Triangular numbers can be represented with equilateral triangles formed by dots the first fire triangle numbers are 1 3 6 10 and 15 is there a direct variation between a triangle number and its position in the sequence explain your reasoning

Answers

Answer 1

Answer:

There's no direct variation

Step-by-step explanation:

Required

Determine if there's a direct variation between the number and its position

I'll start by giving an illustration of how the triangle is represented using stars (*)

*

**

***

****

*****

Represent the line number with y and it's position with x

On line 1:

y = 1, x = 1

On line 2:

y = 2, x = 3

On line 3:

y = 3, x = 6

On line 4:

y = 4, x = 10

On line 5:

y = 5, x = 15

Note that, x is gotten by calculating the accumulated number of stars while y is the line number.

Direct variation is represented by

y = kx

Or

kx = y

Where k is the constant of variation

For line 1:

Substitute 1 for y and 1 for x

k * 1 = 1

k = 1

For line 2:

Substitute 2 for y and 3 for x

k * 3 = 2

Divide through by 3

k = ⅔

Note that the values of k in both computations differ.

This implies that there's no direct variation and there's no need to check further.

Answer 2
Answer:
No, the triangular numbers are not a direct variation. There is not a constant of variation between a number and it's 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.

Step-by-step explanation:

Related Questions

Drag and drop the answer into the box to match each point to its
coordinates.

Answers

Point A is [tex](-\frac{1}{2},-\frac{1}{4})[/tex]

Point B is [tex](-2\frac{1}{2},1\frac{1}{2})[/tex].

Point C is [tex](\frac{1}{4},\frac{1}{2})[/tex].

Simple!

help me find x is this question

Answers

Answer:

12.25

Step-by-step explanation:

You have to work it out like if it was a ratio.

basically you need to make 7/x equal to 4/7

to do this you divide 4 by 7 and the divide 7 by the answer. This will make x equal to 12.25

what is the square root of 16

Answers

Answer:

the square root of 16 is 4

Step-by-step explanation:

n − 23 ≥ 19 solve the inequality

Answers

Answer:

N greater than or equal to 42

Step-by-step explanation:

You have to look at the equation and then add 23 to both of the sides. After you will get 42 and drop down everything.

Im stuck again I SUCK AT MATH please help!!

Answers

Answer:

2 does not belong

Step-by-step explanation:

We know that 2 cups of orange juice make 3 cups of fruit punch. So 2/3 cups of orange juice makes 1 cup of fruit punch. Due to this, you know that 2/3 belongs.

Please help me!!!!! I’m confused

Answers

The negative sign on an exponent means the reciprocal. Think of it this way: just as a positive exponent means repeated multiplication by the base, a negative exponent means repeated division by the base.

Answer:

means you divide.

Step-by-step explanation:

A positive you would multiply and a negative you divide.

Does that make sense>

SOMEONE PLZ HELP! ALSO DONT SPAM!

Answers

Answer

A : (1,-5)

Explanation

Dude, I'm pretty sure the stuff is used to throw you off. Just find the coordinates.

Answer:

A : (1,-5)

Step-by-step explanation:

What is an equation of the line that passes through the point (-2,-6)(−2,−6) and is parallel to the line x+2y=8x+2y=8?

Answers

Answer:

y=

2

1

x−7

Step-by-step explanation:

uii

Answer:

y=1/2x-7

I know it because the guy who typed the other answer was a idiot

PLEASE GIVE ME AN ANSWER QUICKLY! Hiroshi spends 30 minutes on history homework , 60 minutes on English homework, and x minutes on math homework. One fourth of his total homework time is spent on math. Which equation can be used to find the amount of time Hiroshi spends on his math homework?

A. 1/4 (x+30+60)=x

B. 1/4 (x)=x(30+60)

C. 1/4x(30+60)=x

D. 1/4(x)=(30+60)

Answers

Answer:

A

Step-by-step explanation:

He spends:30 mins on History60 mins on Englishx mins on mathso the total time he spends is [tex](TotalTime)minutes=(30+60+x)minutes[/tex] one fourth of this is his math time, since x is math time, then we have [tex]\frac{1}{4}(TotalTime)minutes=(x)minutes[/tex] But we know what totaltime in minutes is so [tex]\frac{1}{4}(30+60+x)minutes=(x)minutes[/tex] or simply: [tex]\frac{1}{4}(30+60+x)=x[/tex]

A rectangle has a perimeter of 38+x 38+x centimeters. The rectangle has a length of 3x−2 3x−2 centimeters and a width of x centimeters. What is the length of the rectangle? A. Substitute the dimensions of the rectangle info the perimeter formula P=2w+2l P=2w+2l b. Solve for x. C. Find the length of the rectangle.

Answers

Answer:

The length of the rectangle is 6 centimeters

Step-by-step explanation:

The perimeter of a rectangle =

P = 2L + 2W

A rectangle has a perimeter of 38+x centimeters. The rectangle has a length of 3x−2 centimeters and a width of x centimeters.

Hence:

38 + x = 2(3x - 2) + 2(x)

38 + x = 6x - 4 + 2x

Collect like terms

38 + 4 = 6x + 2x - x

42 = 7x

x = 42/7

x = 6 centimeters

The length of the rectangle is 6 centimeters

A function is defunded by f(x)=x/4. What is f(-8)?
pls help :(

Answers

-8 is what you are inputting, or the replacement for x in this function. all you gotta do it divide it by 4 to get -2.

Consider the scenario, and use unit rates to determine the better deal.
Nancy’s store is selling pens in bundles of 8 for $2.56. Joe’s store is selling the same pens in bundles of 6 for $2.28. Which store has the better deal?

Answers

Answer:

Nancy’s Store

Step-by-step explanation:

To find which store has a better deal we are going to have to find the unit price per pen. To do this we do the following:

2.56/8 and 2.286 after doing both divisions we find that the cost of price per pens is .32$ from Nancy and .38$ from Joe.

In Carna's desk drawer, there are 16 paper clips and 20 elastic bands. In Noelia's office supply tray, there are 10 paper clips and 13 elastic bands. Who has a lower ratio of paper clips to elastic bands?

Answers

Answer:

Carna has a lower ratio of paper clips to elastic bands

0.2

Step-by-step explanation:

step one

given data

In Carna's desk drawer

number of paper clips 16

number of elastic band= 20

ratio of paper clips to elastic bands

16:20= 1/5 =0.2

Noelia's office supply tray

number of paper clips 10

number of elastic band= 13

ratio of paper clips to elastic bands

10:13= 0.76

Carna has a lower ratio of paper clips to elastic bands

0.2

give the new coordinates. Square WXYZ with vertices W(1,7), X(6,5),
Y(4,0), and Z(-1, 2): (x, y) = (x-7, y-6)

Answers

Given:

The vertices of square WXYZ are W(1,7), X(6,5),  Y(4,0), and Z(-1, 2).

Consider the rule of transformation is [tex](x, y)\to (x-7, y-6)[/tex].

To find:

The new coordinates.

Solution:

We have,

[tex](x, y)\to (x-7, y-6)[/tex]

Using the above rule of transformation, we get

[tex]W(1, 7)\to W'(1-7, 7-6)=W'(-6,1)[/tex]

[tex]X(6, 5)\to X'(6-7, 5-6)=X'(-1,-1)[/tex]

[tex]Y(4, 0)\to Y'(4-7, 0-6)=Y'(-3,-6)[/tex]

[tex]Z(-1, 2)\to Z'(-1-7, 2-6)=Z'(-8,-4)[/tex]

Therefore, the new vertices are W'(-6,1), X'(-1,-1), Y'(-3,-6) and Z'(-8,-4).

1010 rubber stamps cost $ 10.30 $10.30dollar sign, 10, point, 30. Which equation would help determine the cost of 2 22 rubber stamps? Choose 1 answer:

Answers

Answer: See explanation

Step-by-step explanation:

Your question isn't well written. Let's say 10 rubber stamps cost $ 10.30. Which equation would help determine the cost of 22 rubber stamps.

Based on the information in the question, the equation will be:

= $10.30/10 × 22

Therefore, to solve it further will be:

= $10.30/10 × 22

= $1.03 × 22

= $22.66

I start with 100 and subtract 3 repeatedly. (100 - 3, 97 - 3, 94 - 3 and so on). How many subtractions would I have to do to get the FIRST single-digit number?

Answers

31!!!
3(31)=93
100-93=7

Using an arithmetic sequence, it is found that you would need to do 32 subtractions

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term.

In this problem:

Starts with 100, which is the first term, hence [tex]a_1 = 100[/tex].Subtracts 3, which is the common difference, hence [tex]d = 3[/tex]

Then:

[tex]a_n = a_1 + (n - 1)d[/tex]

[tex]a_n = 100 - 3(n - 1)[/tex]

[tex]a_n = 103 - 3n[/tex]

To get a single-digit number, we need that:

[tex]a_n \leq 9[/tex]

Hence, solving the inequality:

[tex]103 - 3n \leq 9[/tex]

[tex]-3n \leq -94[/tex]

[tex]3n \geq 94[/tex]

[tex]n \geq \frac{94}{3}[/tex]

[tex]n \geq 31.3[/tex]

Rounding up, 32 subtractions need to be done.

