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
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!!!!!!!10 POINTS TO WHO EVER ANSWER I WILL BE GIVING MORE ON THE NEXT QUESTION!!!!!!!
Answer: %0.00100010001
Step-by-step explanation:
Suppose the area of a triangle is 36 square inches. The height of the triangle is 12 inches. What is the length of the base of the triangle? PLSSSSSS HELP MEEEEEEEEEEEEEEEEEEEEE
Answer: The base is going to be 6 inches.
Step-by-step explanation:
So to find the area of a triangle we need to know the formula which is A= 1/2bh (A= one half times base times height) So, all we need to do is multiply the area by 2
32*2=72 Then to find the missing length, we divided the area by 12 which is 6.
in the diagram below M is the midpoint of KL
0.0346 written in standard form
Answer:
3.46x10-2
×
10
−
2
3.46
×
10
−
2
Explanation:
a number expressed in
standard form
is.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
∣
∣
∣
2
2
a
×
10
n
2
2
∣
∣
∣
−−−−−−−−−−−−
where
1
≤
a
<
10
and n is an integer
express
0.0346
as a number between 1 and 10
3
∙
46
we now have to move the decimal point 2 places to
the left to retain equality
move to the right
→
then n is positive
move to the left ←
then n is negative
⇒
0.0346
=
3.46
×
10
−
2
Is this graph proportional or non-proportional? How do you know?
Answer:
It is a proportional graph.
Step-by-step explanation:
By definition, a proportional graph is a graph which goes through the origin (O), in this picture the graph appears to indeed go through the origin, and is thus proportional.
what is -7/12 divide 1/7?
PLZ show work!!!!
Answer:
Step-by-step explanation:
When dividing two fractions you would turn the divisor into its reciprocal then multiply. So -7/12 divided by 1/7 would be equal to -7/12 multiplied by 7/1 (7/1 is the reciprocal of 1/7)
-7/12 divided by 1/7 =
-7/12 multiplied by 7/1=
-49/12
Simplify.
Sam made $189 for 9 hours of work. At the same rate, how many hours would he have to work to make S147?
Answer: 7 hours
Step-by-step explanation:
$189/9 hr = $21/hr
$21/hr(x) = $147
x = 147/21
x = 7 hours
Answer:
7 hours
Step-by-step explanation:
We know 9 hours of work paid $189
to find how much Sam makes in one hour we divide the amount made by the time it took to make it
189 / 9 = 21 dollars per hour
then we know she would like to make $147 more at a rate of $21/hr so
147 / 21 = 7 hours
(a−2b)^3 when a=−4 and b=−1\2
Answer:
- 125
Step-by-step explanation:
8b–9b–5b+7b
Simplify the expression:
Answer:
b, or 1b
Step-by-step explanation:
First of all, you have to combine like terms. In this situation though, they are all b. So start at the beginning. 8-9 is -1. -1 - 5 is -6. -6+7 is 1. So you say, b, because it is the same thing as 1 b.
a factory makes lightbulb's out of 400 light bulbs 18 were found to have defective filaments
Answer: If you are asking for percentage, 18/400 bulbs were defective. In other words, 4.5% of bulbs were defective. This also means that 95.5% of bulbs were not defective.
Would appreciate brainly <3
For 0° ≤ x < 360°, what are the solutions to cos(x/2) – sin(x) = 0?
A{0°, 60°, 300°}
B{0°,120°, 240°}
C{60°, 180°, 300°}
D{120°,180°, 240°}
Precalc
Answer:
the answer is c
Step-by-step explanation:
cos30 = sin60
then cos30 - sin 30 = 0
c is the only choice which can satisfy in the problem
I need help I’m revising for a test and l don’t understand this question please help!
Answer:
- 5 ≤ x < 3
Step-by-step explanation:
The lower limit has a solid circle at - 5
This means that x can equal - 5
The upper limit has an open circle at 3
This means that x cannot be equal to 3
The inequality represented by the diagram is then
- 5 ≤ x < 3
Help please I really need it!!!
Answer:
They are similar
Step-by-step explanation:
If a triangle has the same two angle as another one it means that they are similar triangles. this is because all triangles have 180 degrees shared between all of the angles in them. that is the case for these triangles.
hope this helps!
What series of transformation will not map figure H onto itself
Answer:
D
Step-by-step explanation:
Given a square with vertices at points (2,1), (1,2), (2,3) and (3,2)
Consider option D.
1st transformation will map vertices of the square into points
....2nd transformation = reflection over y = -x + 2 will map vertices into points ....These points are not the vertices of the initial square.
I hope it helps.
Write the equation of the line that passes through the points (-8,3) and (0,2). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Answer:
[tex]y = \frac{1}{8} x + 2[/tex]
Anneyonghaseyo,
plss can anyone solve this it's urgent (+_+)
15 points
Anneyonghaseyo!!
Radius = 10.5 m
Diameter = 10.5 × 2 = 21 m
Circumference = πd
= 22/7 × 21
= 66 m.
Cost of fencing 1 metre = ₹ 4
Cost of fencing 2 rounds = ?
2 rounds = 2 × circumference
= 2 × 66
= 132 m
Cost of fencing 2 rounds = 132 × 4
= ₹ 528.
________
꧁✿ ᴿᴬᴵᴺᴮᴼᵂˢᴬᴸᵀ2222 ✬꧂
What is the volume of a sphere with a radius of 4.4 cm, rounded to the nearest tenth
a
of a cubic centimeter?
