answer.
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
algol13
2 years ago
5

Triangular numbers can be represented with equilateral triangles formed by dots. The first five triangular numbers are 1, 3, 6,

10, and 15. Is there a direct variation between a triangular number and its position in the sequence? Explain your reasoning
Mathematics
2 answers:
Alisiya [41]2 years ago
7 0
Direct variation is y = kx  where y  would be the value of the number and x would be its position in the sequence, k is a constant 

so for consecutive values y/x would be a constant k 
In this case its not true becuse for example  3/1 = 3 and 6/3 = 2 

so there is no direct variation here.
Lapatulllka [165]2 years ago
6 0

Answer:

No, there is NOT a direct variation.

Step-by-step explanation:

No, the triangular numbers are not a direct variation. There is not a constant of variation between a number and its position in the sequence. The ratios of the numbers to their positions are not equal. Also, the points (1, 1), (2, 3), (3, 6), and so on, do not lie on a line.

You might be interested in
85 percent of California community college transfers feel that their community college adequately prepared them to handle upper-
suter [353]

Answer:

Ans 1 is correct.

Step-by-step explanation:

We have given that,

p=0.85,

n=20.

we know that

1-P(x=1)=1-(0.85×0.15^19)=0.999

Ans 1 is correct.

7 0
2 years ago
Read 2 more answers
In addition to the facts in the diagram, which other statements are necessary to prove that ∆ABC is congruent to ∆EFG by the ASA
insens350 [35]

It should be B because you have to have 2 angles to know for sure.

8 0
2 years ago
Read 2 more answers
Prof. okamoto selects 3 different students to report on 3 different current events. if there are 27 students in the class, in ho
kenny6666 [7]
Consider this option:
C³₂₇=27!/(3!*24!)=25*13*9=2925 ways to select 3 students.
8 0
2 years ago
Find the real numbers x and y if -3+ix^2y and x^2+y+4i are conjugate of each other. Pls solve with the steps
Firdavs [7]
ANSWER
x = ±1 and y = -4.
Either x = +1 or x = -1 will work

EXPLANATION
If -3 + ix²y and x² + y + 4i are complex conjugates, then one of them can be written in the form a + bi and the other in the form a - bi. In other words, between conjugates, the imaginary parts are same in absolute value but different in sign (b and -b). The real parts are the same

For -3 + ix²y
⇒ real part: -3
⇒ imaginary part: x²y

For x² + y + 4i
⇒ real part: x² + y (since x, y are real numbers)
⇒ imaginary part: 4

Therefore, for the two expressions to be conjugates, we must satisfy the two conditions. 

Condition 1: Imaginary parts are same in absolute value but different in sign. We can set the imaginary part of -3 + ix²y to be the negative imaginary part of x² + y + 4i so that the 

   x²y = -4 ... (I)

Condition 2: Real parts are the same

   x² + y = -3 ... (II)

We have a system of equations since both conditions must be satisfied

   x²y = -4 ... (I)
   x² + y = -3 ... (II)

We can rearrange equation (II) so that we have

   y = -3 - x² ... (II)

Substituting into equation (I)

   x²y = -4 ... (I)
   x²(-3 - x²) = -4
   -3x² - x⁴ = -4
   x⁴ + 3x² - 4 = 0
   (x² + 4)(x² - 1) = 0
   (x² + 4)(x-1)(x+1) = 0

Therefore, x = ±1.
Leave alone (x² + 4) as it gives no real solutions.

Solve for y:

   y = -3 - x² ... (II)
   y = -3 - (±1)²
   y = -3 - 1
   y = -4

So x = ±1 and y = -4. We can confirm this results in conjugates by substituting into the expressions:

   -3 + ix²y 
   = -3 + i(±1)²(-4)
   = -3 - 4i

   x² + y + 4i
   = (±1)² - 4 + 4i
   = 1 - 4 + 4i
   = -3 + 4i

They result in conjugates
4 0
2 years ago
Read 2 more answers
Which system of equations is inconsistent?
Agata [3.3K]

Answer:

Option A is correct.

The system of equation is inconsistent is;

2x+8y=6

5x+20y=2

Explanation:

* A system of equations is called an inconsistent system, if there is no solution because the lines are parallel.

* If a system has at least one solution, it is said to be consistent .

*A dependent system of equations is when the same line is written in two different forms so that there are infinite solutions.

(A)

2x+8y=6

5x+20y=2

This is inconsistent, because as shown below in the  graph of figure 1 that the lines do not intersect, so the graphs are parallel and there is no solution.

(B)

5x+4y=-14

3x+6y=6

this system of equation is Consistent because it has exactly one solution as shown below in the graph of Figure 2 and also it is independent.

(C)

x+2y=3

4x+6y=5

this system of equation is Consistent because it has exactly one solution as shown below in the graph of Figure 3.

(D)

3x-2y=2

6x-4y=4

this is a consistent system and has an infinite number of solutions, it is dependent because  both equations represent the same line. as shown below in the graph of Figure-4.

Therefore, the only Option A system of equation is inconsistent.



8 0
2 years ago
Read 2 more answers
Other questions:
  • A game has 3 possible outcomes, with probabilities p1, p2, and p3. The amount of money that you will win or lose for each outcom
    6·1 answer
  • Find the rate of money collected per sweatshirt sold. Show tour work
    10·2 answers
  • Which data sets have outliers? Check all that apply.
    15·2 answers
  • Ed buys a vase for £24 and adds 25% onto the price before putting it into his shop window.
    9·1 answer
  • Jake made a total of 7 copies at a copy shop, with some being black-and-white copies and some being color copies. Black-and-whit
    14·2 answers
  • Find the second decile of the following data set 24, 64, 25, 40, 45, 34, 14, 26, 28, 24, 58, 51 D2 =
    11·1 answer
  • What can you tell about the mean of each distribution? Annual visit costs- A new leash on Life Animal Clinic
    11·2 answers
  • Question 45 A length of pipe that weighs 45 pounds is cut into two pieces. One of the pieces is 3 feet long and weighs 18 pounds
    7·1 answer
  • What is 80, 023 written in scientific notation?
    13·1 answer
  • A construction company is considering submitting bids for two contracts. It will cost the company \$10{,}000$10,000dollar sign,
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!