Answer:
nth term = 4 + n^2
Step-by-step explanation:
Sorry if the answer is long but I'm hoping my explanation can help.
In order to understand the issue, we should try to find the pattern between the terms given.
The terms given were 5, 8, 13, 20 and 29.
Between the first term and second term, the difference is 3.
Between the second and third term, the difference is 5.
The pattern goes on and we find out that the difference between the (n-1)th term and the nth term is
2n - 1.
Hence, we can determine the pattern of the numbers is
nth term = (n-1) term + 2n - 1
We can use this to find term 0 (before term 1) by plugging in the values for term 1
5 = 0th term + 2 (1) - 1
5 = 0th term + 1
Hence the 0th term = 4
If we expand on the summation,
We can find the nth term
nth term = 4 + 2 (1) - 1 + 2(2) - 1 + ... + 2(n-1) - 1 + 2n - 1
As we can see, the number 1 has been subtracted n times (excluding the -1 in 2(n-1)). Hence, we can split combine all of the subtracted ones into -n.
We can rewrite it as
nth term = 4 + 2 (1) + 2(2) + ... + 2(n-1) + 2n - n
Now, we will move 4 and n to one side.
nth term = 4 - n + 2 (1) + 2(2) + ... + 2(n-1) + 2n
We can factorize 2 out from every term to the right of -n. This would give out
nth term = 4 - n + 2 (1 + 2 + ... + (n-1) + n)
The term (1 + 2 + ... + (n-1) + n) can actually be rewritten by using the triangular formula.
The triangular formula is stated such that
Tn = (n*(n+1))/2
This heavily simplifies the equation into
nth term = 4 - n + 2 [(n*(n+1))/2]
This equation becomes
nth term = 4 - n + n^2 + n.
Now, we can finally simplify into the final equation
nth term = 4 + n^2
Each day Jacob records the number of laps and the distance he walks, in miles, on a track. Graph the relation and determine whether the distance that Jacob walks is a function of the number of laps.
{(3, 0.75), (6, 1.5), (9, 2.25), (2, 0.5), (7, 1.75), (10, 2.5), (4, 1)}
The distance is 6.18 miles that Jacob walks as a function of the number of laps which is represented in the attached graph.
We have been given the relation below:
{(3, 0.75), (6, 1.5), (9, 2.25), (2, 0.5), (7, 1.75), (10, 2.5), (4, 1)}
What is the distance between two points?The distance between two points is defined as the length of the line segment between two places representing their distance.
The formula of the distance between two points is P(x₁, y₁) and Q(x₂, y₂) is given by: d (P, Q) = √ (x₂ – x₁)² + (y₂ – y₁) ².
The given relation of function is represented in the attached graph.
Take two endpoints (3, 0.75) and (9, 2.25)
x₁ = 3, y₁ = 2.25
x₂ = 4, y₂ = 9
distance = √ (9 – 3)² + (2.25 – 0.75)²
distance = √ (6)² + (1.5)²
distance = √ (36 + 2.25)
distance = √ (38.25)
distance = 6.18 miles
Therefore, the distance is 6.18 miles that Jacob walks is a function of the number of laps.
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What is 100X190
I give brainliest to the one who answers correctly.
Answer:
it is 19000 hope this helps!
Answer:
19,000
Step-by-step explanation:
Basically add 2 zeros to 190
Hope this helps!
how do you write 100 s a fraction, mixed number, or whole number
Can someone help me solve this problem? I’m not sure how to solve this type of expression
Answer:
(2x+3)square+2
Step-by-step explanation:
(2x) square +2 (2x)(3)+(3)square
2x square +12x+9
I think so.
pls give me brainliest
What happend when matter condenses??
Plzz Answer???
Answer:
in condensation, gas turns into a liquid
Answer:
Condensation is when a gas becomes a liquid. ... In condensation, matter changes from a gas to a liquid. All matter is made of tiny moving particles called molecules. Evaporation and condensation happen when these molecules gain or lose energy.
B =
Round your answer to the nearest hundredth.
Work Shown:
sin(angle) = opposite/hypotenuse
sin(B) = AC/AB
sin(B) = 2/3
B = arcsin(2/3)
B = 41.8103 approximately
B = 41.81
Note: The arcsine function is the same as the inverse sine function, and that's denoted as [tex]\sin^{-1}[/tex] on many graphing calculators. Your calculator needs to be in degree mode.
Which of these inequalities is graphed below? NA w 1519 he darrer 14 li AN W UM AN ww 12+ 9 6 3 wao WA ME BAL - 15 - 12-9-6-3 - WASSA 6 3 RES WORK 11122 wen M 1215 KA பா VA . BEL MON w AKS SHOP ܝܛܝܝ 1 L- ON IN 2002 151 A. y< 2x - 6 B. y s 2x – 6 C. y> 2x - 6 D. yz 2x – 6
I know the answer I want you to explain it
Answer:(-4,3)
Step-by-step explanation:
Here, Every equation has same slope (-4) and same y-intercept (3), so we don't need to calculate those.
Now, as coordinates are in left-portion, and also touches the line, it would be: y ≥ -4x + 3
Which compound inequality is represented by the graph?
Answer:
A
Step-by-step explanation:
Since the shaded region on the right is greater than or equal to 3, and the shaded region on the left is less than -4 (since numbers decrease as the arrow moves towards the left on the number line).
Simplify please...Simplify Simplify
Answer:
See images.
Step-by-step explanation:
For these kinds of problems, get a common denominator. Put everything over that common denominator and add or subtract the terms in the numerator. Combine like terms. See images.
Answer:
Here are the answers.
Step-by-step explanation:
Parallel, perpendicular, or neither
1. Y=x+6 and x- y=2
2. X-2y=8 and y=-2x+1
Answer:
1. parallel
2. perpendicular
Step-by-step explanation:
Solve the system of equations - 2x + 2y = 2 and - x + 3y = –17 by
combining the equations.
Answer:
x=-10, y=-9. (-10, -9).
Step-by-step explanation:
-2x+2y=2
-x+3y=-17
----------------
-2x+2y=2
-2(-x+3y)=-2(-17)
-------------------------
-2x+2y=2
2x-6y=34
----------------
-4y=36
y=36/-4
y=-9
-x+3(-9)=-17
-x-27=-17
-x=-17+27
-x=10
x=-10
Can someone help me, please? :((((
Answer:
C 132 square units
Step-by-step explanation:
. Happy Friday
This is the question in the photo above.
Answer:
an alternative hypothesis is an angle that is alternate to each other
View Example
After a power fallure, the temperature in a freezer increasettat an average rate of 3.5°F per hour. The total
Increase was 17.5°F. Enter and solve an equation to find the number of hours until the power was
restored. Let x represent the number of hours it takes for the temperature to increase to 17.5°F.
Step-by-step
Video Tutor
The equation to find the number of hours until the power was restored is
Textbook
Print
The number of hours until the power was restored
is
hours
Turn it in
e Save & Close
Question 6 of 6
✓ Check Answer
Answer:
a b c d e f g h i j k l m n o p q r s t u v w x y z
Step-by-step explanation:
yoooooooooooooooooooooooooooo
Please help I am stuck on this
There are 10 pens in a box. There are x red pens in the box. All the other pens are blue. Jack takes at random two pens from the box. Find an expression, in terms of x, for the probability that Jack takes one pen of each colour. Give your answer in its simplest form.
The probability that one of each color is selected is [tex]\frac{10x - x^2}{45}[/tex]
ProbabilitiesThe probability of an event is the chances of the said event
The given parameters are:
Total = 10Red = xBlue = 10 - xCalculating the required probabilityThe probability that one of each color is selected is calculated as follows:
[tex]P = P(Blue) \times P(Red) + P(Red) \times P(Blue)[/tex]
So, we have:
[tex]P = \frac{10 - x}{10} \times \frac{x}{9} + \frac{x}{10} \times \frac{10 - x}{9}[/tex]
This gives
[tex]P = \frac{x(10 - x)}{90} +\frac{x(10 - x)}{90}[/tex]
Take LCM
[tex]P = \frac{2x(10 - x)}{90}[/tex]
Simplify the above expression
[tex]P = \frac{x(10 - x)}{45}[/tex]
Expand
[tex]P = \frac{10x - x^2}{45}[/tex]
Hence, the probability that one of each color is selected is [tex]P = \frac{10x - x^2}{45}[/tex]
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I need help with this math question fast
Answer:I believe the answer is e
Step-by-step explanation:
What is the value of x?
We know that the triangle is an isosceles triangle because the base angles are the same.
=> 4x - 1 = x + 5=> 4x - x = 1 + 5=> 3x = 6=> x = 6/3 = 2Conclusion:Therefore, the answer is 'x = 2'
Hoped this helped.
[tex]BrainiacUser1357[/tex]
Find 34−13.95 . Express your answer in decimal form.
Answer:
34-13.95 = 20.05
Step-by-step explanation:
Answer:
20.05
Step-by-step explanation:
34 - 13.95 = 20.05
Twelve is sixteen less than four times a number.
Use the distributive property to rewrite as an expression
5(x+3)
Answer:
5x+15
Step-by-step explanation:
you mulityply 5*x and 5*3
(50 points) Here are descriptions of four situations in which the volume of water in a tank is
a function of time. Match each description to a corresponding graph. Each graph
is used only once.
