Answer:
We conclude that the rule will be:
aₙ = 31/12 + 1/6n
Step-by-step explanation:
Answer:
we conclude that the rule will be:
[tex]a_n=\frac{31}{12}+\frac{1}{6}n[/tex]
Step-by-step explanation:
Given
[tex]a_6=3\frac{7}{12}=\frac{43}{12}[/tex][tex]a_1=2\frac{3}{4}=\frac{11}{4}[/tex]The nth term of Arithmetic Sequence
We know the arithmetic sequence with the common difference is defined as
[tex]a_n=a_1+\left(n-1\right)d[/tex]where a₁ is the first term and d is a common difference.
To Determine:
The Rule of the nth term of Arithmetic Sequence
Steps to solve the problem
The 6th term of the Arithmetic sequence be defined as
a₆ = a₁ + (6-1) d
substituting a₆ = 43/12 and a₁ = 11/4 to determine d
43/12 = 11/4 + 5d
switch sides
11/4 + 5d = 43/12
subtract 11/4 from both sides
11/4 + 5d - 11/4 = 43/12 - 11/4
5d = 5/6
Divide both sides by 5
5d/5 = [5/6] / [5]
d = 1/6
as
a₁ = 11/4
d = 1/6
Therefore, the nth term of the Arithmetic sequence will be:
[tex]a_n=a_1+\left(n-1\right)d[/tex]
substituting d = 1/6 and a₁ = 11/4
aₙ = 11/4 + (n-1) × 1/6
= 11/4 + 1/6n - 1/6
= 31/12 + 1/6n
Therefore, we conclude that the rule will be:
aₙ = 31/12 + 1/6n
Determine the zeros of the function f(x) = (x - 2)(x + 2)(x+1)^2
Answer:
x=2, x=-2, and x=-1
Step-by-step explanation:
Function: f(x)=(x-2)(x+2)(x+1)²
We can solve each one of the zeros by making the expressions (the ones in the parentheseis) equal zero.
So we have three equations:
1.(x-2)=0
2.(x+2)=0
3.(x+1)²=0
Solve.
1.x-2=0
x=2
2. x+2=0
x=-2
3. (x+1)²=(x+1)(x+1)=0
(x+1)=0
x=-1
(x+1)=0
x=-1
Since those two were the same we can just say x=-1 once.
Here are the three zeros:
x=2, x=-2, and x=-1
hope this helps!
triangles abc, dbe, and fbg are all symmetric about the y-axis. what are the coordinates of the centroid?
please help
Answer:
The coordinates of the centroid are (0, 5)
Step-by-step explanation:
The coordinates of the centroid of a triangle whose vertices (x1, y1), (x2, y2), and (x3, y3) are ([tex]\frac{x1+x2+x3}{3}[/tex] , [tex]\frac{y1+y2+y3}{3}[/tex])
In Δ ABC
∵ A = (-20, 0), B = (0, 15), C = (20, 0)
∴ x1 = -20, x2 = 0, x3 = 20
∴ y1 = 0, y2 = 15, y3 = 0
∴ The centroid = ([tex]\frac{-20+0+20}{3}[/tex] , [tex]\frac{0+15+0}{3}[/tex]) = ([tex]\frac{0}{3}[/tex] , [tex]\frac{15}{3}[/tex]) = (0, 5)
∴ The coordinates of the centroid of Δ ABC are (0, 5)
In Δ DBE
∵ D = (-15, 0), B = (0, 15), E = (15, 0)
∴ x1 = -15, x2 = 0, x3 = 15
∴ y1 = 0, y2 = 15, y3 = 0
∴ The centroid = ([tex]\frac{-15+0+15}{3}[/tex] , [tex]\frac{0+15+0}{3}[/tex]) = ([tex]\frac{0}{3}[/tex] , [tex]\frac{15}{3}[/tex]) = (0, 5)
∴ The coordinates of the centroid of Δ DBE are (0, 5)
In Δ FBG
∵ F = (-5, 0), B = (0, 15), G = (5, 0)
∴ x1 = -5, x2 = 0, x3 = 5
∴ y1 = 0, y2 = 15, y3 = 0
∴ The centroid = ([tex]\frac{-5+0+5}{3}[/tex] , [tex]\frac{0+15+0}{3}[/tex]) = ([tex]\frac{0}{3}[/tex] , [tex]\frac{15}{3}[/tex]) = (0, 5)
∴ The coordinates of the centroid of Δ FBG are (0, 5)
∵ The three triangles are symmetric about the y-axis
→ That means they have the same centroid and it lies on the y-axis
∴ The coordinates of the centroid are (0, 5)
Sandra walks 13 miles in 3 hours. At what unit rate does sandra walk
Answer:
4.25 mph i think
Step-by-step explanation:
4x 3 =12
1/4 x 4 = 1
12 + 1 = 13
Task Radioactive isotopes decay by emitting radiation. A scientist just received a sample of two different radioactive isotopes, tellurium-131 and neptunium-240. This equation can be used to determine 70), the number of grams of tellurium-131 that will remain in the sample after minutes. T() = 1000. 25 A. How many grams of tellurium-131 were in the sample the moment the scientist received it? Provide evidence to support your answer. B. How many grams of tellurium-131 will remain in the sample after one hour? Provide evidence to support your answer.
Answer:
Following are the solution to this question:
Step-by-step explanation:
[tex]\to tellurium-131\\\\ \to T(t) =1000 \times e^{\frac{\log(2)}{25}t}[/tex]
where t = in miles
In part A:
When scientists got t=0, therefore the tellurium quantity.
[tex]\to T(t) = 1000 \times e^{0}[/tex]
[tex]= 1000 \times 1 \\\\= 1000 \ grams[/tex]
In part B:
When 1 hours = 60 min
[tex]T(t) = 1000 \times e^{\frac{\log 2}{25} \times 60} \\\\[/tex]
[tex]= 1000 \times e^{\frac{\log 2}{5} \times 12}\\\\= 1000 \times e^{0.72247199}\\\\\= 1000 \times 2.05951803\\\\=2059.51803\\\\=2059.51 \ grams[/tex]
Task Radioactive isotopes decay by emitting radiation is that :
A) The tellurium-131 were in the sample the moment the scientist received are 1000 grams.
B)The grams of tellurium-131 will remain in the sample after one hour is 2059.51.
Given :
Tellurium-131T(t)=100*[tex]e^{log2/25} t[/tex]where t = in milesPart A:
When scientists got t=0,
t=1000*[tex]e^{o}[/tex]
t=1000*1
t=1000 grams
The tellurium-131 were in the sample the moment the scientist received are 1000 grams.
Part B:
The grams of tellurium-131 will remain in the sample after one hour is :
T(t)=1000*[tex]e^{log2/25} t[/tex]T(t)=1000*[tex]e^{0.7224}[/tex]T(t)=1000*2.059T(t)= 2059.51The grams of tellurium-131 will remain in the sample after one hour is 2059.51.
Know more about "isotopes":
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Given the formula, y = 3x + 4, enter the value of y in the text box below where the value of x is 2.
X
y = 3x + 4
(x, y)
0
Answer:
3x+4=3*2+4
3*2+4=6+4
6+4=10
10=10
It takes Paresh 4 hours to bike 26 miles. He plans to bike 7 hours tomorrow. If he bikes at the same rate, how far will Paresh bike in 7 hours?
Answer:
7x26
Step-by-step explanation:
How do I solve -7x+9=51
Sadie went shopping over the weekend and found a sweater that she liked that was regularly 3
$33. She used her 20% off coupon to save her some money. How much money will Sadie save
on the sweater? *
Select the correct answer from each drop down menu. City
A -10
City B -1
City C -20
City D -2
The city whose temperature is closest to 0C is _____ and the city whose temperature is farthest from 0C is ______
Answer:
b.c
Step-by-step explanation:
This is the second part of that question. What's the answer to this
Answer:
x = -22
Step-by-step explanation:
The given expression is :
-0.57x+0.27x = 6.6
We need to find the value of x.
x(-0.57+0.27) = 6.6
x(-0.3) = 6.6
[tex]x=\dfrac{6.6}{-0.3}\\\\x=-22[/tex]
So, the value of x is -22.
What is the slope of the line that passes through the points (-1, 4) and (2,6)? Use the slope
formula to find the slope.
Answer:
I THINK SLOPE 3
Step-by-step explanation: MY GUT TELLS ME SO...
Brainliest to CORRECT answer!
Which of the following is not an example of kinetic energy?
Group of answer choices
chemical energy
sound energy
radiant energy
electrical energy
Answer:
A
Step-by-step explanation:
Select all the points that are on the graph of the line:
2x + 4y=20
Answer:
B=10
Step-by-step explanation:
worked it out on a graph on the internet
Sydney placed 10 guppies in a fish tank she recorded the number of guppies in the tank
Answer:
[tex]g(n) = 10 * 3^{n}[/tex]
Step-by-step explanation:
Given
See attachment for table
Required
Determine the explicit formula for the table
First, we need to check if the guppies increases at arithmetic progression or geometry progression.
For arithmetic progression:
We calculate the common difference (d)
[tex]d = g(n) - g(n-1)[/tex]
Take n as 1
[tex]d = g(1) - g(1-1)[/tex]
[tex]d = g(1) - g(0)[/tex]
From the table:
[tex]g(1) = 30\ \&\ g(0) = 10[/tex]
[tex]d = 30 - 10[/tex]
[tex]d = 20[/tex]
Take n as 2
[tex]d = g(2) - g(1)[/tex]
From the table:
[tex]g(1) = 30\ \&\ g(2) = 90[/tex]
[tex]d = 90 - 30[/tex]
[tex]d = 60[/tex]
The two differences are not equal. So, this
For geometry progression:
We calculate the common ratio (r)
[tex]r = \frac{g(n)}{g(n-1)}[/tex]
Take n as 1
[tex]r = \frac{g(1)}{g(1-1)}[/tex]
[tex]r = \frac{g(1)}{g(0)}[/tex]
From the table:
[tex]g(1) = 30\ \&\ g(0) = 10[/tex]
[tex]r = \frac{30}{10}[/tex]
[tex]r = 3[/tex]
Take n as 2
[tex]r = \frac{g(2)}{g(1)}[/tex]
From the table:
[tex]g(1) = 30\ \&\ g(2) = 90[/tex]
[tex]r = \frac{90}{30}[/tex]
[tex]r = 3[/tex]
The two ratios are equal.
So, the next step is to calculate the explicit formula using n term of a geometric progression.
Because the progression starts from 0, we make use of the following formula
[tex]g(n) = g(0) * r^{n}[/tex]
Substitute values for g(0) and r
[tex]g(n) = 10 * 3^{n}[/tex]
Hence:
The explicit formula is: [tex]g(n) = 10 * 3^{n}[/tex]
Which linear equations have one solution? Check all that apply.
O 5x–1=3(r + 11)
O 4(r-2) + 4x = 8(x– 9)
O 4(r- 6) + 4 = 2(r-3)
O 2(r- 4) = 5(r- 3) + 3
O 2(- 1) + 3x = 5(r- 2) + 3
Find the sum of -1.5 +3.5 + 2
Answer:
4, see below :)
Step-by-step explanation:
We can rewrite the equation into:
3.5 + 2 - 1.5
First we add 3.5 and 2
3 and 2 are in the ones place so:
5, and then you added the .5
5.5
Then:
5.5 - 1.5
First we subtract the tenths place so:
.5 - .5 = 0
Then the ones:
5 - 1 = 4
Answer:
4 all i did was, i used a calculator
A satellite flies 55584 miles in
7.72 hours. How many miles has it flown in 23.19 hours?
Answer:
Miles flown in 23.19 hours = 166968 miles
Step-by-step explanation:
Given that:
A satellite flies 55584 miles in 7.72 hours
We will find the unit rate first,
Unit rate = [tex]\frac{55584}{7.72}[/tex]
Unit rate = 7200 miles per hour
Miles flown in 23.19 hours,
Miles flown = 7200 * 23.19
Miles flown = 166968 miles
Hence,
Miles flown in 23.19 hours = 166968 miles
Factor: 4y(3x+2)−2(3x+2)
Step-by-step explanation:
4y(3x+2)–2(3x+2)
(4y–2)(3x+2)
2(2y–1)(3x+2)
The Factor of given equation [tex]4y(3x+2)-2(3x+2)[/tex] is [tex](2y-1) (6x+4)[/tex] .
What is Factor ?Factor in an equation is something which is multiplied by something else or we can say that numbers or the variables that are multiplied together.
We have,
[tex]4y(3x+2)-2(3x+2)[/tex]
So, first simplify the expression,
[tex]12xy+8y -6x-4[/tex]
⇒ [tex]12xy-6x+8y-4[/tex]
⇒ [tex]6x(2y-1)+4(2y-1)[/tex]
From we can see that [tex](2y-1)[/tex] is common in both terms,
Therefore,
⇒ [tex](2y-1) (6x+4)[/tex]
So, [tex](2y-1) (6x+4)[/tex] is the factor of the given expression.
Hence, we can say that the Factor of given equation [tex]4y(3x+2)-2(3x+2)[/tex] is [tex](2y-1) (6x+4)[/tex] .
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Check all of the ordered pairs that satisfy the equation below.
A.
(21, )
B.
(7, 14)
C.
(21, 14)
D.
(42, 28)
E.
(14, 21)
F.
(28, 42)
Answer:
what is the y-coordinate for A?
Step-by-step explanation:
Please determine x.
Answer:
6
Step-by-step explanation:
C.
a
C.
If you save 1 paisa the today, 2 paisa the next
day, 4 paisa the succeeding day and so on. The
total savings in two weeks will be in Rs.
b. 183
c. 162.83
d. 164.85
22. The
a. 163
no
Answer:
Step-by-step explanation:
[tex]2^{14}[/tex] paisa =16,384 paisa
DE bisects BC. If BC = 5x-3 and CE= 2x+25 find the value of x
Answer:
x = 53
Step-by-step explanation:
The entire line is BC, the line DE bisects the line BC, meaning it cut the line in half. So CE is half of BC, so the equation for CE has to be multiplied by 2. Therefore:
5x - 3 = (2x + 25)2
multiply
5x - 3 = 4x + 50
ad 3 to both sides
5x = 4x + 53
subtract 4x from both sides
x = 53
Input into the equation to check:
5x - 3 = (2x + 25)2
5(53) - 3 = (2(53) + 25)2
265 - 3 = (106 + 25)2
262 = (131)2
262 = 262, it's correct :)
Answer:
Step-by-step explanation:
2. It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm
from a metal sheet. How many square metres of the sheet are required for the same
Answer:
It's required [tex]7.48\ m^2[/tex] of sheet for the tank
Step-by-step explanation:
Surface Area of a Cylinder
Given a right cylinder of base radius r and height h, the surface area is calculated as follows:
[tex]S=2\pi r^2+2\pi r h[/tex]
The cylindrical tank has a height of h=1 m and a base diameter of 140 cm. The radius is half the diameter, thus r=140/2 = 70 cm = 0.7 m. Substituting:
[tex]S=2\pi 0.7^2+2\pi (0.7)(1)[/tex]
[tex]S=2\pi 0.49+1.4\pi[/tex]
[tex]S=2.38\pi[/tex]
[tex]\boxed{S=7.48\ m^2}[/tex]
It's required [tex]7.48\ m^2[/tex] of sheet for the tank
In the figure at the right AB || XY, and m<1 = 120. Tell weather each statement is true or false with #8, 9, 10, 11, 12, 13, 14, 15, 16, and 17
Answer:
False
Step-by-step explanation:because it is.
pls answer asap no trolls!
Please look at picture
Answer:
This question is so bad but it is most likely 25% or 0. this has no context in the question
Step-by-step explanation:
44 kg of onions cost $308. How much would 30 kg cost?
Answer:
$210
Step-by-step explanation:
Cost of 44kg onions = $308
Cost of 1kg onion = [tex] \frac{308}{44} = 7[/tex]
Cost of 30kg onions = [tex]30 \times 7 = 210[/tex]
Which graph shows a proportional relationship between the number of hours of renting a jet ski and the total amount spent to rent the jet ski? (5 points)
a
A graph is shown. The values on the x axis are 0, 2, 4, 6, 8, 10. The values on the y axis are 0, 18, 36, 54, 72, and 90. Points are shown on ordered pairs 0, 0 and 2, 18 and 4, 36 and 6, 48 and 8, 56. These points are connected by a line. The label on the x axis is Number of Hours. The title on the y axis is Total Amount in dollars.
b
A graph is shown. The values on the x axis are 0, 2, 4, 6, 8, 10. The values on the y axis are 0, 18, 36, 54, 72, and 90. Points are shown on ordered pairs 0, 0 and 2, 18 and 4, 36 and 6, 56 and 8, 56. These points are connected by a line. The label on the x axis is Number of Hours. The title on the y axis is Total Amount in dollars.
c
A graph is shown. The values on the x axis are 0, 2, 4, 6, 8, 10. The values on the y axis are 0, 18, 36, 54, 72, and 90. Points are shown on ordered pairs 0, 0 and 2, 18 and 4, 18 and 6, 18 and 8, 18. These points are connected by a line. The label on the x axis is Number of Hours. The title on the y axis is Total Amount in dollars.
d
A graph is shown. The values on the x axis are 0, 2, 4, 6, 8, 10. The values on the y axis are 0, 18, 36, 54, 72, and 90. Points are shown on ordered pairs 0, 0 and 2, 18 and 4, 36 and 6, 54 and 8, 72. These points are connected by a line. The label on the x axis is Number of Hours. The title on the y axis is Total Amount in dollars.
Answer:
A
Step-by-step explanation:
need the answer please thank you!
Answer:c
Step-by-step explanation:
C
HELO ASAP ILL GIVE BRAINLIST
Answer:
Option C is correct
Step-by-step explanation:
Plz help answer my question my lattes question plz
Answer:
C
Step-by-step explanation: