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
I NEED HELP WITH NUMBER 2
Answers
[tex]5y+2x = -7~~~~~......(i)\\\\y = -2x +5 ~~~~~~.....(ii)\\\\(i) -(ii):\\\\5y+2x -y = -7-(-2x+5)\\\\\implies 4y +2x = -7 +2x -5\\\\\implies 4y +2x -2x = -12\\\\\implies 4y = -12\\\\\implies y = - \dfrac{12}4 = -3\\\\\\\text{Substitute}~ y=-3~ \text{in equation (ii):}\\\\\\-3 = -2x +5\\\\\implies 2x = 5 +3 \\\\\implies 2x = 8\\\\\implies x = \dfrac 82 =4\\\\\text{Hence,}~ x = 4[/tex]
What is the equation of the line with a slope of 4 and passes through the point (1, -4)?
Answers
Answer:
y=4x-8
Step-by-step explanation:
m=4 (1,-4)
-4=4(1) + c
-4=4+c
-4-4=c
-8=c
y=4x-8
Answer: y = 4x - 8
Step-by-step explanation:
The best way to go about this is to first put the information you know into point-slope form, which is:
[tex]y-y_{1} =m(x-x_{1})[/tex]
[tex]y_{1}[/tex] and [tex]x_{1}[/tex] represent the values of our point (1, -4), so:
[tex]y_{1}=-4[/tex], and [tex]x_{1}=1[/tex].
[tex]m[/tex] represents our slope of 4, so:
[tex]m=4[/tex]
From this, we can plug in our values:
[tex]y-(-4)=4(x-1)[/tex]
A little simplification and distrobution takes us to this:
[tex]y+4=4x-4[/tex]
Then simply subract 4 from both sides to get this:
[tex]y=4x-8[/tex]
An easier way to reason this is to visualize the line in your head and figuring out what the y-intercept is so you can go strait into the [tex]y=mx+b[/tex] form where b is the y-intercept.
Solve for y. -6y-31= 5 and thank you
Answers
[tex]-6y -31 =5\\\\\implies -6y = 5+31 = 36\\\\\implies y = -\dfrac{36}6 = -6[/tex]
Step-by-step explanation:
...........y=-6.........
what is an equation in slope-intercept form for the line (-5, 2) and (5,-3)?
Answers
Answer:
y = [tex]-\frac{1}{2} x[/tex] [tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
solved using point-slope form
points given: (-5, 2) and (5, -3)
slope: [tex]\frac{-3-2}{5-(-5)} =\frac{-5}{10} =-\frac{1}{2}[/tex]
y = [tex]-\frac{1}{2}[/tex] x + b
insert x- and y- values of (-5, 2) and solve for b
2 = [tex]-\frac{1}{2}[/tex] (-5) + b
2 = 2.5 + b
subtract 2.5 from both sides
2 - 2.5 = 2.5 + b - 2.5
-0.5 = b
insert b- value
y = [tex]-\frac{1}{2} x[/tex] [tex]-\frac{1}{2}[/tex]
Part G Compare this activity tracker & with the calorie calculator you used in part A. Imagine that a company hires you to make an online tool that uses the best features of each calculator to give users an accurate sense of their physical activity and energy expenditure. What features would you use from each calculator? How would your calculator work?
Answers
Answer:
The physical activity calculator helps calculate minutes of activity and breaks down the types of activities performed every week. The calorie calculator doesn’t keep track of all activities. However, it calculates calorie expenditure. A new calculator might be a combination of the two calculators. It’d be a two-step process. People would be able to enter their age, gender, weight, height, and any medical factors so that they can ensure that their calorie calculations are accurate. Then, they’d be able to track the calories expended each day for a week by adding their activities for the whole day, from sitting to exercising. This information would give them an accurate portrayal of calorie expenditure and estimated caloric requirement.
exact answer
Step-by-step explanation:
Answer:
by seeing how the things they are doing and effecting them and then calulating them to add them up so i can see the amount of thier activity caused them to decrease or increase themselfs
Step-by-step explanation:
own explaination just incase teacher does suspect the answer
to be copied :)
what is the product of 9,028 x 100,000
Answers
Answer:
902,800,000
Step-by-step explanation:add the 5 zeros from 100,000 to 9,028
9. An expression is subtracted from 2p+9q + 100 to get –5p + 7q + 50. What is that expression?
Answers
Answer:
-3p + 16q + 150
0.2(3m − 6) + m = 2 for 8th grade
Answers
Answer:
2
Step-by-step explanation:
0.6m-1.2+m=2
1.6m-1.2=2
1.6m=3.2
m=2
Marking brainliest
Is it possible to change how people see themselves ?
Answers
Answer:
Yes it is possible.
You need to change your mindset first.
If you look in the mirror everyday and call yourself ugly. Theres no way you are going to change the way you are.
But if you look in the mirror and be positive about yourself evantually you will start thinking diffirent about yourself.
Its all in the mindset.
Step-by-step explanation:
Answer my question 4 u could get 10 points
Answers
Answer:
30
Step-by-step explanation:
Split the trapezoid into parts, a rectangle and a triangle. The dimensions of the rectangle will be 3 and 8, so 3*8=24. 24 is part of the answer. The dimensions of the triangle are 4 and 3, and 4*3/2 is 6, so 6 is the other part of the answer. 24 + 6 = 30.
value of complex number i^7+1/i^4
Answers
[tex]i^7 + \dfrac 1{i^4}\\\\=i^2 \cdot i^2 \cdot i^2 \cdot i + \dfrac 1{i^2 \cdot i^2}\\\\=(-1)(-1)(-1)i + \dfrac 1{(-1)(-1)} ~~~;[ i^2 = -1] \\\\\ = (-1)^3 i+ \dfrac 1{(-1)^2} \\\\=-i+1[/tex]
are these lines perpendicular explain
Answers
Answer:
Yes because the slopes are negative reciprocals of each other.
Step-by-step explanation:
The slope of line B is: 1/3
(-2, -4) and (1, -3)
(-3+4)/(1+2) = 1/3
The slope of line A is: 3
(-3, 0) and (-2, -3)
(-3-0)/(-2+3) = -3
Solve for m.
F/m=a
pls help timed
Answers
Answer:
M=F/A
Hope this helps
Given that a [] b = b2 + a. Evaluate 2 [] (6[] - 5).
Answers
Answer:
963
Step-by-step explanation:
Evaluate 6 | - 5 , then the outside part, that is
6 | - 5 ( with a = 6 and b = - 5 )
= (- 5)² + 6 = 25 + 6 = 31
Now evaluate 2 | 31 ( with a = 2 and b = 31 )
= 31² + 2 = 961 + 2 = 963
Solve for n in the equation 39 x 5 = n x 15. 13 15 17 19
Answers
Answer:
n=13
Step-by-step explanation:
39*5=15n
195=15n
13=n
A triangle has side lengths 7, 17, and x. Fill in the inequality for the possible
lengths of x below.
Answers
Answer:
9 < x < 25
Step-by-step explanation:
What would the graph look like
Answers
Answer I cant read the thing sorry
Step-by-step explanation:
hoped that hepled:)
−3.6−1.9t+1.2+5.1t
Khan academy pls help
Answers
Answer:
3.2t - 2.4
Step-by-step explanation:
A karaoke marked at ₽3,750 was sold for ₽3,225. What was the rate of discount?
Answers
Answer:
Step-by-step explanation:
14% increase
A book sold 35,100 copies in its first month of release. Suppose this represents 8.8% of the number of copies sold to date. How many copies have been sold to date?
Answers
Answer:
561,972 copies
Step-by-step explanation:
MATH-
If 60 boxes in a 10-by-10 grid are shaded, which fraction is equivalent?
A) 1/2
B)3/5
C)7/10
D)3/4
Answers
Answer:
B= 3/5
Step-by-step explanation:
If is wrong I'm sorry
Solve for x
TS = 2x - 6
CE = 3x - 6
Answers
Use midpoint theorem :- The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also 'half of the length of the third side'.
So,
2x - 6 = ½ (3x - 6)
2x - 6 = 3x/2 - 3
2x - 3x/2 = -3 + 6
½ x = 3
x = 3 × 2
x = 6
______
Hope it helps ⚜
Given the function below find f(-2).
f(x)=x2−3x+5
Group of answer choices
10
15
20
25
Answers
See picture attached
A sphere has a volume of V=324 in3. Find its surface area.
Answers
Answer:
A≈228.13in²
Step-by-step explanation:
Using the formulas
A=4πr2
V=4
3πr3
Solving forA
A=π⅓(6V)⅔=π⅓·(6·324)⅔≈228.12916in²
that's the answer
Answer:
A≈228.13in²
Step-by-step explanation:
.............
✌️❤️✌️
21. Here are the ingredients for raspberry ripple ice cream.
250g raspberries
225g caster sugar
2 large eggs
4 large egg yolks
600ml double cream
A mother has 5 litres of cream to make ice cream for a party. Sugar comes in 1kg bags.
How many bags of sugar will be needed?
Answers
Answer:
10 bags for 5 litres of cream of ice cream.
2 bags of sugar will be needed.
What are comparing quantities?Comparing quantities is the qualitative relation between two quantities which reflects the relative size of both the quantities.
here, we have,
It is given that,
600ml of cream requires = 225g of sugar
⇒ 1 ml of cream requires = 225/600g of sugar
⇒ 5000ml of cream requires = 225/600 * 5000g of sugar
= 1875g
=1.875 kg
Hence we see that , Sugar comes in 1kg bags.
Similarly, 1.875kg of sugar = 1kg bag + 0.875kg bag
⇒ 2 bags of sugar is needed.
Therefore, 2 bags of sugar will be needed.
To learn more about Comparing quantities :
brainly.com/question/1572596
#SPJ2
HELP PLEASE!!!!! THIS IS DUE TODAY!!!!
Answers
Answer:
nonlinear
Step-by-step explanation:
it's a parabola
teheheh help please :)
Answers
Answer:
Solid line
Step-by-step explanation:
This means that it is equal. The line under the less than sign means it would be a solid line.
What is the perimeter?
14 feet
12 feet
16 feet
Answers
Answer:
14 feet
Step-by-step explanation:
You find this answer by adding each side. The arrow tells us that each side of a square is 1 foot, so you add up the outer sides of each square
this is an area in which objects will interact with a magnet
Answers
ok how do i show work for this tho lolololoololololollloooooool
Answers
Answer:
y=[tex]\frac{1}{5}[/tex]x is linear
Step-by-step explanation:
4x-3y=7y+2x
collect like terms
4x-3y-7y-2x=0
2x-10y=0
simplify
x-5y=0
rewrite it in slope intercept form
y=[tex]\frac{1}{5}[/tex]x which is the equation for a straight line