Available Responses:
Graph 1
Graph 2
Graph 3
Graph 4
Situation A: An empty 20-gallon water tank is filled at a constant rate for 3
minutes until it is half full. Then, it is emptied at a constant rate for 3 minutes.
Situation B: A full 10-gallon water tank is drained for 30 seconds, until it is half
full. Afterwards, it gets refilled.
Situation C: A 2,000-gallon water tank starts out empty. It is being filled for 5
hours, slowly at first, and faster later.
Situation D: An empty 100-gallon water tank is filled in 50 minutes. Then, a dog
jumps in and splashes around for 10 minutes, letting 7 gallons of water out. The
tank is refilled afterwards.
Answer:
A = 3
B = 1
C = 2
D = 3
Situation A is graph 3, situation B is graph 1, situation C is graph 2 and situation D is graph 4.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
Situation A :
The water tank is empty at first. So the graph must start at origin.
Tank is filled at a constant rate for 3 minutes until it is half full, that is until it is 10 gallons.
Then the tank is emptied at a constant rate for 3 minutes, which is also 10 gallons.
So the slope must be equal.
And the graph must start from 0 and ends at zero which is graph 3.
Situation B :
Water tank is already full. So the graph must start at higher value in the Y axis.
The only possibility for this is graph 1, since all others starts at origin.
Situation C :
Water tank starts at empty. So the graph starts at 0.
First the rate is slower, then it becomes faster. So there will be an increase in the slope, which is graph 2.
Situation D :
Graph starts at origin since the tank is empty.
Then there is a slight decrease in the water for some time. So the graph turns down slightly, again tank is refilled, so the graph goes up.
Hence each of the graph corresponds to the situation is found.
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who is better Green Bay packers or the bears
Answer:
green bay packers all dayyy
Step-by-step explanation:
How I can answer this question, NO LINKS, if you answer correctly I will give u brainliest!
Answer: 54 words does Rachel type per minute
Step-by-step explanation:
Rachel types 162 words in 3 minutes Rachel types at a constant rate.
We have to find how many words does Rachel type per minute.
By definition of unit rate: all we do is divide 162 by 3 which gives us 54
Answer:
54 words per minute
Step-by-step explanation:
In 3 minutes Rachel types 162 words
Then
In 1 minutes,Rachel types 162÷3 words
In 1 minutes Rachel types 54 words
.
. . Rachel types 54 words per minute
How to to it with step by step explanation
[tex]15^{5} \div 15 ^{7} [/tex]
Whenever the bases are same, powers are different and there is a division sign between them, The powers are subtracted.[tex]a ^{m} \div a ^{n} = a ^{m - n} [/tex][tex]15 ^{ 5 - 7} [/tex]
[tex]15 ^{ - 2} [/tex]
[tex] \tt \: alternate \: from : \\ \frac{1}{15 ^{2} } [/tex]
can someone help me pls
Answer:
i think you add them not sure...
Step-by-step explanation:
40+44+44+??
ok?
Answer:
x=88°
x-44°=88°-44°=44°
Step-by-step explanation:
angle A+ angle B+angle C=180°
48°+x-44°+x°=180°
=48°-44°+x°+x°=180°
=4°+2x°=180°
=4°-4°+2x°=180°-4°
=2x°=176°
=2x°/2=176°/2
=x°=88°
x°-44°=88°-44°
=x°-44°=44°
Which of the following expresses in sigma notation?
Answer:
A series can be represented in a compact form, called summation or sigma notation. The Greek capital letter, ∑ , is used to represent the sum. The series 4+8+12+16+20+24 can be expressed as 6∑n=14n . The expression is read as the sum of 4n as n goes from 1 to 6 .
Brody worked 8.5 hours at Food Lion this week and made $78.20. Based on the number of hours Brody worked and how much he was paid, how much money does Brody make per hour
Answer:
1 hour = $9.2
Step-by-step explanation:
The question says that:
Brody makes $78.20 in 8.5 hours.
So,
8.5 hours = $78.20
We need to find 1 hour pay.
So, divide both sides of the above equation by 8.5
8.5 / 8.5 hours = $78.20 / 8.5
1 hour = $9.2
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Find the slope of the line passing through the points (8,-4) and (1,-9)
Answer:
Use the slope formula to find the slope of a line given the coordinates of two points on the line. The slope formula is m=(y2-y1)/(x2-x1), or the change in the y values over the change in the x values.
Answer: 0.71429
Step-by-step explanation:
22.68 ÷ 14.65 ayuden pliss
Answer:
1.54
Step-by-step explanation: