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It is desired to pile some logs in layers so that the top layer contains one log, the next layer contains two logs, the next layer contains three logs, and so on; each layer containing one more log than the layer on top of it. There are 190 logs. Can all the log be used in such a grouping, and if so, how many logs are in the bottom layer?
Answer:
Yes all of the logs can be used in such a grouping.
We'll have 19 logs in the bottom row (and have 19 rows)
========================================================
Explanation:
Let n be the number of layers. Let T(n) represent how many logs there are total.
If you have 1 layer, then you have 1 log. So we can say that T(1) = 1.If there are n = 2 layers, then we have 1 log on top of two other logs, which leads to 1+2 = 3 logs total. This shows that T(2) = 3.If there are n = 3 layers, then we have 1 log on top of 2 which are on top of 3 at the very bottom. We have 1+2+3 = 6 logs total. So T(3) = 6.Having n = 4 layers gives 1+2+3+4 = 10 logs. So T(4) = 10Having n = 5 layers gives 1+2+3+4+5 = 15 logs. So T(5) = 15This process continues for however long you like. The sequence 1,3,6,10,15 is the set of triangular numbers, since the logs form a triangular or pyramid shape when stacked this way. To get the nth value in the triangular number sequence, use this formula
T(n) = 0.5*n*(n+1)
---------------
For example, let's say we wanted to find how many logs there were in the fifth layer
T(n) = 0.5*n*(n+1)
T(5) = 0.5*5*(5+1)
T(5) = 15
This matches from earlier.
The purpose of bringing in a formula is to see if we can get T(n) = 190 for some integer n.
-------------------
T(n) = 0.5*n*(n+1)
190 = 0.5*n*(n+1)
190*2 = n(n+1)
380 = n^2+n
0 = n^2+n-380
n^2+n-180 = 0
Applying the quadratic formula will lead to the two solutions: n = -20 and n = 19. We ignore the negative value of n as we can't have a negative number of rows. Therefore, n = 19 is the only valid solution here.
If we wanted to stack 190 logs in this triangular pyramid fashion, then we'll need to have 19 rows. The bottom row will have 19 logs.
----------
Check:
1+2+3+4+5+6+7+8+9+10 = 55
11+12+13+14+15+16+17+18+19 = 135
55+135 = 190
Or you could say,
T(n) = 0.5*n*(n+1)
T(19) = 0.5*19*(19+1)
T(19) = 190
Either way, the answer is confirmed.
WILL GIVE BRAINLIEST THANK AND FIVE STAR!
Which equation is equivalent to 32x−4y+1=0?
y=4x−1y is equal to 4 x minus 1
y=−38x−14y is equal to negative 3 eighths x minus 1 fourth
y=38x+14y is equal to 3 eighths x plus 1 fourth
y=−4x+1
Answer:
y=−38x−14y is equal to negative 3 eighths x minus 1 fourth is the answer.
Which value of x makes the equation true? 1/5 (2x-10) + 4x = -3(1/5x+4)
A -1/5
B 1/5
C 2
D -2
Answer:
Step-by-step explanation:
1/5 (2x - 10) + 4x = -3(1/5x + 4)
a bit ambiguous, I'll ASSUME you mean
1/5 (2x - 10) + 4x = -3(x/5 + 4)
2x/5 - 2 + 4x = -3x/5 - 12
5x = -10
x = -2
My answer being one of your options makes me think my assumption was correct.
Pls help!!!!!!!!!!!!!!!!!!!!!
Answer:
See below:
Step-by-step explanation:
First fill in:
180* . Every triangle has interior measurments of 180* total
Second fill in: Reason is definition of sum of triangle's interior angles
Third fill in: 2x. Everything in this equation is asking for the angles. First angle is 28, second angle is 2x, and third angle is x-4.
Fourth fill in: x=52
I found this by doing the following:
First, 180-28, so we can see how many degree we are left with.
152.
Now, make an equation:
152=2x+x-4
Simplify
152=3x-4
Add 4 to both sides to cancel out the -4.
156=3x
divide 156/3=52.
Now we know that x=52.
Although the question doesn't ask for this, you would now substitue 52 back into each of the equations to find that degree. For example, 2x=2(52), or 104*.
Answer:
See image
Step-by-step explanation:
All the angles of a triangle add up to 180°
The given diagram shows all the measures: 28°, x - 4° , and 2x
So add them up, set equal to 180 and solve for x. Combine like terms and subtract 24 from both sides of the equation. Divide both sides by 3. x = 52
What is the average rate of change on the interval from 3 to 9?
Enter your answer in the grid below. Make sure your answer contain
Answer:
5
Step-by-step explanation:
Scott bought
1
6
ton of rocks. Scott and 9 of his neighbors shared the rocks equally. What fraction of a ton of rocks will each person get?
Answer:
The answer is 16/10 or 1.6
Step-by-step explanation:
I'm guessing Scott bought 16 ton of rocks for this question since the question was written weirdly.
We know that Scott will share his 16 ton of rocks with 9 neighbors and himself.
Which means that the answer is 16/10 because Scott is gonna divide his 16 ton of rocks with 10 people. (9 neighbors and himself)
Hope this helps! :)
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Help I will give brainlest
A positive real number is 2 less than another. When 4 times the larger is added to the
square of the smaller, the result is 16. Find the numbers.
Answer:
by how i was taught its 2
Step-by-step explanation:
Select the graph of the equation y + x + 3 = 0.
Answer:
the fourth image
Step-by-step explanation:
y + x + 3 = 0
y = -x - 3
meaning slope = -1
and y-intercept is -3
answer: image attached
because they all look similar, it is the one that moves exactly one block per unit
x(5)+2=244
help pls
(^_^)
Simplify both sides of the equation
5x+2=244Subtract 2 from both sides
5x+2−2=244−25x=242Divide both sides by 5
[tex] \frac{5x}{5} = \frac{242}{5} [/tex]
Answer[tex] \: x = \dfrac{242}{5} [/tex]
OR
[tex] \: x = 48.4 [/tex]
The solution to the given problem is:
48.4To find the value of x, one would have to spread out the terms.
5x+2 = 244
Then we would make x the subject formula
5x= 244-2
5x=242
Divide both sides by 5 (value of x)
x= 242/5
Therefore, the value of x is 48. 4
Read more about algebra here:
https://brainly.com/question/19566504
3 + 6 x (5 + 4) ÷ 3 -7?
Answer:
Answer: 14
Step-by-step explanation:
[tex]{ \rm{3 + 6 \times (5 + 4) \div 3 - 7}} \\ \\ = { \rm{3 + (6 \times 9) \div 3 - 7}} \\ \\ = { \rm{3 + (54 \div 3) - 7}} \\ \\ = { \rm{14 }}[/tex]
If your gross monthly income is $2,500. What is your net monthly income after the government deducts the following percentages for taxes: Federal 25%, Indiana 3.4%, Social Security
6.1%, Medicare 1.4% and Local tax 1%.
Answer:
$1,577.50
Step-by-step explanation:
25+3.4+6.1+1.4+1= 36.9%
2,500*0.369 = 922.5
2500-922.5= 1577.5
17. Solve for x: 3xyz
i need help i would be very grateful ty :)
Answer:
C. x = P/3yzStep-by-step explanation:
Given equation:
3xyz = PSolve for x, divide both sides by 3yz:
3xyz/3yz = P/3yzx = P/3yzCorrect choice is C
Unit 4 Solving Quadratic equations {and complex number}
classyfying triangles unit 4
Answer:
What do you mean by that?
Step-by-step explanation:
Answer:
Is there more to the question? or a link/ picture you forgot to add?
Step-by-step explanation:
Find the length x. Please help
Step-by-step explanation:
# easy learning
good luck and god Blees you
help!!?1!1!1!1!1!1!1?1?1!?1?1!1?1!1?1?1?1?1??1?1!1
Joshua: 143.826 grams
Phoebe: 144 grams
Oliver: Unsure, but for sure what shouldn't happen
Joshua (advantage): It is actually good to include decimals into your information because more information helps assist in experiments with proper results but you must also not include unnessessary information
Phoebe (disadvantage): You should include decimals in information, especially relating to scale weighing and her method lacks decimals
Oliver (disadvantage): This experiment already involves grams and therefore you shouldn't change the form of measurement unless it requests for it to happen
Joshua: 143.826 grams (advantageous)
Phoebe: 144 grams (Disadvantage)
Oliver: Disadvantage
What is Rounding off?Changing a number's digits so that it approximates a value is known as rounding a number. The provided number is more simply represented by this value. For instance, 700,000 rather than 698,869 could be used to express a town's population.
Joshua:
Although it is beneficial to add decimals in your data since more information aids in experiments producing accurate results, you should avoid including unnecessary information.
Phoebe's method lacks decimals, which is a drawback because it pertains to scale weighing and you should include them in information.
Oliver : As this experiment already uses grammes, you shouldn't modify the units of measurement until specifically instructed to do so.
Learn more about Rounding off here:
https://brainly.com/question/13391706
#SPJ5
On a bird-watching trip, Mei and Jackie counted 68 birds.
Of these, 45 of the birds were sparrows. Which value is a
reasonable estimate of the percent of sparrows in the
birds Mei and Jackie counted?
1. 175%
2.140%
3. 70%
4. 90%
Answer:
The answer is 70% if you round it.
Step-by-step explanation:
45 out of 68 is 66 but if you're rounding it the answer is 70%.
what is the area of 146km 6.3km and 5.4km
Answer:
Step-by-step explanation:
Ask Siri
Answer:
Step-by-step explanation:
Evaluate 2/3p + 3 when p = 3/5=
Answer:
so 2/3X 3/5 + 3
10 + 9 / 15 by LCM method
so 19/15 + 3 = 19/15 + 45/15 = 64/15
hope it helps
Step-by-step explanation:
Answer:
3 2/5
Step-by-step explanation:
2/3 (3/5) + 3
Multiply
6/15 + 3
Reduce fraction
2/5 + 3 = 3 2/5
what is the answer this math problem?
Answer:
HLO Mate here is ur answer
Lisa has $200 in her savings account. This is 40% of the money she needs to take a weekend trip. What is the total cost of the trip she wants to take?
The total cost of the trip Lisa wants to take over the weekend is $500.
Let the total cost of the trip be T.Given the following data:
Savings account balance = $200Percent of trip expenses = 40%To determine the total cost of the trip Lisa wants to take over the weekend:
Since the percentage of the money in Lisa's savings account is equal to forty percent (40%) of what is required for the total cost of the trip. Thus, we would multiply the total cost of her trip by 40% and equate it to $200.
Total cost of her trip:
[tex]\frac{40}{100} \times T = 200\\\\0.4T=200\\\\T=\frac{200}{0.4}[/tex]
Total cost, T = $500.
Read more: https://brainly.com/question/2021001
which expression represents 100 less than 3 times the sum of 18 and 2
Answer: 3 times (18+ 2) - 100
3 (18+2) - 100 = -40
Step-by-step explanation:
this can explain everything . please help
35 - 45 / 9 x 5
Divide 45 by 9 to get 5.
35 - 5 x 5
Multiply 5 and 5 to get 25.
35 - 25
Subtract 25 from 35 to get 10.
= 10
Name the triangle as described
Answer:
scalene triangle
Step-by-step explanation:
Which values from the given replacement set make up the solution set of this inequality?
5m≤10; {0, 2, 4, 6}
{0, 4, 6}
{2}
{0, 2}
{2, 4, 6}
Answer:
the solution to the inequality is m[tex]\leq[/tex] 2, so the solution set can include 2 and 0 since it is less then 2. but the rest do not work. so the answer is {0,2}
Step-by-step explanation:
5m[tex]\leq[/tex]10
divide by 5 on both sides and you are left with
m[tex]\leq[/tex]2
only 2 and 0 are less than or equal to 2
Hope this helps!
Simplify 8 to the second power plus 2
8^2 + 2 = 64 + 2 = 66
The answer is 66 because 8 to the second power is 64 and then you add 2.
Answer:
66
Step-by-step explanation:
8^2 is equal to 64
64 +2 = 66
8^2 is 8x8
so 8x8= 64
64+2 is 66
Two angles are supplementary. The larger angle is 28∘ more than the smaller angle. Find the measure of the larger angle.
Supplementary means that the angles together equal 180°
So we simply do 180 - 28 = 152°
Hope this helps!
HELP!!!!
Solve, 4/9 - 4/10
Answer:
[tex]\frac{2}{45}[/tex]
Step-by-step explanation:
hope this helps! :D
have a miraculous day!! <3
What is meant by a circle's diameter?
Answer:
The diameter is the length of the line through the center that touches two points on the edge of the circle.
Step-by-step explanation:
please mark my answer in brainlist
Answer:
Step-by-step explanation
F u