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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.

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An 8 foot length of 4 inch wide crown molding costs $16. How much will it cost to buy 40 feet of crown molding?
malfutka [58]
Converting feet to inches, 8*12=96 and 96*4=384. Next, 40*12=480. Since 384*x (if x represents the cost per inch of crown molding)=16*100=1600 cents due to that for every inch, we add x amount of money, we can find x to be 1600/384=800/192=400/96=200/48=100/24=50/12=25/6 by simply dividing both the numerator and denominator by 2 each time. Since we add x amount of money for every inch, and we have 480 inches, 480*x=480*25/6=2000 cents=2000/100=20 dollars is our answer
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2 years ago
Naomi and her children went into a bakery where they sell donuts for $1.25 each and cookies for $0.75 each. Naomi has $15 to spe
LiRa [457]

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4 0
1 year ago
In triangle $DEF,$ $\angle D = 30^\circ,$ $\angle F = 60^\circ,$ and $EF = 6.$ Find $DE + DF.$ [asy] unitsize(2 cm); pair D, E,
sergey [27]

Answer:

Step-by-step explanation:

The answer to this question is 12+6sqrt3.

This is because of the 30, 60, and 90 degree rule. The rule states that the hypotenuse is equal to twice the length of the shorter leg, which is the side across from the 30 degree angle.

Using the rule you now know that DF is 12. Then use the Pythagorean Theorem to find the length of DE. 12^2=144, and 6^2=36. 144-36=108.

The square root of 108 simplified=6sqrt3.

Then you add them together and get 12+6sqrt3.

5 0
2 years ago
Mathew rolls a number cube labeled with the numbers 1−6. He then flips a fair coin. What is the probability that he rolls a 4 an
kap26 [50]

Answer: 0.083


Step-by-step explanation:

Numbers on cube=6

faces on coin=2

Therefore, the total outcomes=6\times2=12

Now, the favorable outcome that he rolls a 4 and flips a head=1

The probability that he rolls a 4 and flips a head=\frac{\text{favorable outcome}}{\text{total outcome}}

⇒The probability that he rolls a 4 and flips a head=\frac{1}{12}=0.083333\approx0.83.

Therefore, The probability that he rolls a 4 and flips a head=0.083

3 0
2 years ago
Read 2 more answers
A football filters that is 60 m wide and 110 m long is being paved over to make a parking lot. The builder ordered 660,000,000 c
ad-work [718]
The answer is 10 cm

Imagine cement cover as a rectangle which volume is 660,000,000 cm3. So this rectangle has width (w = 60m), length (l = 110m), and height (h = ?). The height of the rectangle is actually a thickness of the cement layer. So, we will use the formula for the volume (V) of the rectangle to calculate the thickness:
V = w · l · h

It is given:
V = 660,000,000 cm³
w = 60 m = 60 · 100 cm = 6,000 cm
l = 110 m = 110 · 100 cm = 11,000 cm
h = ?

Using the formula: V = w · l · h
660,000,000 = 6,000 · 11,000 · h
660,000,000 = 66,000,000 · h
⇒ h = 660,000,000 ÷ 66,000,000 = 10 cm
4 0
1 year ago
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