte!

The person's weight, in pounds, when rounded to the nearest

the whole number is equal to [tex]1.9\times10^{2} pound[/tex]

We have given that, A pound is approximately 0.45 kilogram.

0.45 kg = 1 pound

Thus if 0.45 kg is equal to= 1 pound

87 kg will be equal to [tex]=\frac{1}{0.45} \times 87=1.9 \times 10^2 pound[/tex]

What are the significant digits?

The number of significant digits in an answer should be equal to the least number of significant digits in any one of the numbers being multiplied, divided, etc.

Thus the answer should contain 2 significant digits.

To learn more significant digits visit:

https://brainly.com/question/24491627

#SPJ2

I need help ASAP PLEASE!
Determine whether this statement is true or false. If the statement is false, give a counterexample.
Statement: All integers are rational numbers.

Answers

heya....

your answer is:

All rational numbers are not integers. But all integers are rational numbers.

The statement is false.

It may help you...☺☺

X divided by 11 equals 10 divided by 12 what’s x

Answers

Answer:

x/11 = 10/12

x = 10*11/12= 55/6

Step-by-step explanation:

Solution:

[tex] \huge \pink {\tt { \frac{x}{11} = \frac{10}{12}}} [/tex]

By cross multiplication, we get

12x = 110

or, x = 110/12 = 55/6

Answer: x = 55/6

5t+1= 9
Please help me​

Answers

Exact Form: t = 8/5

Decimal Form: t = 1.6

Mixed Number Form: t = 1 3/5 (one and three fifths)

Answer:

t = 8/5 or t = 1.6

This will be a fraction buh can be turned into a decimal

Step-by-step explanation:

subtract 1 on both sides 5t + 1 - 1 = 9 - 1

then simplify 5t = 8 after det divide both side 5t/5 = 8/5 and den your answer is t = 8/5...

HOPE DIS HELPS YU OR IS RIGHT!!!!!

¿Cuál es el valor de 0.1561 redondeado a la décima más cercana?
A 0.15
B 0.16
C 0.1
D 0.2

Answers

Answer:

A0.15

Step-by-step explanation:

3/5(1 + p) = 21/20
find the solution to p

Answers

Answer:

3/4

Step-by-step explanation:

3/5(1+p)-21/20

3/5+3/5p=21/20

3/5p=21/20-3/5

3/5p=21/20-12/20

3/5p=9/20

p=9/20÷3/5

p=9/20*5/3

p=45/60

p=3/4

For a science experiment, Marcia dissolved 1.0 kilogram of salt in 3.0 liters of water. For a different experiment, Bobby dissolved 2.0 pounds of salt in 7.0 pints of water. Which person made a more concentrated salt solution? Explain. Use 1 L = 2.11 pints. Round your answer to the nearest hundredth.

Answers

Step-by-step explanation:

The concentration of Marcia's solution is:

1.0 kg / 3.0 L = 0.33 kg/L

The concentration of Bobby's solution is:

(2.0 lb × 1 kg / 2.2 lb) / (7.0 pints × 1 L / 2.11 pints) = 0.27 kg/L

Therefore, Marcia's solution is more concentrated.

How do you solve 2 1/3 + 5y = 4

Answers

Answer:

Not sure but that's my answer

DOES ANYONE KNOW THIS?????

Answers

Answer:

if i;m right its 45 degrees

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

alternative angle theorem lets you know that angle acb is equal to cae and you can find acb since you know all angles add up to 180. 180-105-47=28

Christian's car used 15 gallons to travel 270 miles. How far can he travel on 11 gallons?

Answers

Answer:

198

Step-by-step explanation:

270/15 gives us 18, his miles per gallon. multiply that by 11, and you get 198.

state the domain, the range, and the intervals on which function is increasing, decreasing, or constant in interval notation

Answers

Answer:

domain (-∞, ∞)range (-∞, 4]increasing (-∞, 0)decreasing (0, ∞)constant (only at x=0, not on any interval)

Step-by-step explanation:

The graph is of the equation y = -x^2 +4. It is a polynomial of even degree, so has a domain of all real numbers: (-∞, ∞).

The vertical extent of the graph includes y=4 and all numbers less than that:

  range: (-∞, 4]

The graph is increasing to the left of its vertex at x=0, decreasing to the right.

  increasing (-∞, 0); decreasing (0, ∞)

There is no interval on which the function is constant. It has a horizontal tangent at x=0, but a single point does not constitute an interval.

Hi May I know how to solve this question

Answers

The correct answer is (2) 150
(3) is the correct answer!

Please help :D <3. Do not understand this one.

Answers

Sorry for my messy handwriting but this is the answer

What is the area of this shape? Explain why?

Answers

Answer: 672

1. You need to find the arena of the missing piece so with the 40 on top you will subtract 12 which will give you 28

2. To find the other side subtract 28-12 to get 16 then you will multiple then together to get 448

3. Now just Multiply 40 and 28 to get 1120

4. Subtract 1120 and 448 and you’ll get the answer of 672

5. If x^1/2 =8, what is the value of x?

Answers

the answer would be: x=24
Other Questions
Please help, I don't understand, please 5+(-5) newspaper of future The Latin phrase e pluribus unum means WILL GIVE BRAINLIEST!!!! How did the Great Awakening inspire a change in political thought?O It encouraged people to be more independent by rejecting traditional forms of worship.It motivated people to recommit to their traditional churches and recruit more members.O It created a new system of religious denominations that ensured the power of the church.O It caused a decline in religious commitment and less tolerance toward new forms of worship. what do you mean by levels of professions Draw the conjugate base for the acid (CH3)2C=OH+ Remember to include charges and non-bonding electrons wherenecessary HELP ME PLSEASE I NEED THIS Is it true that square roots can be compared and ordered by comparing and ordering the numbers underneath the radical symbol? Harvey is 3 times as old as Jane. The sum of their ages is 52 years. Find the age of each. Jane is 13 and Harvey is 39 Jane is 12 and Harvey is 48 Jane is 13 and Harvey is 48 Mark wants to put a fence around his square yard.He knows that his yard is shaped like a square and the area of the yard is 110. What would the perimeter be Subtract: 3 x 106 7.197 x 105 = WWW Together Fred and Wilma have saved $345 Wilma has have twice as much money as Fred how much money do they each have define your variables and set up a system of equations with two equations write an article for publication in your school magazine suggesting at least two ways of by which cheating in the BECE can be stopped a 1 mL pipette delivers a measured volume of .98 mL (calculate the percentage error) application of genetics in to legal applications When a peanut farmer adds value to his peanuts by turning them into creamy peanut butter, the farmer is engaging in which of the processes listed below? The English Bible includes twelve books of the Major Prophets.a. Trueb. False help quick plzz i need help Identify which type of source is being described.sources present original research, whereassources summarize scientificinformation. What determines the type of blood a person has?A) Color B) amount of oxygen C) thickness D) molecules present