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 answer?
Answer:
134
Step-by-step explanation:
Juan joins a movie club. He pays $10 to join and each movie costs $5. Which equation represents the relationship between the total cost, y, and the number of movies, x?
14.
Jan spent 3 hours doing homework last week.
She spent 5 hours doing homework this week.
How many more hours did Jan spend on homework
this week than last week?
A. 1 hour
B. 1 hour
D. 11 hours
C. 14 hours
Answer:
D. [tex]\mathrm{1\frac{1}{2}\:hours}[/tex]
Step-by-step explanation:
As it asks how many more, it means plus, plus means addition. So, let find the difference between the two fractions.
This week should be at first, and last week should be after the minus sign.
[tex]5\frac{1}{4} - 3\frac{3}{4}[/tex]
[tex]\mathrm{Convert\:mixed\:numbers\:to\:improper\:fraction}[/tex]
[tex]5\frac{1}{4} = 4\times5=20+1=21\\\\\frac{21}{4} \\\\3\frac{3}{4} = 4\times3=12+3=15\\\\\frac{15}{4}[/tex]
[tex]\frac{21}{4} - \frac{15}{4}[/tex]
[tex]\mathrm{Subtract\: the\: numerators,\: not \:the \:denominators.}[/tex]
[tex]\frac{21}{4} - \frac{15}{4}\\\\21-15=6[/tex]
[tex]\frac{6}{4} \\\\\mathrm{\underline{Simplify:}}\: \bold{1\frac{1}{2}}[/tex]
Select the correct answer.
Which equation has a unit rate greater than the unit rate of the relationship shown in the graph?
7
5
3
3
9
An airline ticket costs $40.
The price is increased by 200%.
Work out the absolute increase.
An airline ticket costs $40. The price is increased by 200 percent. The absolute increase is $80.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
Cost of airline ticket = $40.
Increase in price = 200% of $40
Absolute increase = [tex]\frac{200}{100}* 40 = 80[/tex]
Learn more about percentage here
https://brainly.com/question/13450942
#SPJ2
anybody know this at all?
Answer:
perimeter = 4x³ + 3x² + 2
Step-by-step explanation:
perimeter = sum of the lengths of the sides
perimeter = 2x³ + 3x³ - x² - x³ + 4x² + 2
perimeter = 4x³ + 3x² + 2
( DISCUSSION TOPIC )
NEED WITHIN 10 MINUTES!!!!
Up to this point, the only types of numbers you've seen have been rational numbers.You can write any rational number as a fraction.
The prefix ir- means not.
What do you think it means for a number to be irrational?
Can you think of any numbers that are irrational?
Answer:
A number that is irrational are numbers that cannot be expressed as a terminating or repeating decimals or in the form (a/b) where a and b are integer and b does NOT equal 0.
An example of an irration number is the square root of 10, or pie because it is a infinited number
I hope this helps!
Answer:
the irrational is kind of a part
of the math that includes rational and
irrational numbers
are my answers correct?
Answer:
Partially. Your answer to a is correct but you used the wrong number for b.
Step-by-step explanation:
The amount of money you earn (profit) is taken after all of your expenses. You correctly calculated that Leo made $5000 in profit. Divide that by 40 instead of $12850. (answer: $125/hour)
Please help me with this!
Answer:
9/40
i think it may be like this
Step-by-step explanation:
3/5.3/8
9/40
What is the measurement of this angle?
Answer:
54°
Step-by-step explanation:
All the angle measures of a triangle must add up to equal 180°. So,
59°+67°+x°=180°
x=54°
2x - 3y = -24 solve for y
x + 6y = 18 solve for x when y= 2
I need the answer
01.
2x-3y=-24
-3y=-2x-24
3y=2x+24
y=(2x+24)/3
02.
x+(6*2)=18
x=18-12
x=6
Answer: y = 2/ 3 x+8, and x = 6
Step-by-step explanation: 2x−3y+−2x=−24+−2x −3y /−3 = −2x−24 /−3 y = 2/ 3 x+8 x+(6)(2) = 18 x+12+(-12) = 18+-12 x = 6
if mai runs 21 labs at the same rate ( 4 minutes ), how long does it take her ?
Each year, the students in seventh grade go to an environmental camp. This year, the total cost is $1,580 for 79 students. Which equation represents the cost, y, of attending the camp for x number of students?
Select the correct answer.
y = 20x
y = 79x
y = 79x + 1580
y = 1580x + 79
Answer:
y=20x
Step-by-step explanation:
You have to find the cost by dividing the amount of money by the amount of students, to see house much each student paid. You are finding the unit price. Which is 20 because...
1.580/79=20
In conclusion,
Each student paid $20
Let z = 8 – 3i, and z2 = a + bi. What are the values of a and b?
The values of a and b from the given complex numbers is 8 and -3 respectively.
The standard form of representing complex number is expressed as z = x + iy
Given the complex numbers z = 8 – 3i, and z2 = a + bi
To get the values of a and b, we need to compare both expressions as shown:
For the real part;
a = 8
For the imaginary part:
-3i = bi
-3 = b
Swap
b = -3
Hence the values of a and b from the given complex numbers is 8 and -3 respectively.
