The [tex]nth[/tex] term rule of the quadratic sequence will be [tex]n^2+5n+2[/tex] .
What is quadratic sequence ?Quadratic sequences are sequences that include [tex]nth[/tex] term. They can be identified by the fact that the differences between the terms are not equal, but the second differences between terms are equal.
Quadratic sequence [tex]=an^2+bn+c[/tex]
Here [tex]a,b,c[/tex] are constant and [tex]n[/tex] is the position of term.
First difference [tex]= 3a+b[/tex]
Second difference [tex]=2a[/tex]
We have,
Quadratic sequence [tex]8,16,26,38,52,68,86,....[/tex]
Quadratic sequence [tex]=an^2+bn+c[/tex]
so,
For [tex]n=1[/tex];
[tex]8=an^2+bn+c[/tex]
[tex]8=a+b+c[/tex] [tex]........(i)[/tex]
For [tex]n=2[/tex];
[tex]16=4a+2b+c[/tex] [tex]........(ii)[/tex]
For [tex]n=3[/tex];
[tex]26=9a+3b+c[/tex] [tex]........(iii)[/tex]
Now,
Subtract equation [tex](i)[/tex] from [tex](ii)[/tex]
we get,
[tex]8=3a+b[/tex] [tex]........(iv)[/tex]
Subtract equation [tex](ii)[/tex] from [tex](iii)[/tex] we get,
[tex]10=5a+b[/tex] [tex]........(v)[/tex]
Subtract equation [tex](iv)[/tex] from [tex](v)[/tex] we get,
[tex]2=2a[/tex] (This is second difference mentioned above)
[tex]a=1[/tex]
Putting [tex]a=1[/tex] in [tex](iv)[/tex]
⇒[tex]b=5[/tex]
Now putting values of [tex]a[/tex] and [tex]b[/tex] in equation [tex](i)[/tex]
[tex]8=1+5+c[/tex]
[tex]c=2[/tex]
Now, putting values of [tex]a[/tex] , [tex]b[/tex] and [tex]c[/tex] in,
Quadratic sequence [tex]=an^2+bn+c[/tex]
we get,
[tex]nth[/tex] term rule [tex]=n^2+5n+2[/tex]
Hence, we can say that the [tex]nth[/tex] term rule of the quadratic sequence will be [tex]n^2+5n+2[/tex].
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Anju's office uses paper cups shaped like cones to serve water. Each cup has a maximum diameter of 8 cm and a height of 10 cm. Anju fills the cup to 3/4 of its height to prevent spills. What is the approximate volume of water in Anju's cup?
Answer: 126 cubic centimeters
Step-by-step explanation:
volume = (pi)(r^2)(1/3)(h)
diameter = 8 so radius = 4
4 squared is 16
multiply height by 3/4
10(3/4) = 30/4 = 15/2
Multiply this value by 1/3
15/2 x 1/3 = 15/6 = 5/2
(pi)(25)(5/2)
16x5/2 = 80/2 = 40
(pi)(40)
note: you can substitute 3.14 with pi or use actual pi depending on whether or not you have access to a calculator. they will both round to 196.
126 cubic centimeters
94.2 cubic centimeters is the approximate volume of water in Anju's cup.
To find the approximate volume of water in Anju's cup, we can calculate the volume of a cone using the formula:
Volume = (1/3) × π × r² × h
Given that the cup has a maximum diameter of 8 cm, the radius (r) would be half of that, which is 4 cm.
The height (h) is 10 cm, but Anju fills the cup to 3/4 of its height, so the filled height would be (3/4) × 10 cm = 7.5 cm.
Substituting these values into the formula:
Volume = (1/3) × π × (4 cm)^2 × (7.5 cm)
Volume = (1/3) × 3.14 × 16 cm^2 × 7.5 cm
Volume = 12.56 cm² × 7.5 cm
Volume = 94.2 cm²
Therefore, the approximate volume of water in Anju's cup is approximately 94.2 cubic centimeters (cm³).
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ax2+bx+c=0 is not a linear equation. Discuss the reason
Answer:
Step-by-step explanation:
a linear equation is of degree 1.
It is of degree 2 so it is not a linear equation.
(7,1) and (-5,1)
Find the slope of the line that passes through the 2 points.
m = (Y2 - Y1)/(X2 - X1)
m = (1 - 1)/(-5 - 7)
m = 0/(-12)
m = 0
HELP MEEEEEEEE PLEASE
Answer:
Option A (3/4)
Step-by-step explanation:
Please mark Brainliest
Answer:
THATS CORREC T
Step-by-step explanation:
CAUSE A IS THE RIGHT ONE THE REST BIS WRONG BUT IT CAN E CONFUSING
How do you show that x=6 is an true equation ?
x = 6 can be represented on the number line and hence it is real
Step-by-step explanation:
by simply plugging in 6 for x thus
x=6 becomes 6=6 which is true
plz help I need answer asap!