A similar problem is given at https://brainly.com/question/23842987

Which ones form a square?

Answers

Answer:

the first one

Step-by-step explanation:

One week, Isabella bought two bags of apples and three bags of oranges. The next week, she bought one bag of apples and two bags of oranges. If a represents the cost of each bag of apples and are represents the cost of each bag of oranges, which expression could Isabella used to calculate the difference between the amount she spent each week?
A: 3a-r
B: 3a-r
C: (2a-3r)-(a-2r)
D: (2a+3r)-(a+2r)

Answers

Answer:

c

Step-by-step explanation:that is the answer

Can someone help me with 1,2,3

Answers

Answer:

I think its

1. AC=14

2.x=6

3.x=4

There are 88 students in 4 classes. If there are equal number of students in each class, how many students per class?

Answers

Answer:88

Step-by-step explanation: cause it say 88 students in class then it say how many students per class its 88 i think

Answer:

22

Step-by-step explanation: divided 88 by 4

Complete the equation of the line whose interpret is (9.0) and slope is -2. Remember to use y=mx+b format

Answers

Answer:

y = - 2x + 18

Step-by-step explanation:

Step 1:

y = mx + b          Slope Intercept Form

Step 2:

y = - 2x + b         Input Slope Value

Step 3:

0 = - 2 ( 9 ) + b           Input x and y values

Step 4:

0 = - 18 + b        Multiply

Step 5:

b = 18          Add 18 on both sides

Answer:

y = - 2x + 18

Hope This Helps :)

Jane made a mistake when writing down a mutliplication , and she multiplied by 54 instead of 45. Her answer was 198 more than it should have been. What number did she multiply 54 by?

Answers

Answer:

22

Step-by-step explanation:

Given that:

Let number multiplied by 54 = x

Let output = y

x * 54 = y + 198

x * 45 = y

54x = y + 198 - - - (1)

45x = y - - - (2)

Put y = 45x in (1)

54x = 45x + 198

54x - 45x = 198

9x = 198

x = 22

Number multiplied by 54 is 22

Which of the following in the picture is true about the function f(x) = (x-7)^2 + 9

Answers

Answer:

A).a. The vertex is in quadrant IV and the graph opens down.

Step-by-step explanation:

The price of a smart phone was reduced from $800 to $500. By what percentage was the price of the phone reduced?

Answers

-37.5 hope this helps!!!

Will give brainliest screenshot Will give brainliest screenshot Will give brainliest screenshot Will give brainliest screenshot attached

Answers

Answer:

one 5 and 2 ones hope this will help u

Answer:

One and five should be the answer.

Help please!! This is hw and it’s due soon.

Answers

Answer:

B

Step-by-step explanation:

Am i right???
plss check and dont lie
will give brainliest

Answers

Answer:

by the looks of it yeah you are

Step-by-step explanation:

The ice cream shop sells sundaes for $2 each and banana splits for $3 each. One day, the shop sold 8 more sundaes than banana splits and also made a total of $156. Which system of equations represents the situation?

Answers

Answer:

[tex]s = 8+b\\2s+3b=156[/tex]

Step-by-step explanation:

To find which systems of equation represents the situation, we can break down the key information and create two variables:

Variables:

Let [tex]s[/tex] = number of sundaes sold.

Let [tex]b[/tex] = number of banana splits sold.

Given information:

Sundae: [tex]\$2[/tex]

Banana Splits: [tex]\$3[/tex]

8 more sundaes sold than banana splits. This can be expressed by [tex]s=8+b[/tex].

Total sold was [tex]\$156[/tex]. This can be expressed as [tex]2s+3b=156[/tex].

∴ The systems of equation that expresses this situation are [tex]s=8+b[/tex] and [tex]2s+3b=156[/tex].

Hope this helps :)

What is the height of the prism shown below?
25
13
7
10

Answers

13 inches is the height

What is the equation of the line that passes through the point (7,−3) and has an undefined slope

Answers

Answer:

The equation of the line that passes through the point (7,−3) and has an undefined slope will have the equation:  x = 7.

Step-by-step explanation:

As the line has an undefined slope, meaning the line is vertical.

As we know that the vertical line passes through (7, -3), so it can never pass through any x-value other than x = 7, although it can pass through infinite y-values.

so the equation of line will be: x = 7

Therefore, the equation of the line that passes through the point (7,−3) and has an undefined slope will have the equation:  x = 7.

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