Answers
Step-by-step explanation:
al nth term:
numerator:
[tex] = {n}^{2} [/tex]
denominator:
[tex] = n + 1[/tex]
so nth term :
[tex] = \frac{ {n}^{2} }{n + 1} [/tex]
b). 1; 11; 27; 49
first difference: 10; 16; 22
second difference :6
formula for 1st difference:3a+b
formula for 2nd difference:2a
Therefore:
2a=6
a=3
3a+b=10
sub in a
3(3)+b=10
9+b=10
b=1
sub into quadratic formula
[tex] {an}^{2} + bn + c[/tex]
[tex](3) {(1)}^{2} + (1)(1) + c = 1[/tex]
[tex]3(1) + 1 + c = 1[/tex]
[tex]3 + 1 + c = 1[/tex]
[tex]4 + c = 1[/tex]
[tex]c = - 3[/tex]
So Tn:
[tex]3 {n }^{2} + 1n - 3[/tex]
Step-by-step explanation:
a)
it is clearly a sequence of the square numbers over the numbers+1.
1/2 = 1²/(1+1)
4/3 = 2²/(2+1)
9/4 = 3²/(3+1)
16/5 = 4²/(4+1)
so, the nth term would be
n²/(n+1)
b)
an² + bn + c creates the sequence with increasing n (n = 1, 2, 3, 4, ...)
since for sequence the first starting value is often not generated by the general expression, we have to focus on n = 2, n = 3 and n = 4, and with that we get 3 equations with 3 variables (a, b, c) that we can solve :
n = 2
a×2² + b×2 + c = 11 = 4a + 2b + c
n = 3
a×3² + b×3 + c = 27 = 9a + 3b + c
n = 4
a×4² + b×4 + c = 49 = 16a + 4b + c
the first equation gives us
c = 11 - 4a - 2b
when we use this in the second equation, we get
27 = 9a + 3b + 11 - 4a - 2b = 5a + b + 11
b = 16 - 5a
now we use both of that in the third equation :
49 = 16a +4(16 - 5a) + 11 - 4a - 2(16 - 5a) =
= 16a + 64 - 20a + 11 - 4a - 32 + 10a =
= 2a + 43
2a = 6
a = 3
b = 16 - 5a = 16 - 5×3 = 16 - 15 = 1
c = 11 - 4a - 2b = 11 - 4×3 - 2×1 = 11 - 12 - 2 = -3
Related Questions
Is - 4 the absolute value of 3 – 7? Explain.
Answers
Answer:
See below:
Step-by-step explanation:
Hello! I hope you are having a nice day. My name is Galaxy and I will be helping you today!!
We can solve this problem in a single step, we just need to know more about absolute value.
Absolute value is the distance a number is away from 0. For example, if we need to find the absolute value of -7, it would be 7 as the distance can not be negative.
Since we know that, we can solve the problem using algebra and our new logic we got.
[tex]|3-7|=-4?\\4\neq -4[/tex]
We can see that -4 is not the absolute value, 4 is as the distance is 4 and cannot be negative.
Cheers!
please help me thank you!
ty ty :)
Answers
Answer:
the slope is flatter
the line is shifted 7 down
Step-by-step explanation:
PLS HELP
First answer- (5,0) (10,0)
Second answer- (0,1//20) (0,20)
Answers
2/5x+1/10(0)=2
2/5x=2
X= 5
X-intercept = (5,0)
Y-intercept means x= 0
2/5(0)+1/10y=2
1/10y=2
y=20
Y-intercept = (0,20)
Determine if the two triangles are congruent. If so, select the appropriate congruence postulate. If not, select the reason why.
Answers
Answer:
Asa
Step-by-step explanation:
Because if u look left to right on one triangle there is a angle and in between they have a com on line and on the right theres another angle so There for it’s angle side angle
A package of Oreos typically contained 45 cookies. Recently, Nabisco reduced the number to 39 cookies in a package because of inflation! What is the percent of change?
Answers
Answer:
Percentage of change - 15.4% (simplified)
Step-by-step explanation:
15.384%
i need answer please
Answers
The unknown side of the right angle triangle is the hypotenuse side of the triangle and the length to the nearest tenth is 20.5 cm.
What is a right angle triangle?Right angle triangle are triangle that has one of its angles as 90 degrees. The sides can be found using Pythagoras theorem.
Therefore,
c² = a² + b²
where
c = hypotenusea and b are the other legsHence,
15² + 14² = x²
225 + 196 = x²
x = √421
x = 20.5182845287
x ≈ 20.5 cm
learn more on right angle triangle here:https://brainly.com/question/3770177
Sarahi has p number of pencils, if she finds 2 more and then triples her amount she still has less than Damaris
who has 40. Write an inequality for how many pencils Sarahi has.
Answers
Answer:
I believe the inequality would be: p+2x3<40
Step-by-step explanation:
Not exactly sure if it is correct but p (number of pencils Sarahi has) added too the 2 more she finds, and then x3 (when she triples her amount). This is less then (<) what Damaris has (which is 40) so it would be p+2x3<40.
Again not sure if its completely correct, but i hope it helps :,)
help me please .
Ester purchased a used car, a Ford Focus, for $8400. The car is expected to decrease in value by 20% per year over the next couple of years.
At this rate, what can Ester expect the approximate value of the car to be after 6 years?
Question 6 options:
$1,409
$2,202
$4,200
$1,762
Answers
Answer:
$2,202
Step-by-step explanation:
If the car decreases in value 20% per year, that means that the car is only worth 80% of its value for the next year.
80% can be written as .80.
Multiply the value of the car by .80 6 times.
8400 multiplied by .80 = 6720
6720 multiplied by .80 = 5376
repeat this sequence 4 more times to come to an answer of 2,202
Pleaseeee helpppp asappp
Answers
Answer:
14
Step-by-step explanation:
A consumer magazine wants to figure out which of two major airlines lost a higher proportion of luggage on international flights. The magazine surveyed Standard Air (population 1) and Down Under airlines (population 2). Standard Air lost 45 out of 600 bags. Down Under airlines lost 30 of 500 bags.
Does Standard Air have a higher population proportion of lost bags on international flights?
Calculate the appropriate p-value.
i. 0.0817
ii. 0.1634
iii. 0.8366
iv. 0.9183
Answers
75,15,3 find the 6th term
Answers
Answer:
0.024
Step-by-step explanation:
75, 15, 3, ...
Now, let's take a look at thus pattern.
You'll notice how the numbers decrease.
Divide 75 by 5.
We get 15
Divide 15 by 5.
We get 3.
Then we have the pattern now.
3 ÷ 5 = 0.6 (4th term)
0.6 ÷ 5 = 0.12 (5th term)
0 12 ÷ 5 = 0.024 (6th term)
I hope it helps.
Dr.Goode prescribed 0.2 grams of cold medicine. This medicine comes in tablets that are 0.5 grams or 0.05 grams. Should his patient take 4 of the 0.5 gram tablets or 4 of the 0.05 gram tablets? Why?
90 POINTS PLS HELP
Answers
Answer:
4 of the 0.05 gram tablets
Step-by-step explanation:
4 of the 0.5 tablets would be 2 grams
4 of the 0.05 tablets would be 0.2 grams
someone please help me
Answers
Answer:
Area = 6cm^2
Step-by-step explanation:
Pythagorean Theorem = [tex]a^{2} + b^{2} = c^{2}[/tex]
[tex]a^{2} + 3^{2} = 5^{2}[/tex]
or
[tex]a^{2} + 9 = 25[/tex]
Subtract 9 from 25.
25 - 9 = 16
Square root 16 to get 4.
a = 4
Now to find the area.
Area = 1/2(3*4)
12/2 = 6
During her vacation, Leslie traveled 578.78 miles in 3 days.
On the first day, she traveled 197.07 miles, and on the second day, she traveled 187.11 miles. how many did she travel the 3rd day?
Answers
Answer:
I think the answer is 194.6 miles on the third day
Step-by-step explanation:
Mrs phillubum has $200 in her bank account and is saving at a rate of $25 each week.
Answers
The product of 0.4 and a number is 8
Answers
8/0.4=20
Hope you get a good grade on your quiz/test!!
A hexagon has equal side lengths and angle measures. How many reflectional symmetry does the regular hexagon have?.
Answers
The regular hexagon has 6 reflectional symmetries.
A regular hexagon has 6 congruent sides.
The number of sides of a polygon is the number of reflectional symmetry the polygon have.
Since the number of congruent sides of a regular hexagon is 6, then the regular hexagon has 6 reflectional symmetries.
Read more about reflectional symmetry at:
https://brainly.com/question/24584937
Answer:
It´s 6
Step-by-step explanation: Hope it helps ^w^
Help me please! I need help ill give brainliest
Answers
Answer:
26 1/4
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
You add up both fractions, sorry for the lazy explanation
PLEASE HELP
Jed has 352 stickers in his sticker collection. He wants
to put them in an album. The album holds 8 stickers per
page. How many pages will Jed need? *Show your work
for full credit using any method to solve the problem.
Answers
Hope my answer helped!
Your parents have given you some money to spend with your friends at Water World. You already have purchased a banana split for $7, and you end the day with $17. WRITE AND SOLVE an equation to find how much money you started the day at Water World with.
Answers
Answer:
$17=x-$7
x=$24
Step-by-step explanation:
Carry the 7 to the other side
$17+$7=x
x=$24
will mark brainliest for 2 possible answers (WITH NO LINKS AND ANSWERS WITHOUT EXPLANATION)
Answers
Answer:
Equation in cubed form is x^3+7x^2+7x-15
Step-by-step explanation:
Julio just bought a $267,900 house. He had a 20 year mortgage with a fixed rate of 5. 875%. Julio’s monthly payments are $1,558. 9. What percent of the purchase price was Julio’s down payment? a. 13% b. 15% c. 18% d. 20%.
Answers
Julio's down payment was 22.08% of the purchase price.
Given that Julio just bought a $ 267,900 house, and he had a 20 year mortgage with a fixed rate of 5.875%, and Julio's monthly payments are $ 1,558, to determine what percent of the purchase price was Julio's down payment the following calculation must be performed:
(267,900 x 1.05875) - (1558 x 12 x 20) = X
582,682.50 - 373,920 = X
208,762.50 = X
267,900 = 100
208,762.50 = X
208,762.50 x 100 / 267,900
77.92 = X
100 - 77.92 = 22.08
Therefore, Julio's down payment was 22.08% of the purchase price.
Learn more about maths in https://brainly.com/question/25917920
A machine takes 15 minutes to scan 1,125 pages. At this rate, how many pages can the machine in a hour?
Answers
Answer:
4500 pages
Step-by-step explanation:
an hour has 60 minutes. This means in 1 hour the machine will scan 60/15 more pages. 60/15 =4.
1125*4 =4500 pages/hour
In one hour the machine will scan 4500 pages.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that a machine takes 15 minutes to scan 1,125 pages.
The machine takes 15 minutes to scan 1,125 pages.
Then, in 1 minute, it will scan (1125/15) = 75 pages.
So, in 1 hour, it will scan -
x = 75 x 60
x = 4500
Therefore, in one hour the machine will scan 4500 pages.
To solve more questions on algebraic expressions, visit the link below -
brainly.com/question/1041084
#SPJ2
PLEASE HELP!!!
Which of the following are equations for the line shown below? Check all that
apply.
(5,1)
5
5
(-5,-3)
5
A. y + 3 = 0.4(x + 5)
B. Y-1 = 0.4(x - 5)
C. y - 3 = 0.4(x - 5)
Y5-06
1)
Answers
Answer:
The answer is A and B
Step-by-step explanation:
y-y=m(x-x)
y-(-3)=m(x-(-5))
y+3=0.4(x+5)
y-y=m(x-x)
y-1=0.4(x-5)
If for an A. P d = -4 then t20 - t15 is what?
Answers
Step-by-step explanation:
[tex] - 20 \: is \: your \: answer[/tex]
Supposition of Terms in an A.P.(1) Three terms as : a -d, a,a + d .(2) Four terms as : a -3d , a - d , a + d , a + 3d .(3)Five terms as : a -2d , a - d , a , a+ d, a + 2d.To know the solution with Proof
Refer To the above attachment .
Hope this helps you !! Carry on learning!!Find an equivalent ratio in simplest terms: 56 : 40
Answers
Answer:
7:5 is another ratio equivalent to 56:40
Step-by-step explanation:
56/8 = 7
40/8 = 5
Answer:
hope this helps
Step-by-step explanation: an equivalent ratio in simplest form would be 7:5
this is found by dividing 56 by 8 which is 7 and 40 dividd by 8 which is 5
7:5
If 333 + 555 = 999 And 123 + 456 = 488 And 505 + 213 = 809 Then 344 + 732 = ???
Answers
Answer:
1076
Step-by-step explanation:
I just need points lol
The sales tax on a surfboard is $12 what is the percent of sales tax?
Answers
How i can answer this question, NO LINKS, if you answer correctly i will give u brainliest!
Answers
Answer:
Sir your answer is 15
Step-by-step explanation:
Hope this helps luis
Write an equation for the nth term of the arithmetic sequence. Then find 230 -
-9, -6, -3,0, ...
=
a30
Helpquick
Answers
Answer:
hope it helps you ✨✨✨✨✨✨