O 223.8
0 294.4
O. 299.1
O 356.8
Answer:
V = 356.8 cubic centimeter
Step-by-step explanation:
[tex]V = \frac{4}{3} \pi r^{3}[/tex]
[tex]\pi V = \frac{4}{3} \pi (4.4)^{3}[/tex]
[tex]V = \frac{4}{3}\pi (85.184)[/tex]
V = 356.8179048
V = 356.8
what is 39/17 as a decimal rounded to the nearest tenths?
the nth The nth term of a sequence is n-4 what is the tenth term
Step-by-step explanation:
the nth term is n-4, so the 10th term (that means n = 10) is then 10-4 = 6
n-4 is the rule of the sequence.
Simply replace "n" with a number and solve your equation.
For example, if you are finding the 5th term, you do it like this:
= n - 4
= (5) - 4
= 1
Now, as you asked, the tenth term:
= n - 4
= (10) - 4
= 6
The ratio of students in Class X to Class Y is 2 : 5. There are 24 more students in Class Y than Class X. How many students must transfer from Class Y to Class X so that both classes have equal number of students?
Answer:
The answer will be 12 students. 12 students must transfer from Class Y to Class X so that both classes have equal number of students.
Step-by-step explanation:
Since the ratio is 2 : 5, we would multiply both number to 8 and get 16 : 40.
Now find the average of those two numbers: (16 + 40) / 2 which gets you 28. Now either subtract 16 from 28 or subtract 28 from 40 and you will get 12.
28 - 16 = 12 students
40 - 28 = 12 students.
What is 100,000×1,000,000
Answer:
100,000 × 1,000,000 = 1.E11
Answer:
100000000000
Step-by-step explanation:
what is the answer too 2y-3=-5
2 − 3 = −5
First we need to Add 3 to both sides of the equation:
2 − 3 + 3 = −5 + 3
Then we simplify:
2 = −5 + 3
2 = −2
Now we divide both sides of the equation by the same term:
2 / 2 = −2 / 2
Final answer: = −1
I hope this helps!
Answer:
Y= - 1
Step-by-step explanation:
2y-3= - 5
+3 +3
2y= -2
/2 /2
Y= -1
Step 1: Add 3 to both sides because you want to cancel out the 3 so you do the opposite of what is say's. For example, if it says 2y-3 add 3 or 2y+3 subtract 3 from both sides.
Step 2: Add 3 to -5 which would be -2
Step 3: Since you're "multiplying" Y to 2 you're going to divide 2 to get Y by itself. So 2/2 cancels out and now you're left with y
Step 4: Divide 2 form -2 and you get -1
Let me know if you have any questions and I hope this helps
A triangle has two side of lengths 10 and 14. What value could the length of the third side be?
Use the Pythagorean Theorem [tex]a^2 + b^2 = c^2[/tex].
Since we have 2 sides we can easily solve for the third.
[tex]c^2 = 10^2 + 14 ^2[/tex]
[tex]c = \sqrt{100 + 196}[/tex][tex]= \sqrt{296}[/tex] ≈[tex]17.205[/tex]
help needed please im stuck
Answer:
a) b^3
b) x^3
Step-by-step explanation:
It can be helpful to think of the exponent as specifying the number of times the base is a factor in the product. Of course, common factors in the numerator and denominator cancel.
a)[tex]\dfrac{b^7}{b^4}=\dfrac{b\cdot b\cdot b\cdot b\cdot b\cdot b\cdot b}{b\cdot b\cdot b\cdot b}=b\cdot b\cdot b=b^{7-4}=\boxed{b^3}[/tex]
__
b)[tex]\dfrac{x\cdot x^5}{x^2\cdot x}=\dfrac{x\cdot x\cdot x\cdot x\cdot x\cdot x}{x\cdot x\cdot x}=x\cdot x\cdot x=x^{6-3}=\boxed{x^3}[/tex]
24 marbles were shared equally amongst a group of children. each child received 4 Marbles how many children were in the group?
Answer:
6
Step-by-step explanation:
24/6=4
6x4=24
6+6=12
6+6=12 12+12=24
Solution:
Given,
No. of marbles =24
No. of marbles each child received=4
No. of children in the group=?
Here,
No. of children in the group = No. of marbles/
No. of marbles
each child received
=24/4
=6
Hence, There were 6 children in the group.
Can someone help? Will give brainly if correct!
Answer:
7.03, 6.75, 6.72, 6.08, 6.4
Step-by-step explanation:
Fred buys flags from a manufacturer
for $12.50 dollars and then sells
them in his store for a 26% markup.
What price do his customers pay for
a flag?
Answer:
15.75
Step-by-step explanation:
26%of12.5
=12.5*26/100
=3.25
customers pay for a flag is 3.25+12.5=15.75
(30 Points) A catering company has small tables and large tables. Small tables seat 2 people and large tables seat 5 people. You are planning a party for at most 75 guests. Write an inequality that represents this situation. Let s represent the small tables and I represent the large tables.
Answer:
75 ≥ 2s + 5l
75 = guests
2 is = amount of people per small table
5 is = amount of people per big table
SOMEONE, PLEASE HELP!!! I'll mark brainliest for the fastest, correct answer. I'm giving 15pts!
Evaluate P(6, 2).
Answer: Permutation is 30
Step-by-step explanation:
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!
Answer:
D i think sorry if wrong
Step-by-step explanation:
