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
Schach [20]
3 years ago
11

Classrooms on one side of the science building are all numbered with consecutive odd integers. If the first​ room, the room with

the smallest classroom​ number, on this side of the building is numbered k​, write an expression in k for the sum of the first five classroom numbers in a row. Then simplify this expression. The sum of the first five classroom numbers in a row is
Mathematics
1 answer:
liubo4ka [24]3 years ago
8 0

Answer:

The sum of the first five classroom numbers in a row is 5k + 20

Step-by-step explanation:

Since the smallest classroom​ number on the side of the building is numbered k​ and each consecutive odd integer is separated by a difference of  

2.

Therefore:  

k is the first class room.

k +  2  is the second class room.

k +  4  is the third class room.

k + 6 is the third class room.

k + 8 is the fifth class room.

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

k + (k + 2) + (k + 4) + (k + 6) + (k + 8)

collecting alike terms we get

=  k + k + k + k + k + 2 + 4 + 6 + 8

= 5k + 20

Therefore, The sum of the first five classroom numbers in a row is 5k + 20.

You might be interested in
How would you answer this question? thanks
Bogdan [553]

Answer:

What is the question so we can answer

6 0
2 years ago
Colin has a pad with x pieces of paper on it. For his first class, he wrote on 5 fewer than half of the pieces of paper in the p
PIT_PIT [208]

Answer:

Colin has <em>8 sheets </em>left for his third class.

Step-by-step explanation:

Given that:

Total Number of pieces of papers = x

Number of pieces of papers used for 1st class = 5 fewer than half of the pieces in the pad

Writing the equation:

\text{Number of pieces of papers used for 1st class =} \dfrac{x}{2} -5 ...... (1)

Also, Given that number of pieces of papers used for the 2nd class are 2 more than that of papers used in the 1st class.

\text{Number of pieces of papers used for 2nd class =} \dfrac{x}{2} -5+2 = \dfrac{x}2 -3 ...... (2)

Now, number of pieces of papers left for the third class = Total number of pieces of papers in the pad - Number of pieces of papers used in the first class - Number of pieces of papers used in the first class

\text{number of pieces of papers left for the third class = }x-(\dfrac{x}{2}-5)-(\dfrac{x}{2}-3)\\\Rightarrow x-\dfrac{x}2-\dfrac{x}2+5+3\\\Rightarrow x-x+5+3\\\Rightarrow 8

So, the answer is:

Colin has <em>8</em> <em>sheets </em>left for his third class.

5 0
3 years ago
1. Ada purchased a house using a fixed rate mortgage. The annual interest rate is 6.3%
vlabodo [156]

The monthly  payment on the mortgage is option C) $2537.44

<u>Step-by-step explanation</u>:

  • Principal (P): $ 295,000
  • Rate (r): 6.3%  = 0.063
  • Number of times compounded (n): 12months\times15 years = 180
  • Number of years = 15

The formula is A = P(1 + r/n)^nt

⇒ A = 295000(1+0.063/180)^(180\times15)

⇒ A = 295000(180.063/180)^2700

⇒ A = 295000 (1.00035)^2700

⇒ A = 758854.5

Interest = Amount - Principle

⇒ 758854.5 - 295000

⇒ Interest = 463854.5

∴ The monthly payment for 15 years = 463854.5 / (15\times12)

The monthly  payment on the mortgage = 2576.9 (approximately option C)

8 0
3 years ago
The measure of angle P is five less than four times the measure of angle Q. Of angle P and angle Q are supplementary angles, fin
Andru [333]

Answer:

m∠P=140°

Step-by-step explanation:

Given:

∠P and ∠Q are supplementary angles.

The measure of angle P is five less than four times the measure of angle Q.

To find m∠P

Solution:

The measure of angle P can be given as:

A) m\angle P=4(m\angle Q-5)

And

B) m\angle P+ m\angle Q=180 [Definition of supplementary angles]

Substituting equation A into B.

4(m\angle Q-5)+ m\angle Q=180

Solving for m\angle Q

Using distribution:

4m\angle Q-20+ m\angle Q=180

Simplifying by combining like terms.

5m\angle Q-20=180

Adding 20 to both sides.

5m\angle Q-20+20=180+20

5m\angle Q=200

Dividing both sides by 5.

\frac{5m\angle Q}{5}=\frac{200}{5}

m\angle Q=40

Substituting m\angle Q=40 in equation B.

m\angle P+ 40=180

Subtracting both sides by 40.

m\angle P+ 40-40=180-40

m\angle P=140

Thus, we have:

m∠P=140° (Answer)

7 0
3 years ago
8 + 8 hshshdhhdhfbfbcbcbcbcbcbbxbxbxbxbcbcbcb
Sidana [21]

Answer:

16

Step-by-step explanation:

8+8=16

6 0
3 years ago
Read 2 more answers
Other questions:
  • A cup of broth can have 870 mg of salt, which is 30% of the recommended daily allowance. What is the recommended daily amount
    11·1 answer
  • which graph represents a function with the domain of all real numbers greater than or equal to -7 and less than 2
    12·2 answers
  • Will someone please tell me the values of X and Y ?
    14·1 answer
  • Please help! <br><br> which of the following is a trinomial with a constant term?
    5·1 answer
  • Could someone help me understand this?
    7·1 answer
  • In a school of 500 students, a random sample of 60
    5·1 answer
  • What is the area of a triangle with a base of 8 yards and a height of 3 yards
    15·2 answers
  • The ratio of men to women working for a company is 3 to 5. If there are 152 employees total, how many women work for the company
    13·1 answer
  • Which of the following relations are not functions? Select all that apply
    15·1 answer
  • Find the missing side of The Triangle ​
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!