Learn more about complex numbers here: https://brainly.com/question/12375854
If 40 hours is a full work week and any thing over 40 is overtime or time and a half. If u worked 50 hours one week, and 55 hours the second week how much would ur pay check be
Assuming u make 15 dollars a hour for normal pay?
Answer:
first week would be $750 second week would be $825
If your pay is every two weeks it would be $1575
Step-by-step explanation:
please i really need help
The perimeter of each shape is 3 units? True or False?
simplify this addition 2m+3m+(-6m)
Answer:
-m
Step-by-step explanation:
2m+3m+(-6m)=2m+3m-6m
=5m-6m
=-m
Answer:
-m
Step-by-step explanation:
2m+3m+(-6m)
Remove parentheses.
2m+3m-6m
Add and subtract.
-1m or -m
Hope this helps :)
w+(−2.8)=4.3 whats the answer
Answer:
w=7.1
Step-by-step explanation:
Answer:
w=7.1
Alternate form
w= [tex]\frac{71}{10}[/tex] , w= 7[tex]\frac{1}{10}[/tex]
Graph the equation and identify the intercept(s). If the equation is linear, find the slope of the line.
4. 2x - 3y = 6
5. y = 4.5
6. y = | x - 1 | -2
Answer:
Graphs shown below.
4.) x-intercept: (3,0) y-intercept: (0,-2) slope: 2/3
5.) x-intercept: none y-intercept: (0,4.5) slope:0
6.) x-intercept: (3,0) and (-1,0) y-intercept: (0,-1) slope: none
#4 is blue graph, #5 is green graph, #6 is red graph
Step-by-step explanation:
** #4 is blue graph, #5 is green graph, #6 is red graph **
lacie is making bracelets. if each has 11 beads, and each bead has 2 colors, red and green, how many different bracelets can lacie make if the bracelet can be rotated without losing its uniqueness but cant be flipped
Answer:24
Step-by-step explanation:
A math class consists of 20 female students and 12 male students. Two students are selected at
random to participate in a probability experiment. Compute the following probabilities. Write your
answers in decimal form. Round to the nearest thousandth as needed.
a. A male is selected, then a female.
b. A female is selected, then a male.
5
c. Two males are selected.
d. Two females are selected.
s
e. No males are selected.
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Yeah
Answer:
b
Step-by-step explanation:
Dan was thinking of a number. Dan doubles it and adds 0.8 to get an answer of 58.9. Form an equation with
x
from the information.
Answer:
2x + .8 = 58.9
His number, x, is 29.05
Step-by-step explanation:
2x + .8 = 58.9
2x = 58.1
x = 29.05
An item is originally priced at $68.89. It is on sale for 42 percent of the original price. Which is an estimate of the sale price?
Answer:
The answer is $28.93.
Step-by-step explanation:
Using the butterfly method I got $28.93 as my answer.
$68.89 x 42%= $2,893.38
$2,893.38÷100%= $28.9338
$28.9338 rounded to the nearest hundredth is $28.93. I hope this helps.
Answer:
answer is D.
68.89 x .42= $28
Step-by-step explanation:
to get your answer you multiply the numbers.
$68.89 x .42 = $28
your answer is $28.
hope this helps!
please make me brainliest !
How does the equation change when the radius changes? Unlike h and k, why is r always positive?
Answer:
When the radius is changed, the constant term (r2) in the equation changes—it becomes bigger as the radius becomes bigger. The term r is always positive because it denotes the length of the radius, which is a distance and not a position or location.
Step-by-step explanation:
given f(x) and g(x) = f(x) + k, use the graph to determine the value of k.
PLEASE HELP
Answer:
k=5
Step-by-step explanation:
The graph of g(x) is raised by 5 units so k is 5
185/6 helppppppppopppooooooooo meee
Answer:
30 5/6
Step-by-step explanation:
185 = 30x6 + 5
Answer:
30 5/6
Step-by-step explanation:
goodluck guyssSana Tama yanPLZZZZZZZZZZZ HELP 1000 POINTS AND BRAINLIEST
Answer:
you would have to subtract the points a and b to get question a. And for c, you would have to mark it on a graph in order for it to show. I am pretty sure this is how you do it. Sorry I tried my best, plz don't come at me if it is wrong.
Step-by-step explanation:
Answer:
you need to subtract the points a and b to get the question a. for c, you need to mark it on a graph in order for it to show. I sure this is how you do it
i tried my best
hope it helps
What is the equation to the parallel of 7x-y=8 passing through the point (-2,3)
Answer:
y =7x + 17
Step-by-step explanation:
7x-y=8
y = 7x - 8......convert to slope intercept form
m = 7
parallel lines have the same slope
put in point slope form using the points of the equation of the line that you want to find
y - 3 = 7(x+2)
y -3 = 7x + 14.........distribute
y = 7x +14 + 3.........add 3 to both sides
y = 7x +17................simplify
help please nfvribwibfvwbifvibbiurw
Answer: A, D, E
Step-by-step explanation: