Given :
[tex]a_1=-25[/tex] .
[tex]a_n=a_{n-1}-14[/tex] .
To Find :
The general equation of [tex]a_n[/tex] .
Solution :
We know , when difference between any two consecutive terms in an A.P is equal , then the series is in arithmetic progression .
Now , common difference ,
[tex]d=a_n-a_{n-1}\\\\d=-14[/tex]
Also , first term is -25 .
Now , general term of an A.P is given by :
[tex]a_n=a+(n-1)d\\\\a_n=-25+(n-1)(-14)\\\\a_n=-25-14n+14\\\\a_n= -11-14n[/tex]
Hence , this is the required solution .
Function g is a transformation of the parent quadratic function f. Which statements are true about this function?
g(x) = -(x - 4)2 + 6
Select all the correct answers.
Function g reflected function facross the x-axis.
Function g translated the vertex from (0,0) to (-4,6).
For function g, as x approaches negative infinity, 8(x) approaches negative infinity.
Function g is always decreasing,
Function g is always negative.
Function g is symmetrical about the point (4,6).
Answer: Function g reflected function f across the x-axis.
For function g, as x approaches negative infinity, g(x) approaches negative infinity.
Function f is symmetrical about the point (4,6).
The correct options are Option A and Option C : Function g is reflected of function f across the x-axis. and as x approaches to the -∞, g approaches to the -∞.
Here given that the function g(x)= -(x-4)²+6
vertex of the graph of the function g is
dg/dx=0
⇒2(x-4)=0
⇒x-4=0
⇒x=4
putting x=4 in g(x) , g(4)= -(0-0)²+6=6
Hence the vertex of the graph of g is (4,6).
The parent function is f(x)= x²
here the vertex of the function is (0,0).
Option A: This option is true as the graph of function g is the inverse image of f. So, Function g is reflected of function f across the x-axis.
Option B: This option is incorrect. as the vertex of the function f is transformed to (4,6) which is the vertex of g(x).
Option C: This option is true because
[tex]\lim_{x \to- \infty} g(x)[/tex]
= [tex]\lim_{x \to- \infty} -(x-4)^2+6\\[/tex]
= -(∞-4)²+6
=-∞²+6
=-∞
Hence as x approaches to the -∞, g approaches to the -∞
Option D. This option is incorrect because
if the function is always decreasing its derivative is negative for all x∈R
dg/dx<0
⇒2(x-4)<0
⇒x-4<0
⇒x<4
so the function is decreasing for x<4 not for all x.
Option E: This option is incorrect. because g is not always rather it is positive for 4-√6 < x < 4+√6
g(x)>0
⇒-(x-4)²+6 >0
⇒-(x-4)²>-6
⇒(x-4)²<6
⇒|x-4|<√6
⇒4-√6<x<4+√6
so, g(x) is positive for 4-√6 < x < 4+√6
Option E:
This option is incorrect as g(x) is symmetrical about line x=4.
Therefore the correct options are Option A and Option C : Function g is reflected of function f across the x-axis. and as x approaches to the -∞, g approaches to the -∞.
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can someone help me?
thanks
Answer:
A
Step-by-step explanation:
2w means 2 pounds per week
you need less than or equal to because think about it like this
you want to be LESS THAN or EQUAL TO 190 pounds. on the right side is reality , what you really are. you need the right side to be LOWER or EQUAL to the left side!
write 10 places in India and write their population in Indian and international system
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Solution :-
Following are the population of five major cities of India according to the Census of 2011.
1) Mumbai
a) Indian System :
1,24,42,373 - One Crore Twenty Four Lakh Forty Two Thousand Three Hundred Seventy Three.
b) International system :
12,442,373 - Twelve Million Four Hundred Forty Two Thousand Three Hundred Seventy Three.
2) Delhi
a) Indian System :
1,10,34,555 - One Crore Ten Lakh Thirty Four Thousand Five Hundred Fifty Five.
b) International System :
11,034,555 - Eleven Million Thirty Four Thousand Five Hundred Fifty Five.
3) Bangalore
a) Indian System :
84,43,675 - Eighty Four Lakh Forty Three Thousand Six Hundred Seventy Five.
b) International system :
8,443,675 - Eight Million Four Hundred Forty Three Thousand Six Hundred Seventy Five.
4) Hyderabad
a) Indian System :
67,31,790 - Sixty Seven Lakh Thirty One Thousand Seven Hundred Ninety.
b) International System :
6,731,790 - Six Million Seven Hundred Thirty One Thousand Seven Hundred Ninety.
5) Ahmedabad
a) Indian System :
55,77,940 - Fifty Five Lakh Seventy Seven Thousand Nine Hundred Forty.
b) International System :
5,577,940 - Five Million Five Hundred Seventy Seven Thousand Nine Hundred Forty.
Answer:
Mumbai 12,442,373Delhi 11,007,835Bangalore 8,436,675Hyderabad 6,809,970Ahmadabad 5,570,585Chennai 4,681,087Kolkata 4,486,678Surat 4,467,797Pune 3,124,458Jaipur 3,046,163.Step-by-step explanation:
Please a BrainliestComment me if you want to help me find my lost love
In a normal distribution, 51 is the score that is two standard deviations above the mean, and 36 is the score one standard deviation below the mean. Find the mean
Answer:
The mean is 41
Step-by-step explanation:
Here , we are interested in finding the mean.
Firstly, let the standard deviation be x and the mean be y.
We are told that 51 is 2 standard deviations above the mean. What this mean is that if we subtract 2 standard deviations from 51, we will arrive at the mean.
Mathematically;
51 - 2(x) = y
y + 2x = 51 •••••••••(i)
We are also told that 36 is one standard deviation below the mean. What this mean is that if we subtract one standard deviation from the mean, we will have 36
Mathematically, that would be;
y-36 = x •••••••(ii)
Substitute ii into i directly;
We have
y + 2(y-36) = 51
y + 2y -72 = 51
3y -72 = 51
3y = 51 + 72
3y = 123
y = 123/3
y = 41
Point A is located at coordinates (-4,3). What are the new coordinates of A' after a a translation two units to the right, then a reflection using the x-axis?
Answer:
(-1,-3)
Step-by-step explanation:
after you find (-4,3) on the graph you move 2 units to the right which would become (-1,3)after that you go over the x-axis and you reflect (mirror) that and your answer is (-1,-3)I hope this help
My brother ate 4 of the cupcakes my mother just finished baking for her back sale. That was 2/5 of all of them! With how many cupcakes did she start with?
Answer:
10
Step-by-step explanation:
if 4 cupcakes were 2/5 of what she started out with, i divided 4/2 and got 2 so 2 cupcakes per 1/5, 2*5=10 so 5/5 is the 10 cupcakes
Does anyone know how to do this?
What is f(-2) of the function given below? *
f(x) = 3x2 - 4x + 1
Answer:
f(-2) = 21
Step-by-step explanation:
Step 1: Define
f(x) = 3x² - 4x + 1
f(-2) is x = -2
Step 2: Substitute and Evaluate
f(-2) = 3(-2)² - 4(-2) + 1
f(-2) = 3(4) + 8 + 1
f(-2) = 12 + 9
f(-2) = 21
!!30 points!!
Are points A, B, and E collinear or noncollinear?
A. Noncolinear
ABE although they are in the same side, but they don't lie on the same line.
so its a noncolinear.
Answer:
ABE although they are in the same side, but they don't lie on the same line.
so its a noncolinear.
Step-by-step explanation:
Michael and Pedro both solved the equation: -5 + 7p + 14 + 11p = 9 (2p + 1) Michael says that there are no solutions to the equation. Pedro says that there are infinitely many solutions. Who is correct?
Answer:
Step-by-step explanation:
-5 + 7p + 14 + 11p = 18p + 9
18p + 9 = 18p + 9
0 = 0
Pedro is correct
write an equation to represent m varies inversely as the square of q ?
Answer:
m = [tex]\frac{k}{q^2}[/tex]
Step-by-step explanation:
Given m varies inversely as q² then the equation relating them is
m = [tex]\frac{k}{q^2}[/tex] ← k is the constant of variation
how do i divide an equation over a negitive number?
Multiply both sides by negative four to get rid of the fraction
j+18=-32
subtract 18
j=-50
Please help due tonight very urgent being graded need help please Tom makes $25 an hour working at the local video game store. Over the past year he has saved $150 toward a new iPhone. If the iPhone cost $300, how many hours will he need to work to be able to buy the iPhone? make an equation or inequality and solve. Show your work
Hey there! I'm happy to help!
Tom has 150 already saved and for every hour he works, he will gain an extra $25. After h hours, he will have $300,
So, we multiply 25 by n, because for every hour he will have 25 added to his total, and repeated addition is multiplication, so we multiply 25 by n.
We add 150 as that is what we already have saved.
Finally, we want this to equal 300.
So, here is our equation.
25n+150=300
Now we solve. We subtract 150 from both sides.
25n=150
We divide both sides by 25.
n=6
Tom will have to work six hours to buy the iPhone.
Have a wonderful day! :D
Answer:
25(6)+150=300
Step-by-step explanation:
25x+150=300
25x=300-150
25x/25=150/25
x=6
WILL GIVE BRAINLYIEST Which item, A or B has a higher overall net force? Show your work and include units.
Answer:
a does because 5-3= 2 net force to the right and b would total out to 1 to the right
Step-by-step explanation:
what is (3x – 2)(4x + 1) =
Answer:
[tex]12x^{2} -5x -2[/tex]
Step-by-step explanation:
We multiply the first term 3x by 4x and then 3x multiplied by one. We proceed to multiply by -2 by 4x and multiplied by -2 +1. We finally add and get the result.
[tex]12x^{2} -5x -2[/tex]
6 over 7 subtracted by 1 over 7
Answer:
5/7
Step-by-step explanation:
6/7-1/7=5/7
The answer is 6/7 - 1/7 = 5/7
Step by step explanation is in the image below. :)
{(1, 3), (2,5), (-3, -4), (4, -3) (5,-1)} the above is
a function or not a function
the answer is it is function
I need a fast answer !! A bag has 7 blue marbles and 3 red marbles. What is the probability of drawing two red marbles, if the first marble is replaced after it is drawn? A. 1/7 B. 1/3 C. 3/10 D. 9/100
Answer:
Step-by-step explanation:
9/100 i believe as you would multiply 3/10 by 3/10 due to the fact the marble is being replaced so the probability of getting a red marble the second time will be more unlikely. If I'm right please thank me or give me brainly. Hope this helps :)
The probability of drawing two red marbles, if the first marble is replaced after it is drawn, is 9/100.
What is Probability?
It is a branch of mathematics that deals with the occurrence of a random event.
The probability of drawing a red marble on the first draw is 3/10, since there are 3 red marbles out of a total of 10 marbles.
Since the first marble is replaced before the second draw, the probability of drawing a red marble on the second draw is also 3/10.
To find the probability of drawing two red marbles in a row, we multiply the probabilities of the individual events, since they are independent:
P(drawing two red marbles) = P(red on first draw) × P(red on second draw)
P(drawing two red marbles) = (3/10) × (3/10)
= 9/100
Therefore, the probability of drawing two red marbles, if the first marble is replaced after it is drawn, is 9/100.
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HELP ME PLSEASE I NEED THIS <33
Since the measure of angle DOC = 44 degrees and it's the central angle of arc DC, the measure of arc DC = 44 degrees
Round the following number to the place indicated: 65,327; thousands
65,330
70,000
65,000
65,300
On his first day of school, Kareem found the high temperature in degrees Fahrenheit to be 76.1°. He plans to use the function C of F = five-ninths (F minus 32) to convert this temperature from degrees Fahrenheit to degrees Celsius. What does C(76.1) represent?
Answer: the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius
Step-by-step explanation:
Answer:Aka) A
Step-by-step explanation:
(-6) to the power of negative 5 in fraction form ,
Answer:
-6430041/50000000000
Step-by-step explanation:
so -6 to the power of negative 5 is -0.00012860082 which as a fraction is -6430041/50000000000
in a class of 35 students 19 take Spanish, 18 take French and 3 take neither. Calculate how many take:
a) both French and Spanish
b) just Spanish
c) just French
Answer:
Hope that will help you
Points P, Q, R, and S are collinear. Point Q is between P and R, R is between Q and S, and PQ =RS. If PS = 21 and PR = 16, what is the value of QR? QR = (Simplify your answer.)
Greetings from Brasil...
→ Collinear points = points belonging to the same line
→ PQ is said to be equal to RS. Let’s call this distance X
→ let's call QR Y
With this information and the figure in the annex we can conclude that:
refer to attached
PQ = X
QR = Y
RS = PQ = X
then
PR = PQ + QR
16 = X + Y i
PS = PR + RS
21 = 16 + X
X = 5 putting in i
16 = X + Y
16 = 5 + Y
Y = 11
So,
PQ = 5QR = 11RS = 5Collinear points are points on the same line.
The value of QR is 11
From the question, we have:'
Q between P and RR between Q and SThis means that:
[tex]\mathbf{PR = PQ + QR}[/tex]
[tex]\mathbf{QS = QR + RS}[/tex]
[tex]\mathbf{PS = PR + RS}[/tex]
The given parameters are:
[tex]\mathbf{PS = 21}[/tex]
[tex]\mathbf{PR = 16}[/tex]
[tex]\mathbf{PQ = RS}[/tex]
Substitute the above values in [tex]\mathbf{PS = PR + RS}[/tex]
[tex]\mathbf{21= 16 + RS}[/tex]
Solve for RS
[tex]\mathbf{RS = 21- 16}[/tex]
[tex]\mathbf{RS = 5}[/tex]
This means that:
[tex]\mathbf{PQ = RS = 5}[/tex]
Substitute 5 for PQ in [tex]\mathbf{PR = PQ + QR}[/tex]
[tex]\mathbf{PR = 5+ QR}[/tex]
Substitute [tex]\mathbf{PR = 16}[/tex] in [tex]\mathbf{PR = 5+ QR}[/tex]
[tex]\mathbf{16 = 5+ QR}[/tex]
Solve for QR
[tex]\mathbf{QR = 16 - 5 }[/tex]
[tex]\mathbf{QR = 11}[/tex]
Hence, the value of QR is 11
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1.1f Homework: Creating and Solving Linear Equations to Model Real World Problems Part I
he document will
1) Use the story below about Sanjeet and his friends' end-of-season basketball statistics to answer the
questions that follow.
Story
Points Scored
Terrence's points:
Sanjeet and his teanit members were looking
Sanjeet's points:
Cole's points:
at the total points scored by each player
during the season. Sanjeet scored twice ay
many pointy ay Terrence. Cole scored 12
more points than Sanjeet. Together the boys
scored 992 points during the season. How
many points did each boy score?
Equation:
At a hardware store, you can buy a set of four wrenches for seven dollars and a set of 16 screwdrivers for $28. The prices are proportional. True or false?
Answer:
Yes
Step-by-step explanation:
The constant is $1.75 each
Resolved
1. 2(y+4) +4 (2y+2)
Answer:
10y+16
Step-by-step explanation:
Distribute and combine like terms
Find the coordinate of the midpoint of the segment formed by the given points: (7, 11) and (3, -5)
Answer:
[tex]MP = (5,3)[/tex]
Step-by-step explanation:
[tex]MP= (\frac{x_1+x_2}{2}) (\frac{y_1+y_2}{2} )\\MP= (\frac{7+3}{2}) (\frac{11+-5}{2} )\\MP= (\frac{10}{2}) (\frac{6}{2} )\\MP= (5,3)[/tex]
Mt. Everest is 29,029 feet above sea level. The dead sea is 1,411 feet below sea level what is the difference between the elevations?
Answer:
30,440 feet
Step-by-step explanation:
You simply just add 29,029 and 1411 because if you picture it on a number line, 29,029 would be to get to zero as well as 1411 going up in elevation.
why did the chicken cross the road
Answer:
To get to the other side
Obviously
Answer:
"To get to the other side".
What is even the point of that "joke"?:
"Why did the chicken cross the road?" is a common riddle joke, with the answer being "To get to the other side". It is an example of anti-humor, in that the curious setup of the joke leads the listener to expect a traditional punchline, but they are instead given a simple statement of fact.