I need help with #61 to #64 ASAP please and thank you …. Could someone please help me with it… I need to get it done ASAP
Answers
Problem 61
The nth triangular number is
T(n) = n(n+1)/2
I'll rewrite this into
T(n) = 0.5n(n+1)
The triangular number right after this is
T(n+1) = 0.5(n+1)(n+2)
I replaced every n with n+1 and simplified
Let's see what we get when we add up the two expressions
T(n) + T(n+1)
0.5n(n+1) + 0.5(n+1)(n+2)
0.5n^2+0.5n + 0.5(n^2+3n+2)
0.5n^2 + 0.5n + 0.5n^2 + 1.5n + 1
n^2+2n+1
(n+1)^2
This shows that the sum of any two consecutive triangular numbers results in a square number
Here's a few examples
0+1 = 11+3 = 43+6 = 96+10 = 1610+15 = 25Note each sum is a perfect square, which visually would plot out a square figure.
For quick reference, the set of the first few triangular numbers is {0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55,...}
Answer: Square number==========================================================
Problem 64
Let's say we go with n = 5.
This means,
T(n) = 0.5n(n+1)
T(n-1) = 0.5(n-1)(n-1+1)
T(n-1) = 0.5n(n-1)
T(5-1) = 0.5*5(5-1)
T(4) = 10
This says that when n = 5, the 4th triangular number is 10
Triple that result and add on n = 5
3*T(4) + n = 3*10+5 = 35
This result is beyond obvious which category of figurate number it belongs to. It's not a triangular number since it's not in the form n(n+1)/2. It's not a square number either.
Through a bit of trial and error, you should find it's a pentagonal number
Pentagonal numbers are of the form n(3n-1)/2
If you plugged n = 5 into that, it leads to 35
n(3n-1)/2 = 5*(3*5-1)/2 = 5*14/2 = 70/2 = 35
The diagram shown below represents the first few pentagonal numbers. The number of blue dots corresponds to the pentagonal number itself. Note the equal spacing when dealing with dots on each segment (eg: some interior blue dots are midpoints, others are quarter points, etc.)
Answer: Pentagonal number
Related Questions
9 of the students in Sarah's grade like to watch football and 12 like to watch figure skating. 7 students like to watch both football and figure skating. How many students like to watch football but not figure skating?
Answers
Answer:
Step-by-step explanation:
Total for football: 9 +7
Total for figure skating: 12 +7
NEW Total for football: 16
NEW Total for figure skating: 19
The question says that 9 people like football
The question says that 12 people like to watch figure skating
The question also says that 7 people like to watch both, and because of that, you should add 7 to both 9 and 12, but keep the new numbers separated from each other. So once we know the sum of 9 +7 is 16, and 12 + 7 is 19, we can subtract the two numbers, and get 3 as the answer. Because you are counting the number of times that you have to travel up or down to the other number, and so if you are on a set of stairs that go up to the 16 level and you are on the 14th level, you need to travel up 2 sets of stairs to get to level 16.
Hope that example helps and can help in the future with other problems!
You are offered a weekly salary of $200 plus 5% commission on all your sales
a. Identify the input and output variables in this situation
Answers
Answer:
input: $200,5% Output: 10
Step-by-step explanation:
One of the two equal factors of a number is a _______?
Answers
Answer:
A square root
Step-by-step explanation:
A square root is one of two equal factors of a number.
how do you solve x/4+7=-2
Answers
[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]
How do you solve x/4+7 = -2[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
[tex] \large \sf \frac{x }{4} + 7 = - 2 \\ [/tex]
Multiply both sides of the equation by 4.[tex] \large \sf \: x+28=-8 [/tex]
Subtract 28 from both sides.[tex] \large \sf \: x=-8-28 [/tex]
Subtract 28 from -8 to get -36.[tex] \large \boxed{ \bf \: x=-36 }[/tex]
Which expression is equivalent to 3x(bx+10−(x2−5x+c)
A
(3b−1)x2−5x+10+c
B
−x2+(3b+35)x−c
C
−3bx2+25x+c
D
(3b−1)x2+35x−c
Answers
Answer:
Step-by-step explanation:
Angle A is three times the size of angle B.
The sum of the angle measures is 128 degrees.
What is the measure of angle A?
O 32 degrees
O 90 degrees
O 96 degrees
O 30 degrees
Answers
First, let's declare our variables
B = x+2
A = 3(x+2)
Now, let's create our expression.
A + B = 128
Plug in the values for A and B
x+2 + 3(x+2) = 128
We need to solve for x. Start off by simplifying the left side.
x+2 + 3x + 6 = 128
Combine like terms.
4x + 8 = 128
Subtract 8 from both sides.
4x = 120
Divide both sides by 4
x = 30
B = x+2 = 30 + 2 = 32 degrees
A = 3(x+2) = 3(30+2) = 3(32) = 96 degrees
Find the 14th term of the geometric sequence 5, -10, 20, ...5,−10,20,
Answers
Answer:
40,960
Step-by-step explanation:
To find the multiplier, set up an equation like this:
[tex]5x=-10[/tex]
The above equation will allow us to find what number, when multiplied with 5 will result in -10. If we divide both sides of the equation by 5, we'll find that the number, x, is -2:
[tex]x=-2[/tex]
We need to find the 14th term. To do this, simply multiply the lattermost number in the sequence by our multiplier, -2.
[tex]20*(-2)=40[/tex]
Since 5 is the first term in the sequence, -10 is the second term in the sequence, and 20 is the third term in the sequence, 40 is the fourth term. Now we just need to find the next ten so that we can find the 14th term. To do that, repeat the process of multiplying the lattermost number by -2 ten more times:
[tex]40*-2=-80\\-80*-2=160\\160*-2=-320\\-320*-2=640\\640*-2=-1280\\-1280*-2=2560\\2560*-2=-5120\\-5120*-2=10240\\10240*-2=-20480\\-20480*-2=40960[/tex]
Therefore, the 14th term is 40,960.
Answer:
-40,960
Step-by-step explanation:
you have to add the negative because there partners in crime
Multi-Step Two friends compare the amount of change they
have in their pockets. Ashley has 12 nickels, 2 dimes, and
4 quarters. Beto has 10 nickels, 4 dimes, and 3 quarters.
Who has more money?
Answers
Answer:
Ashley
Step-by-step explanation:
Ashley:
12n (n=5) = 60+2u (u=10)=80
4 quarters equal a dollar
$1.80
Beto:
10n (n=5)= 50+ 4u (u=10) = 90
3 quarters equal .75
$1.65
Kayla found the difference of 32 and 18. What is the difference?
Answers
Step-by-step explanation:
Just Subtract
32-18
14 Answer
Answer:
Answer is 14
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
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Answers
Answer:
"B"
~~~~~~~~~~~
a = 2/3
C they are both ratios
d 2*sqrt(2) = 2
Step-by-step explanation:
The temperature in Celsius would be,
Answers
First derisive the equation for C
[tex]\\ \sf\longmapsto F=\dfrac{9}{5}C+32[/tex]
[tex]\\ \sf\longmapsto C+32=\dfrac{5}{9}F[/tex]
[tex]\\ \sf\longmapsto C=\dfrac{5}{9}F-32[/tex]
F=101F[tex]\\ \sf\longmapsto C=\dfrac{5}{9}101-32[/tex]
[tex]\\ \sf\longmapsto C=\dfrac{505}{9}-32[/tex]
[tex]\\ \sf\longmapsto C=56.1-32[/tex]
[tex]\\ \sf\longmapsto C=24.1°C[/tex]
Superman bought two leggings for $25.80 each at KryptonCromie. How much did he spend?
Answers
Answer:
51.6
Step-by-step explanation:
$25.80 + $25.80 =
OR
25.80 x 2.
Answer $51.6
Step-by-step explanation:
because 25.80+25.80 is...$51.6
Given that f(x) = 9 – 5x and g(x) = x2, find a simplified expression for
g(f(x))
Answers
The answer is f(g(x))=x^2-30x+216
May i have brainliest
For her car, Joan paid $99.01 on speakers and $98.32 on new tires with
two $100 bills. How much did Joan get in change?
Answers
200-(99.01+98.32)
200-197.33
2.67 left in change
Hello :D
2 x $100 = $200
$99.01 + $98.32 = $197.33
$200 - $197.33 = $2.67
The answer is $2.67. I hope this helps :)
-124 = -7(5x+ 6)- 6x how do I solve this
Answers
Answer:
Step-by-step explanation:
-124 = -7(5x+ 6)- 6x Remove the brackets
-124 = -35x - 42 - 6x Combine like terms
-124 = -41x - 42 Add 42 to both sides
-124+42 = - 41x Combine
-82 = - 41x
-82/-41 = x
x = 2
Need help with number 5 ASAP.
Answers
Answer:
A) ahead 1 space
Step-by-step explanation:
2-3 = -1
-1-2 = -3
-3+4= 1
EXPLANATION:
2 - 3 - 2 + 4= 1
what is formula for volume of a cylinder?
Answers
Answer:
V = π × r² × h
Step-by-step explanation:
All you need to do is multiply the base times the height and since the base is a circle whose formula is π × r², we get π × r² × h.
What is the unit rate for 12 juice boxes for $3.35?
Answers
Explanation: All you have to do is multiply 3.35 and 12! :)
what is the anwser to this on the number line 7 - 6y > 19
Answers
Answer:
y < -2
Step-by-step explanation:
7 - 6y > 19
Subtract 7 from each side
7-7 - 6y > 19-7
-6y > 12
Divide each side by -6. remembering to flip the inequality
-6y/-6 < 12/-6
y < -2
Pls help and no links
Answers
Max owes $20 pays 10(1st week) then pays 5(2nd week)
10+5=15
20-15=5
So Max gotta pay 5 more
152-20=132
132+84=216
5 yards +15 yards=20 yards
Gains 12 yards back so
20-12=8
or 5+15-12=8
10. In a 2 hour Mathematics paper, there are
20 questions to be answered by Yao. After
1 hour he had answered 5 questions.
b) What fraction of the time had gone?
Answers
Answer:
1/2
Step-by-step explanation:
1 hour=60 minutes
2 hours=120 minutes
60/120=1/2
hope you got it
If you have any problem just ask me
If you think this is the best answer please mark me as brainliest
After 1 hour, Yao had completed 25% (1/4) of the 2-hour Mathematics paper.
In order to understand the fraction of time Yao had spent on the Mathematics paper after 1 hour, let's break down the problem. Yao was given a 2-hour Mathematics paper to complete, and he answered 5 questions in the first hour.
Now, let's calculate the fraction of time that had passed. To do this, we can set up a ratio of the time Yao had spent to the total time available. The time Yao spent is 1 hour, and the total time available is 2 hours. So the fraction of time that had gone can be represented as:
= Time spent / Total time
= 1 hour / 2 hours
= 1/2
Therefore, after 1 hour, Yao had completed half of the allotted time. However, we are asked to express this fraction in terms of questions answered. Yao had answered 5 questions out of a total of 20 questions.
To express the fraction of time in terms of questions answered, we can set up another ratio. The questions Yao answered is 5, and the total number of questions is 20. So the fraction of time that had gone can be represented as:
= Questions answered / Total questions
= 5 questions / 20 questions
= 1/4
Hence, after 1 hour, Yao had completed 1/4 of the total questions in the Mathematics paper. This means he still had 3/4 (or 75%) of the questions to complete in the remaining hour.
To know more about Fraction here
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Perform the indicated operations. Write the answer in standard form, a+bi.
-5-7i / 13+4i
Answers
Answer:
[tex]thank \: you[/tex]
PLEASE HELP I WILL MARK YOU BRAINIEST PLEASE
At their last babysitting gig, Zainab made $44 for 8 hours of work and Keziah made $47.25 in 9 hours. Each girl charges a different hourly rate. For a 10 hour job, which girl will make more money? How much more?
