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
1. Name a midsegment in the triangle.
Answers
Answer:
EF
Step-by-step explanation:
Hope this helps!
2. The graph represents the amount
of water, y, left in a 13.5-gallon tub
after x minutes. What is the slope of
the line? What does the slope mean
in this context?
Answers
Answer:
Slope: -3/2
With the question, we can determine that the slope with two points: (0,13.5) and (9,0). To calculate use the equation [tex]\frac{y2-y1}{x2-x1}[/tex] and get [tex]\frac{0-13.5}{9-0} =\frac{-13.5}{9} =\frac{-3}{2}[/tex]
This slope means that the water is decreasing at a rate of 3/2 gallons per minute.
Which of the following is equal to
(x - 3)(2x + 4x - 1)?
A 2x3 - 2x2 - 11x + 3
B 2x3 -- 2x2 - 13x + 3
Answers
Answer: [tex]2x^3-2x^2-13x+3[/tex]
======================================================
Work Shown:
I'm assuming you meant to say [tex](x - 3)(2x^2 + 4x - 1)[/tex]
Let [tex]y = x-3[/tex]
So,
[tex](x - 3)(2x^2 + 4x - 1)\\\\y(2x^2 + 4x - 1)\\\\y2x^2 + y4x - y\\\\2x^2(y) + 4x(y) - (y)\\\\2x^2(x-3) + 4x(x-3) - (x-3)\\\\2x^3-6x^2 + 4x^2-12x - x+3\\\\2x^3-2x^2-13x+3\\\\[/tex]
The basic idea is to use the distribution rule (line 3 and line 6) and then combine like terms.
Which relationship has a zero slope? A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 2, 2, 2, 2. A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 3, 1, negative 1, negative 3. A coordinate plane with a straight line starting at (negative 5, negative 5) and passing through the origin, and ending at (5, 5) A coordinate plane with a straight line starting iat (negative 2, 5) and passing the x-axis at (negative 2, 0), and ending at (negative 2, 5).
Answers
Answer:y =3 x=1 hope this helps :)
Step-by-step explanation:
The difference between three times a number and seven is twenty. What is the number?
20
7
13
3
O9
O 27
Answers
Answer:
the number is 9
Step-by-step explanation:
hope this helps
Explain the steps in solving 2.14x-12.18=-576 , and write the solution to the equation.
Answers
Answer:
x = 274 91/107
Step-by-step explanation:
This is called a "two-step linear equation" because it is solved in 2 steps.
Step 1. Identify the constant on the same side of the equation as the variable term, and add its opposite to both sides of the equation.
2.14x -12.18 +12.18 = 576 +12.18
2.14x = 588.18
__
Step 2. Identify the coefficient of the variable and multiply both sides of the equation by its reciprocal.
2.14x(1/2.14) = 588.18(1/2.14)
x = 274.850467... = 274 91/107 . . . the decimal fraction repeats
The solution to the equation is x = 274 91/107.
Answer:
x = 274 91/107
Step-by-step explanation:
Step-by-step explanation:
This is called a "two-step linear equation" because it is solved in 2 steps.
Step 1. Identify the constant on the same side of the equation as the variable term, and add its opposite to both sides of the equation.
2.14x -12.18 +12.18 = 576 +12.18
2.14x = 588.18
__
Step 2. Identify the coefficient of the variable and multiply both sides of the equation by its reciprocal.
2.14x(1/2.14) = 588.18(1/2.14)
x = 274.850467... = 274 91/107 . . . the decimal fraction repeats
The solution to the equation is x = 274 91/107.
Triangle UVW is dilated by a scale factor of 6 to form triangle U'V'W'. Side W'U'
measures 18. What is the measure of side WU?
Answers
Answer:
WU= 3
Step-by-step explanation:
Know that, W'U'÷ (scale factor) = WU
18÷6 is equal to 3
scale factor= 3
(2 + 10) × 5 = (2 × 5) + ( __ × 5)
Answers
Answer:
10
Step-by-step explanation:
We can use the distributive property to get:
[tex]5(2+10)=5(2)+5(10)[/tex]
Therefore, the blank is 10.
solve 5/4 × (− 9/2 )
Answers
Answer:
-40/8= -5
Step-by-step explanation:
Multiply the top to get -40 then the bottom to get 8. When you simplify, you get -5.
Answer:
-5.625
Step-by-step explanation:
5/4 × (-9/2)
=5×(-9)/4×2
=-45/8
=-5.625
During British History from 1550-1650. What was going on in Britain during the time just before, during and just after Shakespeare lived? Who were the rulers? What was the political atmosphere? What were the people concerned about? How did the people live?
Answers
Answer:
What was going on in Britain during the time just before Shakespeare lived?
Elizabeth had settled the religious question by establishing the Church of England as the official religion of the country, insisting on church services in English, the English Bible and prayer book in churches etc, but not going as far in extreme Protestantism as, for instance, the Puritans would have liked her to do.
Step-by-step explanation:
please mark me brainliest!!
The period from 1550-1650 in British history was a time of significant political, social, and cultural change.
What is British History?England, which had absorbed Wales under Henry VIII in the 16th century, merged with Scotland in 1707 to form a new sovereign state known as Great Britain.
Here are some key events and factors that were happening during the time just before, during, and just after Shakespeare lived:
Queen Elizabeth I reigned as Queen of England from 1558 until her death in 1603.Religious strife: The 16th century in England saw religious strife, with tensions between Catholics and Protestants leading to violence and persecution.Political unrest: Throughout the 17th century, England experienced a number of political conflicts and upheavals, including the English Civil War between royalists and parliamentarians.Economic changes: Significant changes occurred in the English economy during the 16th and 17th centuries, including the expansion of international trade and the rise of capitalism.Early modern England's daily life was marked by significant social stratification and inequality.Thus, the period from 1550-1650 was a time of significant change and upheaval in England, with political, religious, and economic developments shaping the lives of its people.
For more details regarding British History, visit:
https://brainly.com/question/29880473
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a rectangular parking lot has a perimiter of 500 feet and a width of 100 feet. find the lenght of the parking lot be sure to show all four steps
Answers
Answer:
50,0
Step-by-step explanation:
So we know 500×100=50,000
So it's 50,000
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
What situation could be modeled with the equation of 40 devided by 8 equals 5
Answers
Answer:
Go to explanation
Step-by-step explanation:
You can say: At your birthday party, you have 7 friends who were there with you. There are 40 cookies to be shared with all of you, and you want it to be split equally. How many cookies does each person get?
Pentagon ABCDE and pentagon A’B’C’D’E are shown on the coordinate plane below:
Answers
the first one ((x+8, y+2), r x-axis)
4)Find the value of x and y
Answers
x=48, y=110
Explanation:
55-7=48
55+55=110
The difference between eight times a number and three is equal to negative nineteen. What is the number?
-2
2
-3
3
Answers
Answer:
-2
Step-by-step explanation:
3 - 19 = 8(x)
-16 = 8(x)
-16/8 = x
x = -2
Answer:
I believe that it is -2
Step-by-step explanation
I had this math question too
Find the slope of the line containing the points (-3, 8) and (-1, 0).
Select one:
a.
zero slope
b.-4
c. -1/4
d.-3
Answers
Hope this helps!
Answer: the slope 4
Step-by-step explanation:
the slop is y^2 - y^1 / x^2 - x^1 = 0 -8 / -1 - - 3 = 8/2 = 4
Hope that helps :)
WILL GIVE BRAINLY,5 STARS,AND THANKS
Answers
Answer: Yes, he does.
Step-by-step explanation:
55 x 12 = 600 Also can I see the answers for the question
2. Quinnel made 14 shots out of the 40 he took during his first season of basketball.
Suppose he took 60 shots during his second season. How many shots would you expect
Quinnel to make during his second season of basketball?
Answers
Answer:
21
Step-by-step explanation:
his ratio of shots from the first game would be 14:40 or 7:20
so if he made the same ratio from 60 shots it would be
21:60
help pls please again and again anf again
Answers
2*2*2*2*2 = 32.
The equation simplified is 32 or 2^5.
I’m very confused! Please help me (I’ll mark brainliest if you explain!)
Answers
Answer:4 **rounds
Step-by-step explanation:
It’s dividing by 2 each time.
Answer:
4 more rounds
Step-by-step explanation:
you will see there is a pattern which is dividing by 2
16/2=8
8/2=4
4/2=2
2/2=1
but since thats not an option i think it would be 8 dont ask its would be eight if not 4
estimate the area of the following irregular shapes
will give brainliest
Answers
Answer: You need to count how many squares are shaded(at least half of it), therefore the area is 32 square units.
8. If the measure of one side of a square is increased by 2 centimeters and the measure of
the adjacent side is decreased by 2 centimeters, the area of the resulting rectangle is
32 square centimeters. Find the measure of one side of the square (the original figure).
Answers
Answer:
6 cm
Step-by-step explanation:
If the original side length is x, then the modified square has an area of ...
A = LW
32 = (x +2)(x -2) = x^2 -4
36 = x^2 . . . . . . . . add 4
6 = x . . . . . . . . . . take the square root
The original figure has a side length of 6 cm.
__
Check
The modified figure is 8 cm by 4 cm = 32 cm^2.
Evaluate the expression to find out how much she will pay if she drives 100 miles.
250 + 0.80m
Answers
Each figure shows a pair of similar triangles, one contained in the other.
For each pair, describe a point and a scale factor to use for a dilation
moving the larger triangle to the smaller one. Use a measurement tool
to find the scale factor.
Answers
Dilation involves enlarging or reducing the size of a shape.
The scale factor of dilation is 1/6
From the complete question, the side lengths of corresponding sides of both triangles are:
[tex]AC =18cm[/tex]
[tex]AC' =3cm[/tex]
This means that, the larger triangle is ABC, while the smaller triangle is AB'C'.
So, the scale factor of dilation from the larger triangle to the smaller triangle is:
[tex]k = \frac{AC'}{AC}[/tex]
This gives
[tex]k = \frac{3cm}{18cm}[/tex]
Remove the common units
[tex]k = \frac{3}{18}[/tex]
Reduce fraction
[tex]k = \frac 16[/tex]
Hence, the scale factor of dilation is 1/6
Read more about dilation at:
https://brainly.com/question/3457976
During a checkers game, there are 16 pieces left. The ratio of black to red is 3 : 5. How many black pieces are on the board? Explain how you found your answer.
Answers
Answer:
6 black pieces
10 red pieces
Step-by-step explanation:
The way to interpret ratios is like so:
Adding up both parts of the ratio gives 8, i.e. 3 + 5
So for every 8 pieces, 3 are black and 5 are red;
There are 16 pieces, which is 2 × 8;
So, there are (2 × 3) black pieces and (2 × 5) red pieces, i.e. 6 black and 10 red
So, to solve:
Add all parts of the ratio (3 + 5);
Divide the number of pieces (16) by this sum of ratio parts (8);
Multiply the value from the division (2) by each part of the ratio
Tip:
It is important to take note of the order in the ratio, so the ratio of black to red means the number that comes first in the ratio represents parts black and the one that comes second represents parts red;
If the wording was the ratio of red to black, the number that comes first would represent parts red and the second would represent parts black
At a restaurant, 30% of customers donate to charity in exchange for a coupon. Estimate the probability that it will take at least four customers to find one who donates.
Answers
Answer:
75.99%
Step-by-step explanation:
To calculate this, we can use complements. We can find, instead the probability that at least one will donate, the probability that not none of them will donate.
First, we can find the probability that none will donate, which will be (70%)^4, since the chance each will not donate is the same. From this we get 24.01%.
To find the probability that at least one donates, we do the complement:
100%-24.01%=75.99%
a train is leaving the station and goes from 3m/s to 30 m/s in 12 s. The acceleration of the train is
Answers
Answer:2.25 m/s^2
Step-by-step explanation:
a = (v-u)/t = 27/12 = 2.25 m/s^2
If f(x) = 14
then what does f(-3) equal?
Answers
Answer:
27 I do believe so sorry if im wrong
Step-by-step explanation:
In the equation "y=mx+b" to find the answer do you have to multiply m and x then add b?
Answers
Answer: no.
Explanation:
As an example, let's use y=2/3x-8.
In this formula, the 2/3 before the x I the slope of the problem. The -8 would be the y-intercept. You use this formula to find both of those to graph a line, you do not multiply the slope and the x together.