Answer:
x=2.4
Step-by-step explanation:
for this one we find the scale factor you can pick any two similar points i picked 3 and 1.8 i did 1.8/3 and found the scale factor is .6 so x= ML or 4 * .6 (our scale factor) which gives x=2.4
Answer:
x=2.4
Step-by-step explanation:
This is simple! If you know how to find scale factor then then problem is a breeze.
Look at side JK and side PQ. To find the scale divide 3 by 1.8 This gives you 1.66666666667. We don’t want this long number but we can work with it :3
Now to find that missing side= x
4 / 1.66666666667= 2.4
x=2.4
( pssstt! This “/“ means division ;-)
hope this helped :D
After solving the next three terms in
5120, 1280, 320, 80, …
How could you find the explicit rule?
a (n)=a1 × r^(n-1)
a1=5120
a2=1280
a3=320
a4=80
-->a2/a1=1280/5120=0.25
-->a3/a2=320/1280=0.25
-->a4/a3=80/320=0.25
ration(r) =0.25
■■■a(n)=a1 × r^(n-1)■■■
a (5)=5120×0.25^(5-1)
a (5)=5120 × 0.25 ^(4)
a (5) = 5120 × 0.00390625
a (5) = 20
what is the equation of a line that passes through the points (6,9) and is perpendicular to the line
Answer:
the line is perpendicular to what line you didn't mention that
Step-by-step explanation:
write a quadratic equation for the points (2,0) and (12,5). make sure to include the axis and five points used to graph the parabola
Using the Factor Theorem, the parabola is given by: [tex]f(x) = 0.05(x^2 - 4x + 4)[/tex]
The graph is sketched at the end of this answer.
The Factor Theorem states that a polynomial function with roots is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
In this problem:
The graph is a parabola, which means that the function is of the 2nd degree.One zero, with multiplicity 2, at [tex]x = 2[/tex], hence, [tex]x_1 = x_2 = 2[/tex].Then:
[tex]f(x) = a(x - 2)(x - 2)[/tex]
[tex]f(x) = a(x^2 - 4x + 4)[/tex]
Point (12,5) means that when [tex]x = 12, y = 5[/tex], and this is used to find a.
[tex]f(x) = a(x^2 - 4x + 4)[/tex]
[tex]5 = a(12^2 - 4(12) + 4)[/tex]
[tex]100a = 5[/tex]
[tex]a = \frac{5}{100}[/tex]
[tex]a = 0.05[/tex]
Hence, the parabola is:
[tex]f(x) = 0.05(x^2 - 4x + 4)[/tex]
At the end of this answer, the graph with five points is sketched.
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"5 more than a number™ translates to an equation.
O
True
M
w
O False
True
5 more than a number is an equation because you are adding two values.
Answer:
n+5
Step-by-step explanation:
If we choose the number to be n then 5 more than is 5 added to the number.
hence: n + 5
Help me solve this -> g(x) = 2x + 3
g(7)
Answer:
17
Step-by-step explanation:
g(7) = 2(7) +3
substitution
Consider the equation below.
-5n + 31 - 14n -
5–59 + 31 = –14n – 5
-
Select the equation that has the same solution.
-1 – 22n
20n – 9–1 – 22n = –20n - 9
0
1 = 0.75n + 3.251 = 0.75n + 3.25
In + 2 = −3+ min + 2 =
3 + 1
3 – 6n + 3n = – 3 + 4 – 4n3 – 6n + 3n = -3 + 4 – 4n
Answer:
-1 - 22m
Step-by-step explanation:
A sandwich store charges a $10 delivery fee,and $4.50 for each sandwich.
a. Graph the total cost of sandwiches and delivery based on the number of sandwiches ordered. let x represent the number of sandwiches and y represent the total cost. Be sure to label your axes and scale them by labeling each grid line with a number.
PLEASE PLEASE PLEASE answer this i need to get a good grade on my test its worth 70% of my grade.
The required graph shows equation y = 10 + 4.50x which represents the total cost of sandwiches and delivery based on the number of sandwiches ordered.
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
Let x represent the number of sandwiches and y represent the total cost.
Here is a graph of this equation:
y = 10 + 4.50x
This graph shows that the total cost of sandwiches and delivery is a straight line that increases by $4.50 for each additional sandwich ordered. The $10 delivery fee is the y-intercept of the line, which is the point where the line crosses the y-axis (when x = 0).
The slope of the line is 4.50, which indicates the change in the total cost for each unit change in the number of sandwiches.
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Determine if the table represents a linear function, quadratic function, or exponential function.
That would be linear because its going at a constant rate of change
a, b, c and d are positive integers, such that a+b+ab = 20, c+d+cd = 34. Find (a+b+c+d)·a·b·c·d
When 8 goes in,5 comes out
When 24 goes in.13comes out
when 70 goes in,__ comes out
What is the missing answer?
When 70 goes in, 36 comes out.
The pattern for this is x/2 + 1.
