What is the nth term rule of the quadratic sequence below?
-4,-3,0,5, 12, 21, 32,...
I need help quick!!
Answer:
The nth term = n^2 - 2n - 3.
Step-by-step explanation:
Here, we will be finding the nth term of a quadratic number sequence. A quadratic number sequence has nth term = an² + bn + c
Example 1
Write down the nth term of this quadratic number sequence.
-3, 8, 23, 42, 65...
Step 1: Confirm the sequence is quadratic. This is done by finding the second difference.
Sequence = -3, 8, 23, 42, 65
1st difference = 11,15,19,23
2nd difference = 4,4,4,4
Step 2: If you divide the second difference by 2, you will get the value of a.
4 ÷ 2 = 2
So the first term of the nth term is 2n²
Step 3: Next, substitute the number 1 to 5 into 2n².
n = 1,2,3,4,5
2n² = 2,8,18,32,50
Step 4: Now, take these values (2n²) from the numbers in the original number sequence and work out the nth term of these numbers that form a linear sequence.
n = 1,2,3,4,5
2n² = 2,8,18,32,50
Differences = -5,0,5,10,15
Now the nth term of these differences (-5,0,5,10,15) is 5n -10.
So b = 5 and c = -10.
Step 5: Write down your final answer in the form an² + bn + c.
2n² + 5n -10
Example 2
Write down the nth term of this quadratic number sequence.
9, 28, 57, 96, 145...
Step 1: Confirm if the sequence is quadratic. This is done by finding the second difference.
Sequence = 9, 28, 57, 96, 145...
1st differences = 19,29,39,49
2nd differences = 10,10,10
Step 2: If you divide the second difference by 2, you will get the value of a.
10 ÷ 2 = 5
So the first term of the nth term is 5n²
Step 3: Next, substitute the number 1 to 5 into 5n².
n = 1,2,3,4,5
5n² = 5,20,45,80,125
Step 4: Now, take these values (5n²) from the numbers in the original number sequence and work out the nth term of these numbers that form a linear sequence.
n = 1,2,3,4,5
5n² = 5,20,45,80,125
Differences = 4,8,12,16,20
Now the nth term of these differences (4,8,12,16,20) is 4n. So b = 4 and c = 0.
Step 5: Write down your final answer in the form an² + bn + c.
5n² + 4n
What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form in the box.
Answer:
slope= 1/4
Step-by-step explanation:
8-5 over 8-(-4)= 3/12=0.25 = 1/4
You ordered several pizzas from
Tonys Pizzeria, The pizzas cost
$50 but you also have to pay 6%
tax and want to leave a 10% tip.
How much will you pay in total,
after the tax and tip?
Sin x= cos y show that x+y=90
Answer:
just do sinx and cos y equal when x=y= multiple of pie by 4
Step-by-step explanation:
pie by 4 plus pie by 4 = 90
If I helped please mark brainliest it means a lot to my progression! <3 Thanks!
fully simplify 124:72:48
Answer:
31:18:12
............................
1.
Which of the following equations describes the graph?
A. y= -x^2 + 1
B. y= x^2 - 1
C. y= x^2 + 1
D. y= -x^2 - 1
Answer:
A. y= -x^2 + 1
Step-by-step explanation:
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Down
Vertex:
(
0
,
1
)
Focus:
(
0
,
3
4
)
Axis of Symmetry:
x
=
0
Directrix:
y
=
5
4
x
y
−
2
−
3
−
1
0
0
1
1
0
2
−
3
________________________________
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex:
(
0
,
−
1
)
Focus:
(
0
,
−
3
4
)
Axis of Symmetry:
x
=
0
Directrix:
y
=
−
5
4
x
y
−
2
3
−
1
0
0
−
1
1
0
2
3
__________________
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex:
(
0
,
1
)
Focus:
(
0
,
5
4
)
Axis of Symmetry:
x
=
0
Directrix:
y
=
3
4
x
y
−
2
5
−
1
2
0
1
1
2
2
5
_________________
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Down
Vertex:
(
0
,
−
1
)
Focus:
(
0
,
−
5
4
)
Axis of Symmetry:
x
=
0
Directrix:
y
=
−
3
4
x
y
−
2
−
5
−
1
−
2
0
−
1
1
−
2
2
−
5
10. What percent of 25 is 10? (1 point)
O10=r. 25: 40%
O 10=r. 25: 250%
025=x: 10; 40
025=r. 10; 250%
Answer:
40%
Step-by-step explanation:
To change a fraction into a percentage, multiply by 100% , then
[tex]\frac{10}{25}[/tex]
= [tex]\frac{10}{25}[/tex] × 100%
= 0.4 × 100%
= 40%
[tex]\bf 5x-6=3x-8[/tex]
Can you help me please?
Answer:
B
Step-by-step explanation:
The Pythagoras theorem states that [tex]c^{2} = a^{2} + b^{2[/tex], where [tex]c[/tex] is the hypotenuse and a and b are the adjacent and opposite sides of the hypotenuse. If we made [tex]a[/tex] the subject of the expression, the expression will be re-written as [tex]a^{2} = c^{2} - b^{2}[/tex], which is the correct answer.
Find the perimeter. Simplify the answer.
Answer:
34p-16
Step-by-step explanation:
Perimeter of parallelogram
= 2(9p-10)+2(8p+2)
= 18p-20+16p+4
= 34p-16
Find the perimeter. Simplify your answer.
