Answer:
The 10th term of the sequence is:
[tex]a_{10}=\frac{1}{27}[/tex]Step-by-step explanation:
Given the number
729, 243, 81, 27...
A geometric sequence has a constant ratio 'r' and is defined by
[tex]a_n=a_0\cdot r^{n-1}[/tex]
Computing the ratio of all the adjacent terms
[tex]\frac{243}{729}=\frac{1}{3},\:\quad \frac{81}{243}=\frac{1}{3},\:\quad \frac{27}{81}=\frac{1}{3}[/tex]
The ratio of all the adjacent terms is the same and equal to
[tex]r=\frac{1}{3}[/tex]
also
[tex]a_1=729[/tex]
Therefore, the nth term is computed by:
[tex]a_n=729\left(\frac{1}{3}\right)^{n-1}[/tex]
Putting n = 10 to find the 10th term
[tex]a_{10}=729\left(\frac{1}{3}\right)^{10-1}[/tex]
[tex]=729\cdot \frac{1}{3^9}[/tex]
[tex]=\frac{1\cdot \:729}{3^9}[/tex]
[tex]=\frac{729}{3^9}[/tex]
[tex]=\frac{3^6}{3^9}[/tex]
[tex]=\frac{1}{3^3}[/tex]
[tex]a_{10}=\frac{1}{27}[/tex]
Therefore, the 10th term of the sequence is:
[tex]a_{10}=\frac{1}{27}[/tex]
Marcel is purchase a boad to build a bookcase he wants to divide the board into 1.75-foot sections he needs 6 sections what size board dose marcel need.
Answer: 10.5 feet
Step-by-step explanation:
From the question, we are informed that Marcel is purchasing a board to build a bookcase he wants to divide the board into 1.75-foot sections and that he needs 6 sections.
The size of the board that Marcel need will be calculated by multiplying 6 by 1.75 foot. This will be:
= 6 × 1.75
= 10.5 feet
What is the slope of the line 4x - 8y = 16 ?*
Step-by-step explanation:
4x - 8y = 16
8y = 4x - 16
y = 0.5x - 2
Hence the slope is 0.5.
Answer:
1/2
Step-by-step explanation:
Slope from a standard form equation is [tex]-\frac{A}{B}[/tex].
A is 4 and B is -8.
[tex]-\frac{A}{B}=\frac{-4}{-8}= \boxed{\frac{1}{2}}[/tex]
Hope this helps.
There is a proportional relationship between minutes and dollars per minute, shown on a graph of printing expenses. The graph passes through the point (1, 4.90). What is the slope of the graph? What is the unit rate? Complete the explanation. plz help 100 points and brainliest.
Answer:
if the graph of a proportional relationship passes through the point (1 , R) then r equals the slope and the unit rate , which is $4.75 per min
Step-by-step explanation:
write the equation
i’ll give a BRAINIST & 20 POINTS:)
Answer:
y=5/2x-16
Step-by-step explanation:
First, we want to find the slope of the original line.
m= -4+8/-1-9
m= 4/-10
m= -2/5
Because we want the perpendicular bisector, we will need the slope to be the opposite reciprocal. Therefore, our slope is
m=5/2
Now, we want to find the midpoint of the line.
9-1/2
8/2=4
-8-4/2
-12/2= -6
So, the midpoint is (4,-6)
Using the information we have, we now can find b.
-6=5/2(4)+b
-6=10+b
-16=b
That gives us our equation
y=5/2x-16
an underground mine elevator descends 12% of the total depth every minute. the total depth of the elevator is 75 meters below the ground. How many meters below the ground is the elevator after 2 mins
a. -18 meters
b. -9 meters
c. -4.5 meters
d. -22.5
Can anyone simplify
6c+2c+4
Answer:
Sure!: 8c + 4
Step-by-step explanation:
Collect Like Terms: (6c+2c)+4
Simplify: 8c + 4 (You add 6c and 2c, then just keep 4.)
Brainliest Please!!?!!!!!!!!!
- ElizabethKate
ANSWER ASAP!!! Which table correctly lists the reasons to prove <1 = <3, given that AB intersects CD?
Answer: B
Step-by-step explanation:
Took the test
First table correctly list the reasons.
Given from fig two lines intersect each other and form angles as shown in fig.
Now we have to prove angle 1 equals to angle 3.
From table first all the step by step statement and reasons are correct but in table second 4th statement is correct but its reason is wrong. similarly in 3rd table 5th statement is correct but its reason is wrong.
So we can say now first table is correctly list the reasons to prove angle 1 equals to angle 2.
For more details on Transitive property follow the link below:
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Easy 6th grade math
Answer:
18 in
Step-by-step explanation:
Answer:
18 in
Step-by-step explanation:
1 ft = 12 in
Hioe this helps. Pls give brainliest.
1)a bike costs $200 but is reduced by 35% in a sale.How much is the bike reduced by?What does it cost in the sale?
Answer:
The amount of discount $70
New price $130
Step-by-step explanation:
To find how much 35% of 200 is, we multiply 200 with 35 then divide it with 100
200 × 35 ÷ 100 = 70 the bike's price is reduced by 70$ and the new price
20ü - 70 = 170$
The difference between two num-
bers is 24. What are the numbers
if their sum is 78?
(Please help me!)
Answer:
51 and -27
Step-by-step explanation:
The sum of two numbers is 24 and their difference is 78. What are the two numbers? Let's start by calling the two numbers we are looking for x and y.
The sum of x and y is 24. In other words, x plus y equals 24 and can be written as equation A:
x + y = 24
The difference between x and y is 78. In other words, x minus y equals 78 and can be written as equation B:
x - y = 78
Now solve equation B for x to get the revised equation B:
x - y = 78
x = 78 + y
Then substitute x in equation A from the revised equation B and then solve for y:
x + y = 24
78 + y + y = 24
78 + 2y = 24
2y = -54
y = -27
Now we know y is -27. Which means that we can substitute y for -27 in equation A and solve for x:
x + y = 24
x + -27 = 24
X = 51
Summary: The sum of two numbers is 24 and their difference is 78. What are the two numbers? Answer: 51 and -27 as proven here:
Sum: 51 + -27 = 24
Difference: 51 - -27 = 78
Answer:
The numbers are 27 and 51
Explanation
x - y = 24
x + y = 78
Add together the equations
2x = 102
x = 51
Put into equation
51 - y = 24
27 = y
On Wednesday at camp, Melissa went for a hike at 6:30 A.M. The hike took 2 hours and 55 minutes. As soon as she got back from the hike, Melissa played volleyball for 1 hour. What time did Melissa finish playing volleyball
Answer:
10:25 AM
Step-by-step explanation:
Solving the question above, we are total that:
On Wednesday at camp, Melissa went for a hike at 6:30 A.M. The hike took 2 hours and 55 minutes. As soon as she got back from the hike, Melissa played volleyball for 1 hour.
The time that Melissa finished playing volleyball is calculated as:
6:30AM + 2 hours 55 minutes + 1 hour
= 6:30 am + 3 hours 55 minutes
= 9:85 minutes
60 minutes = 1 hour
85 minutes = 1 hour 25 minutes
= 10:25 AM
Hence: Melissa would finish playing volleyball at 10:25 AM
HURRY PLSS
the cost for 5 members to join a chess club is 125. The cost includes a clock and a chessboard. If each clock cost 10 dollars what is the cost of each chessboard use the equation 5[x+10]=125
15
23
25
35
Answer:
The answer is 15
Step-by-step explanation:
125/5=25
25-10=15
An= 5[15+10]=125
2x + 3y = 10
4x - y = -1
Solve the simultaneous equation.
x=__
y=__
The value of x = 1/2 , y = 3 of the simultaneous equation.
What are simultaneous equation ?"Simultaneous Equation is an essential Chapter in the Algebra branch of Mathematics. There are times when you come across two or more unknown quantities and two or more equations relating to them. These are called Simultaneous Equations. When you are asked to solve such equations, you must find values of the unknowns which satisfy all the given equations at the same time. They are Simultaneous Equations because the equations are solved at the same time. Simultaneous Equations need algebraic skills to find the values of letters within two or more equations."
Given, The equations
[tex]2x + 3y = 10[/tex] ----------- eq 1
[tex]4x - y = -1[/tex] ------------ eq 2
multiplying eq 1 by 2
[tex]4x + 6y = 20[/tex] ----------- eq 3
now subtracting eq 3 from eq 2
we get, [tex]7y = 21[/tex]
y = 3 and x = 1/2
Hence, the values of x and y = 1/2, 3 respectively.
To know more about Simultaneous Equation here
https://brainly.com/question/16763389
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Find the sum of the integers from -6 to 57
A. 1,500
B. 1,621
C. 1,734
D. 1,512
Answer: it D. 1,512
Step-by-step explanation: i hop this helps if it wrong sorry about that
Can anyone show me how to solve this problem? I know that its 5 weeks. (The problem is “Ahmed is saving his money to buy a Ipad that costs $319.50. Right now he has $21.95, and can save $63.00 each week. How many weeks will it take for Ahmed to have enough money to buy the Ipad)
Answer:
5 weeks
Step-by-step explanation:
Substract 319.5 (the amount he has to save) to the amount he has already saved, which is 21.95. Now the constant amount of change is 63 dollars each week so divided it by that. So the equation should be (319.5-21.95) and divide all that by 63 to get 4.72 or rounded to the nearest number, is 5.
What is the gradient of the straight line 2y = -3x - 8 ?
Answer:
- [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope (gradient) and c the y- intercept )
Given
2y = - 3x - 8 ( divide all terms by 2 )
y = - [tex]\frac{3}{2}[/tex] x - 4 ← in slope- intercept form
with gradient = - [tex]\frac{3}{2}[/tex]
The gradient of the straight line 2y = -3x - 8 will be -1.5.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.
The slope(gradient) 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that the equation of the line is, 2y = -3x - 8
Rearrange the equation in the standard form of the equation as
2y = -3x - 8
y=-3/2 x-8/2
y= -1.5x - 4
Compare the obtained equation with the standard equation,y=mx+b. Where m is the gradient of the straight line.
m= -1.5
Thus, the gradient of the straight line 2y = -3x - 8 will be -1.5.
Learn more about the straight line here:
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Which list shows only multiples of 8?2, 4, 8
24, 32, 40
32, 96, 108
34, 42, 50
Answer:
24,32,40
Step-by-step explanation:
Answer:
24,32,40
Step-by-step explanation:
hope im right!
Compare the process of solving
|x - 11 + 1 < 15 to that of solving
|x - 11 + 1 > 15.
Answer:
I have solved them but I don't know what to o next
Step-by-step explanation:
1) lx- 11+ 1< 15
+11 on both sides
lx+ 1< 26
-1 on both sides
lx< 25
2) lx-11+1>15
+11 on both sides
lx+1>26
-1 on both sides
lx> 25
Answer:
Both absolute values would need to be isolated first.
You would need to write a compound inequality for each.
Both compound inequalities would compare
x – 1 to –15 and 15.
The inequality with “<” would use an “and” statement, while the “>” would use an “or” statement.
Step-by-step explanation:
What is the difference between 2 2/3 - 1 2/3
Answer:
1
Step-by-step explanation:
Subtract
Since they have the same denominator you can subtraact normally
so 2 2/3- 1 2/3
That would be 1
A company collected $7,800 by selling shoes. The company had $6,084 left after paying the tax. What was the percentage of tax?
Answer:
22%
Step-by-step explanation:
The percentage of tax can be found by calculating the percent change.
new - old / old
6084 - 7800 / 7800
= -0.22 or -22%
This means the price decreased by 22%, meaning you paid 22% in taxes.
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18x^3 divided by 2x^2
the answer to this question is 9x
50 points!!!!!!!
Jeremy has heard a lot of people in the club talking about tackling a 950-foot rock formation. Jeremy has set a limit that they won’t climb anything that takes longer than 7 hours, so they have enough time to travel to and from the place. Will it be possible to climb a 950-foot rock formation within Jeremy’s time constraint? Explain why or why not.
Answer:
Depends on how fast they climb. If we knew how fast they climb then we can tell, but without knowing how fast they climb we can't tell.
Step-by-step explanation:
The total cost of renting a movie for different numbers of days is shown in the table.
Which equation was used to create this table?
Movie Rentals
Total Cost,
Number of Days, d
(in dollars)
1
3
2
4
5
7
2
10
12
C = 20
d = 20
C = 2 +
d = 2 +
Answer:C
Step-by-step explanation:
Can anyone help? Tysm!
Answer:
c
Step-by-step explanation:
.
Answer:
C) 44
Step-by-step explanation:
The team won 22 games. 22 is supposedly 50% or half of them. Half plus half is whole. If 22 is half, then we do 22 + 22 to find the total number of games played by the team. 22 + 22 is 44.
Hope it helps!
Answer correctly please !!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!!!
Answer:113
Step-by-step explanation:
I’m not really sure but the exterior angle lies on a straight line meaning that it has to amount to 180 degrees. 67 + x =180 so x = 180-67 which is 113. But I’m not entirely sure bout this.
Step-by-step explanation:
67-180=113
x=113
and the third corner =15 degrees
Richard measured the auditorium and made a scale drawing. The scale of the
drawing was 0.5 inch : 4 feet. If the stage is 11 inches in the drawing, how
long is the actual stage?
Answer:
oml yall really on here
Step-by-step explanation:ion know do you homework
help pleasee and show workk!!!!!!!
Answer:
WAP MOMENTYSHEHWJWUE
Last month, you joined an online strategy game. When you joined, there were
25 members. This month, there are 47 members. What is the percent change in
the number of members from last month to this month? *
answers fast please
Answer:
its 24
Step-by-step explanation:
you count all the way up to 47 from 25
Answer:
46.8
Step-by-step explanation:
formula is change/ original x 100
!!!!URGENT!!!!
Ivan's gas tank is 1/4 full. After he buys 10 gallons of gas, it is 2/3 full. How many gallons can Ivan's tank hold?
Answer:
How many gallons can Ivan's tank hold? 24
What is the slope of -8,0 and -3, 15 please explain to me
Answer:
m=3
Step-by-step explanation:
rise/run or y/x
using the y coords/x coords
15-0/-3-(-8)
=15/-3+8
=15/5
=3