Answers
Answers:
Zainab made more moneyShe made $2.50 more=======================================================
Explanation:
To find the hourly rate, we divide the money made over the number of hours.
Zainab's hourly rate = 44/8 = $5.50 per hourKeziah's hourly rate = 47.25/9 = $5.25 per hourThen we'll multiply each of these results by 10 to figure out how much they made over the 10 hours
Zainab: 5.50*10 = 55 dollarsKeziah: 5.25*10 = 52.50 dollarsWe see that Zainab made more money and she made 55-52.5 = 2.50 dollars more.
math test please help, thank you if you do.
Answers
Answer: y=-4/3x+(-3)
Step-by-step explanation: y= (slope)x+(y-intercept)
Factorise : a²+b²-c²+2ab
Answers
Answer:
Step-by-step explanation:
a²+b²-c²+2ab
=a²+b²+2ab-c²
=(a+b)²-c²
=(a+b+c)(a+b-c)
You have an stick that is 25x long. 23 is 7/25th of the length. What is the length?
Answers
Answer:
82 1/7 unitsStep-by-step explanation:
The length is 25x and 7/25th of the length is 23:
7/25*25x = 237x = 23x = 23/7The length is:
25*23/7 = 575/7 = 82 1/7 unitsATQ
[tex]\\ \sf\longmapsto \dfrac{7}{25}\:of\:25x=23[/tex]
[tex]\\ \sf\longmapsto \dfrac{7}{25}\times 25x=23[/tex]
[tex]\\ \sf\longmapsto 7x=23[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{23}{7}[/tex]
Now
Length=[tex]\\ \sf\longmapsto 25x[/tex]
[tex]\\ \sf\longmapsto \dfrac{25(23)}{7}[/tex]
[tex]\\ \sf\longmapsto \dfrac{575}{7}[/tex]
Evaluate 2(x + 1) - 3 when x = 6.
O A. 5
OB. 10
O C. 11
O D. 8
Answers
Answer:
C. 11Step-by-step explanation:
2(x + 1) - 3
(Putting x = 6)
= 2(6 + 1) - 3
= 2 × 7 - 3
= 14 - 3
= 11 (Ans)(
Because you multiply the 2 into the () then add the two new numbers and subtract 3
For a project in her Geometry class, Madelyn uses a mirror on the ground to measure
the height of her school's flagpole. She walks a distance of 8.75 meters from her
school, then places a mirror on flat on the ground, marked with an X at the center.
She then steps 1.7 meters to the other side of the mirror, until she can see the top of
the flagpole clearly marked in the X. Her partner measures the distance from her eyes
to the ground to be 1.65 meters. How tall is the flagpole? Round your answer to the
nearest hundredth of a meter.
1.65 m
1.
1.7 m
-8.75 m
Answers
An image is always formed at the back of a mirror. Thus, the appropriate option is D. -8.75 m. The flagpole is 8.75 m tall.
Let the angle of depression from Madelyn's point of view be represented by θ. Then applying the required trigonometric function, we have;
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
= [tex]\frac{1.65}{1.7}[/tex]
Tan θ = 0.9706
θ = [tex]Tan^{-1}[/tex] 0.9706
= [tex]44.2^{o}[/tex]
θ = [tex]44.2^{o}[/tex]
Let the height of the flag be represented by h. And for a given mirror, the angle of incidence is equal to that of reflection. Then;
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
= [tex]\frac{h}{8.75}[/tex]
0.9706 = [tex]\frac{h}{8.75}[/tex]
h = 0.9706 x 8.75
= 8.49275
h = 8.5 m
Since the image is formed at the back of the mirror, then the flagpole is 8.5 m.
Therefore the appropriate answer is option D. -8.75 m
Visit: https://brainly.com/question/14374661
Answer:
10.77
Step-by-step explanation:
i did it
3.2 less than a number t is at most 7.5.
Answers
Answer:
10.7
Step-by-step explanation:
10.7-3.2 is at most 7.5
A man is three times as old as his son in 10 years time their combined ages will be 68 how old is each person now person now
Answers
Answer:
The dad is 36 and the son is 12
