Use the formula an = d (n − 1) + aj to write a formula for the arithmetic sequence below.
2, 6, 10, 14, 18,
Answers
Answer:
[tex]a_{n}[/tex] = 4n - 2
Step-by-step explanation:
There is a common difference d between consecutive terms in the sequence, that is
6 - 2 = 10 - 6 = 14 - 10 = 18 - 14 = 4
This indicates the sequence is arithmetic with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 2 and d = 4 , thus
[tex]a_{n}[/tex] = 2 + 4(n - 1) = 2 + 4n - 4 = 4n - 2
Related Questions
A box contains 15 large marbles and 11 small marbles. Each marble is either green or white. 9 of the large marbles are green, and 3 of the small marbles are white. If a marble is randomly selected from the box, what is the probability that it is small or white? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answers
Answer:
The probability of selecting a small or white marble is 10/13
Step-by-step explanation:
The total number of marbles is 15 + 11 = 26 marbles
The probability that we want to calculate is if the marble selected is small or white.
So we need to find the number of small marbles as well as the number of white marbles
We can construct a table to see the distribution of the marbles. Please check the attachment for this.
From the table , we can see that there are 11 small marbles and a total of 9 white marbles
The probability of selecting a white marble is;
number of white marbles/total number of marbles = 9/26
The probability of selecting a small marble will be ;
number of small marbles/total number of marbles = 11/26
In probability, whenever we have or, we tend to add
So therefore, the probability of selecting a white or small marble = Probability of selecting a white marble + Probability of selecting a small marble
Mathematically, that would be 9/26 + 11/26 = 20/26
So the probability is 10/13
Select the interval where f is negative
Answers
Answer:
The negative regions of a function are those intervals where the function is below the x-axis. It is where the y-values are negative (not zero). y-values that are on the x-axis are neither positive nor negative. The x-axis is where y = 0.
Step-by-step explanation:
hope this helps :)
I really need help....
..
Answers
Answer:
show the whole number line plz
Step-by-step explanation:
The graph shows the relationship between distance driven and gallons of gas used.
Continuous graph on a coordinate plane shows distance driven, numbered 20 to 60 along the horizontal axis, and gallons of gas used, numbered 1 to 4 on the vertical axis. Solid circles appear at points (0, 0), (30, 1), (60, 2).
Use the graph to complete the statements.
The car gets
miles to the gallon.
After the car has traveled
miles, 2 and two-thirdsgallons of gas have been consumed.
Answers
Answer: 30 and 80
So the care gets *30* miles gallon.
After the car has traveled *80* miles, 2 2/3 gallons.
Answer:
30 and 80 is the answers
Step-by-step explanation:
i need help right now and asap this is the question and if u answer i will give brainliest and whatever it is i will give it anyway here it is
Philosophers during the Enlightenment of the 1600s and 1700s
a were most concerned with faith and religion.
b were disdainful of art and science.
c used emotion as a guiding principle.
d used reason to try to improve people’s lives.
Answers
Answer:
Sorry if I'm late!!!
D. Used reason to improve people's lives
Explanation:
The enlightenment was a time when philosophers challenged the teachings of the catholic church.
whats 100+100 try to guess :)
Answers
Answer:
100+100=200
Step-by-step explanation:
hope it helps :)
Answer:
200
Step-by-step explanation:
100 + 100 = 200
Construct an explicit rule in function notation for the arithmetic sequence represented in the table. Then determine the value of the given term, and explain what it means. Darnell starts saving the same amount from each week′s paycheck. The table shows the total balance f(n) of his savings account over time in weeks. Time (weeks) n 1 2 3 4 Savings account balance ($) f(n) 260 360 460 560 Determine the value of f(11) and tell what it represents in this situation. f(n) = + (n − 1) f(11) = After 11 weeks, Darnell′s savings account will have a total of $ .
Answers
Answer:
After 11 weeks, Darnell′s savings account will have a total of $8,360.
Step-by-step explanation:
The data provided is as follows:
n: 1 2 3 4
f (n): 260 360 460 560
Consider the data for f (n).
The series f (n) follows an arithmetic sequence with a common difference of 100 and first term as 260.
The nth term of an arithmetic sequence is:
[tex]a_{n}=\frac{n}{2}[2a+(n-1)d][/tex]
Compute the value of f (11) as follows:
[tex]f(11)=\frac{11}{2}[(2\times260)+(11-1)\times 100][/tex]
[tex]=5.5\times[520+1000]\\\\=5.5\times 1520\\\\=8360[/tex]
Thus, after 11 weeks, Darnell′s savings account will have a total of $8,360.
Pls help me with this question
Answers
Answer:
option C, x=1
Step-by-step explanation:
[tex]2^{9x-3} = 8^{3-x}[/tex]
[tex]2^{9x-3} = (2^3)^{3-x}[/tex]
[tex]2^{9x-3} = 2^{9-3x}[/tex]
cut 2 from LHS and RHS you will get,
9x-3 = 9-3x
9x + 3x = 9 + 3
12x = 12
x = 12/12
x = 1
therefore, option C is the correct option
hope it helps you!
Answer:
[tex] \huge{ \boxed{ \bold{ \tt{x = 1}}}}[/tex]
Option C is correct.
Step-by-step explanation:
[tex] \text{First ,\: let's \: know \: about \: exponential \: equation} : [/tex]
Exponential EquationAn equation in which variables appears as an exponent of a base is known as exponential equation. The following axioms are useful while solving the exponential equations :
If [tex] \sf{ {a}^{x} = {a}^{b} }[/tex] , then x = bIf aˣ = 1 , then aˣ = a⁰ and x = 0Thus , while solving an exponential equation, we should simplify the equation till the equation is obtained in the form [tex] \sf{ {a}^{x} = {a}^{b}} [/tex] or aˣ = 1 .
Now, let's start to solve :
[tex] \sf{ {2}^{(9x - 3)} = {8}^{( 3 - x)}} [/tex]
➸ [tex] \sf{ {2}^{9x - 3} = {2}^{3(3 - x)} }[/tex]
➸ [tex] \sf{ {2}^{9x - 3} = {2}^{9 - 3x}} [/tex]
➸ [tex] \sf{ \cancel{2} ^{ \: 9x - 3} = \cancel{2} ^{ \: 9 - 3x} }[/tex]
➸ [tex] \sf{9x - 3 = 9 - 3x}[/tex]
➸ [tex] \sf{9x + 3x = 9 + 3}[/tex]
➸ [tex] \sf{12x = 12}[/tex]
➸ [tex] \sf{ \frac{12x}{12} = \frac{12}{12}} [/tex]
➸ [tex] \boxed{ \sf{x = 1}}[/tex]
The value of x is 1 .
Hope I helped!
Best regards! :D
~[tex] \text{TheAnimeGirl}[/tex]
Pool #1 is a rectangle that is 14 feet wide. The length is (14– 8)2ft.
The dimensions of the pool are: Length=________ ft Width=_________ft
Answers
Answer: the length is 6 feet. The width is 2 feet
Step-by-step explanation:
The garden pool is rectangular in shape.
Let L represent the length of the rectangular garden.
Let W represent the width of the rectangular garden.
The area of a rectangle is expressed as L× W. The area of the rectangular garden pond is 12ft^2. It means that
L× W = 12 - - - - - - - - - - 1
The length of the pool needs to be 2ft more than twice that width. This means that
L = 2W + 2 - - - - - - - - - - - 2
Substituting equation 2 into equation 1, it becomes
W(2W + 2) = 12
2W^2 + 2W = 12
2W^2 + 2W - 12 = 0
W^2 + W - 6 = 0
W^2 + 3W - 2W - 6 = 0
W(W + 3) - 2(W + 3) = 0
W - 2 = 0 or W + 3 = 0
W = 2 or W = - 3
Since the Width cannot be negative, then the width is 2 feet
Substituting W = 2 into equation 2. It becomes
L = 2×2 + 2 = 6 feet
Mr. Peters uses a phone card to call relatives in France. It costs him 48 cents to talk for 12 minutes. What is the call rate for the phone card?
Answers
Answer:
The ratio is 1:4
Step-by-step explanation:
For every minute of talking, it costs him 4 cents, and so on.
Explanation:
12*4=48
2 1⁄4 × 1 1⁄2 × 5⁄3 =
please help me
Answers
The answer is:
5 5/8
I got this by multiplying 2 1/4 and 1 1/2 first and i got 3 3/8, then multiplied that number with 5/3
If A ⊂ B, then A ∩ B = A ∪ B. a) sometimes b) always c) never
Answers
The Answer is Never- Hope this helps and have a great day!
Explanation:
We are given that set A⊂B .
This means that set A is properly contained in set B.
i.e. A≠B
This means that there are some elements in set B which are not in set A.
Now we have to show whether the following property A∩B=A∪B
always, sometimes or never hold.
As A is a proper set of B.
This means that: A∩B=A ( Since A is a smaller set)
Also, A∪B=B (Since B is a bigger set)
Hence, A∩B ≠ A∪B (Since A≠ B)
Credit to -virtuematane
Which equation correctly applies the distributive property?
Answers
Answer:
What are the anwser choices?
Step-by-step explanation:
?
A car wash washes 68 cars in 8 hours. At this rate, how many cars are washed in 1 hour?
Answers
Answer:
8.5 (If just pure cars then 8.)
Step-by-step explanation:
To find this, just divide 68/8 to find how many cars are washed in an hour. Plugging it into a calculator, we find out that it is 8.5. If you need elaboration, just comment.
Simplify.
[tex] {8}^{4} \times {8}^{5} = {8}^{?} [/tex]
Enter the missing exponent.
Answers
is the correct answer when multiplying exponents with the same base, you keep the base add the exponents.
Answer:
The answer to your question is simply just 9.
Find the equation of the perpendicular bisect of the given segment by following these steps
1. Determine the slope of the given segment
Answers
Answer:
3/2
Explanation: Just did this on Edge
Which is greater -3 or -5
Answers
Answer: -3
Step-by-step explanation:because -3 looks like it is smaller, but when a number is negative, the smaller the number, the greater the value actually is.
If f(a) = 3a – a2, which of the following are not true statements?
Select all that apply.
A. f(-5) = -40
B. f(4) = -4
C. f(-1) = 2
D. f(0) = 3
C. f(3) = 0
Answers
Select all that apply.
B. f(4) = -d
Solve the inequality:
2x – 3 < x + 2 < 3x + 5
Show your work.
Answers
Answer:
x+2/3
Step-by-step explanation:
Hope this helps!
Step-by-step explanation:
2x−3<x+2≤3x+5
Solve 2x−3<x+2 for x.
x<5
Solve x+2≤3x+5 for x.
x≥−32
Find the intersection of x<5 and x≥−32.
−3/2≤x<5
Hope this helps! :) Plz mark as brainliest
5. Suppose a bunny's second hop is 8% higher than her first hop. Is the
statement below true or false? If the statement is false, correct it.
"The bunny's second hop is 108% of her first hop."
Answers
The length of a rectangle is 3.7 inches when rounded to the nearest tenth of an inch. Select all of the following that could be the actual length of the rectangle.
Answers
Answer:
poop
Step-by-step explanation:
if f(x)=3^x+10x and g(x)=5x-3, find (f-g)(x)
Answers
Check all of the polynomial functions that have 2 as a root.
h(m) = 8 – m3
f(g) = g3 – 2g2 + g
f(a) = a3 – 4a2 + a + 6
f(x) = x3 – x2 – 4
Answers
Answer:
Explained below
Step-by-step explanation:
Polynomial Roots
If x=a is a root of f(x), then f(a)=0
We will test the following functions to check if a=2 is a root.
[tex]h(m)=8-m^3[/tex][tex]h(2)=8-2^3=8-8=0[/tex]
Thus m=2 is a root of h
[tex]f(g)=g^3-2g^2+g[/tex][tex]f(2)=2^3-2\cdot 2^2+2[/tex]
[tex]f(2)=8-2\cdot 4+2=8-8+2=2[/tex]
Thus g=2 is not a root of f
[tex]f(a) = a^3 - 4a^2 + a + 6[/tex][tex]f(2) = 2^3 - 4\cdot 2^2 + 2 + 6[/tex]
[tex]f(2) = 8-16+8=0[/tex]
Thus a=2 is a root of f
[tex]f(x) = x^3 - x^2 - 4[/tex][tex]f(2)=2^3 - 2^2 - 4[/tex]
[tex]f(2)=8 - 4 - 4=0[/tex]
Thus x=2 is a root of f
Answer:
answers are A, C, and D
Step-by-step explanation:
THIS IS CORRECT
What's b/2-14=8 Equal ?
Answers
Answer:
1. add 14 to both sides
b/2 = 8E + 14
2. multiply both sides by 2
b = (8E + 14) x 2
3. regroup terms
b = 2(8E + 14)
Hope this helped :)
Max and Maddy race. Max runs at a speed of 2mph. Maddy runs at a speed of 3mph. If Max takes 3 hours, what is Maddy's speed?
Plz answer!
Answers
Answer:
The question has the answer in it.. Maddy's speed.. which is 3 MPH :/ but... if you need to find the thing that isn't known... Maddy's time.. here is how..
Step-by-step explanation:
Max takes 3 hours at 2 mph.. soo 3x2=6 miles that max traveled
Maddy runs at 3 mph so .. 6 miles / 3MPH =2 hours, Maddy takes 2 hours
please help fast! i will give brainliest
Answers
Answer:
0.39
Step-by-step explanation:
Answer:
1.87
Step-by-step explanation:
c. How many doughnuts are in 7.80 dozen doughnuts
Answers
Answer:
93.6 becasue there are 12 donuts in a dozen. So you multiply 12 by 7.80.
Please help me help me
Answers
2) 80 • 3/5= 32
3)5 1/3 • 9= 48
4) 1 7/8 • 1/6= 15/48
Which of these equations has a negative sloping line?*
O y=-2/3x +8
O y = 2/3x - 8
O y = 4/3x +10
O y = 9/5x - 3
Answers
Answer:
Option 1.
Step-by-step explanation:
That option is the only one with a negative x coefficient, which is the slope.
Answer:
y=-2/3x +8
Step-by-step explanation:
the coefficient of x determines the slope of the line so negative coefficient, negative slope line
Write an equation of the line in STANDARD FORM with a slope of 3 and passes through the point (6,-2) in standard form.
Answers
Standard form:
Ax + By = C
First make it into slope-intercept form first:
y = mx + b
Find b by substituting the given to their respective positions:
-2 = 3(6) + b
-2 = 18 + b
-2 - 18 = b
-20 = b
Now the complete version is:
y = 3x - 20
Arrange the equation:
y = 3x - 20
-3x + y = -20
Easy :)