8/2 = 4, 4+1 = 5
24/2 = 12, 12+1 = 13
70/2 = 35, 35+1 = 36
Which graph represents the function f (x) = –| x - 3| + 1
Answer:
D
last one
Step-by-step explanation:
Thank you to anyone who can help!!
Answer:
Pentagon (the 5 sided shape) = 1
Cross-looking shape = 6
Star = 8
Square/Rectangle = 5
Hope this helps!
Find the value of x and y
Answer:
x=4
y=5
Step-by-step explanation:
because this lines are all parallel, so 17x-y equals to 180°-117°= 63, then you get 17x-y = 63
also, equally you can get the below one
6x+7y = (180°-121°)
6x+7y = 59.
put them together
17x-y=63 (1)
6x+7y =59 (2)
you can transform the (1) to y= -(63-17x)
then you get the second one
6x+7(-(63-17x))=59
then you get x
finally you get the result of x into any of the equation
you get y ultimately.
4x−7y=48? i need the fraction
Answer: y = -48/7 + 4x/7
I will give you brainliest
Which equation represents the sentence?
The sum of 10 and a number is 3 times the number.
10 + n = 3n
10 + n = 3 + n
10 + 3n = n
10(n + 3) = n
Answer:
the first one
10+n = 3n
Step-by-step explanation:
n is the number
and 3n means 3*n
Answer: the answer the first one 10+n=3n
Step-by-step explanation:
n is the number
and 3n means 3*n
could you show me the step please and thank you
[tex]\dfrac{(2 x^{-3} y^{-2})^5}{(6x^{-1} y^{-8})^2}\\\\\\=\dfrac{32x^{-15} y^{-10}}{36 x^{-2} y^{-16}}\\\\\\=\dfrac{8}{9} \left(\dfrac{x^{-15}}{x^{-2}} \right) \left(\dfrac{y^{-10}}{y^{-16}} \right)\\\\\\=\dfrac 89 \left(x^{-15+2} \right) \left(y^{-10 +16} \right)\\\\\\=\dfrac 89 \cdot x^{-13} \cdot y^6\\\\\\=\dfrac{8y^6}{9x^{13}}[/tex]
how many teaspoons are in 15 milliliters? 1 tsp = 5 mL
Answer:
The number of teaspoons in 15 ml is 3 tsp.
Step-by-step explanation:
All you have to do is divide 15 by 5 and get 3. This is because for every 5 ml there is 1 tsp. So for the 15 ml, there is 3 tsp.
Of the pies that Lorenzo's Pie Shop sold last month, 1/2 were blueberry pies and 2/5 were blackberry pies. What fraction of the pies sold were either blueberry or blackberry?
A digital music service sells 12 songs for $9. 96. At this rate, how many songs can you purchase for $4. 15?.
Someone help me pls!
You can buy 3 apples at Quick Mart for $1.17. You can buy five of the same apples at Shop & Save for $2.40
How much will you save per apple if you buy them at the cheaper store?
Answer:
You save $0.09 at Quick Mart for price per apple
Step-by-step explanation:
Quick mart = 1.17/3 = $0.39 per apple
Shop & Save = $0.48
$0.39 - $0.48 = $0.09
You save $0.09 per apple at Quick Mart
-Chetan K
Assume you invest $5,000 in an account paying 8% interest compounded annually. How much money will be in the account after 5 years?
Answer:
$7346.64
Step-by-step explanation:
Amount after 5years=P(1+r/100)^t
let A = amount after 5years
A=$5000(1+8/100)^5
A=$7346.64 to 2 decimal places
express the following as decimal. 25/1000
20/50
3/50
2/3
Answer:
[tex]\frac{25}{1000}[/tex] = 0.025
[tex]\frac{20}{50}[/tex] = 0.4
[tex]\frac{3}{50}[/tex] = 0.06
[tex]\frac{2}{3}[/tex] = 0.(66) or 0.66666666666666666
4) A line has a slope of -5 and passes through the point (2, 2). An equation for this line is
Answer:
[tex]D: y= -5x+12[/tex]
Step-by-step explanation:
Since the slope is -5 is either C or D. Let's replace [tex]x= 2[/tex] in either to see what we get.
C: [tex]-5(2)-2 = -12[/tex] Nope.
D: [tex]-5(2) +12 = 2[/tex] Good!
Help please I really don’t understand due in 4 days
Answer:
I will clear you.
Step-by-step explanation:
or,x/3-2<4
or,x/3<4+2
or,x<6/3
or,x<2
Answer:
x < 18
Step-by-step explanation:
You solve it like an equation.
First, isolate the x-value to one side by adding 2 to each side:
x/3 - 2 + 2 < 4 + 2
The twos on the left side cancel out:
x/3 < 6
Now multiply both sides by 3:
x/3 x 3 < 6 x 3
The threes on the left side cancel out, leaving you with the x-value:
x < 18
Hope this makes sense :)