Step-by-step explanation:
perimeter =
2(L+B)
=2× (7z+3 +3z+5)
2×10z +8
=20z+16
Geometry hw help please.
Answer:
6
Step-by-step explanation:
You can solve this using Pythagorean Theorem;
a² + b² = c²
c is always the hypotenuse or the longest length in the triangle which is always opposite to the forming 90° angle.
a and b values can be the other 2 legs, doesn’t matter which one is which
we are given;
a = 8
c = 10
a² + b² = c²
(8)² + b² = (10)²
64 + b² = 100
b² = 100 - 64
b² = 36
√b² = √36
b = 6
Therefore the answer = 6
Hope this helps!
HELP ANSWER ASAP
ANSWER???
A proportional relationship means that two or more things are directly proportional, or that the quantities increase or decrease according to equivalent ratios. We can state this proportional relationship with the formula, y = kx. Y and x here are the quantities that are proportional to each other.
How to find the theoretical mean and standard deviation using central limit therom.
Answer:
I can even see anything can you reupload your answer, please?
Step-by-step explanation:
A barrel of oil was filled at a constant rate of 7.9 gal/min. The barrel had 12 gallons before filling began.
The equation that models this situation is z = 7.9y + 12.
A linear equation is a function that has a single variable raised to the power of 1. An example is x = 4y + 2.
Where:
2 is the constantx = dependent variable y = independent variableFrom the equation given, 12 would be the constant, the independent variable would be 7.9 and z would be the dependent variable.
z = 7.9y + 12
Here is the complete question: A barrel of oil was filled at a constant rate of 7.9 gal/min. The barrel had 12 gallons before filling began. write an equation in standard form to model the linear situation.
A similar question was answered here: https://brainly.com/question/2238405
Due in an hour help me
Please I have to pass
Answer:
A is answer
Step-by-step explanation:
WILL GIVE BRAINLIEST!
Answer:
1 1/3
Step-by-step explanation:
it's bc the number is closer to one and not in the middle. have a great day
Answer:
The arrow is pointing to 1 1/3. From 1 to 2, there are 3 marks. These three marks are each 1/3. So, from 1 the next mark will be 1 1/3.
:)
Can anyone help, im stuck
Answer:
The second one is right
Step-by-step explanation:
anyone help, im stuck
Answer:
The third one
Step-by-step explanation:
Since, 1 can be represented by x we can make an equation
2 can be represented y
and 4 can be represented by x
Since x + y = 180 and x + z = 180
y = z
Or 2 = 4
Brainliest please :)
Wha ratio is equivalent to the ratio 6 : 12
Answer:
1:2
Step-by-step explanation:
1:2 would be a equivilant
also most simplified
Answer:
1 :2
Step-by-step explanation:
Find:x , if |x |=6; |x |=3.2; |x |=0
* like x= ...
Answer:
|x|=6 we have x1=-6 x2=6
|x|=3.2 we have x1=-3.2 x2=3.2
|x|=0 x=0
Jack estimates that a piece of wood measures 4.5 cm. If it actually measures 4.72 cm, what is the percent error of Jack’s estimate? (Show all of your work)
Answer:
ion
Step-by-step explanation:srry
mike drove 10 miles in 30 minutes, what's the average speed in miles per hour
What is Part 1 and Part 2? I think I have these correct.
Step-by-step explanation:
part 1. Alternate Exterior angle
part 2. 110°
HOPE THIS ANSWER HELPS YOU DEAR! TAKE CARE
Circle A has been enlarged to create circleA prime . The picture below shows the diameters of both circles.
Based on the information in the picture, what scale factor was used to create circle A prime ?
Answer:
Step-by-step explanation:
9514 1404 393
Answer:
5/2
Step-by-step explanation:
The ratio of the diameters is equal to the scale factor:
sf = (15 in)/(6 in) = 5/2
The scale factor used to create circle A' is 5/2.
#20 i
Find the coordinates of the midpoint of the line segment with the endpoints R(-5, -7) and
S(2, -4)
Answer:
First, we need to know the relationship between "a" and "c". And "10" is not a co-ordinate. A co-ordinate has 2 or 3 numbers in it like 10,17, or like 10,17,5.
Step-by-step explanation:
Can someone please help me with this?
Hello,
Ali is right, Khamis is wrong. Why because Khamis forgot to put the negative sign in front of 5b, it should be wrote -5b in the second line and not 5b.
And then Khamis should have divided -5b by -5b.
Good Luck
What is the common difference for this arithmetic sequence 45,40,35,30,25,
Answer:
-5
Step-by-step explanation:
Simplify this expression 3(2h + 5)
if 4 watches cost 76.800. Find the cost of 9 watches pls answer my question
Answer:
1 watch cost 19,200 (76800/4=19200)
9 watches cost 172,800 (9×19200=172800)
Step-by-step explanation:
Answer:
$172.8
Step-by-step explanation:
divide 76.800 by 4 to figure out how much each watch cost. Than once you got that answer multiply by 9 to find out the cost of 9 watches
76.800÷4= 19.2
19.2×9= 172.8
If the worker worked for 15.5 hours, how much money would they earn? Round to the nearest
hundredth.
$135.63 or Choice B
Step-by-step explanation:
If the worker works for 15.5 hours and earns $8.75 per hour, you would multiply 15.5 and 8.75, you get 135.625. Round it to the nearest hundredth gives you the answer of $135.62
