Answer:
The 9th term of the sequence is:
[tex]a_9=\frac{65536}{6561}[/tex]Step-by-step explanation:
Given the sequence
1, 4/3,16/9
computing the ratios of all the adjacent terms
[tex]\frac{\frac{4}{3}}{1}=\frac{4}{3},\:\quad \frac{\frac{16}{9}}{\frac{4}{3}}=\frac{4}{3}[/tex]
The difference between all the adjacent terms is the same and equal to
[tex]r=\frac{4}{3}[/tex]
A geometric sequence has a constant ratio 'r' and is defined by
[tex]a_n=a_1\cdot r^{n-1}[/tex]
As
[tex]a_1=1[/tex][tex]r=\frac{4}{3}[/tex]so substituting [tex]a_1=1[/tex] and [tex]r=\frac{4}{3}[/tex] in the nth term of the equation
[tex]a_n=a_1\cdot r^{n-1}[/tex]
[tex]a_n=\left(\frac{4}{3}\right)^{n-1}[/tex]
Now, substitute n = 9 to determine the 9th term
[tex]a_9=\left(\frac{4}{3}\right)^{9-1}[/tex]
[tex]a_9=\left(\frac{4}{3}\right)^8[/tex]
[tex]a_9=\frac{4^8}{3^8}[/tex]
[tex]a_9=\frac{65536}{6561}[/tex]
Therefore, the 9th term of the sequence is:
[tex]a_9=\frac{65536}{6561}[/tex]A box of a dozen fruit tarts costs $15. How much money does 1 fruit tart cost?
1 dozen = 12 so 15/12 is 1.25
which means 1 fruit tart is $1.25
Find the Circumference of the circle.
30 points for whoever answers this
Answer:
87.92
Step-by-step explanation:
(2)(3.14)=6.28
(6.28)(14)=87.92
2(pi)(r)
complete the equation of the line through (-8,-2) and (-4,6). use exact numbers. We need to find out what y=?
Answer:y = 2x + 14
Step-by-step explanation:
First, you have to find the slope by using
In other words,
The slope is 2.
Then you plug the rest into point-slope form (you can use either of the points, I used the first one)
Remember that m is the slope.
Distribute the slope to the par
Step-by-step explanation: first you do this then that then this then that then this
A fish is 12 Meters below the surface of the ocean. what is it's evelation
Help
Which one is for 1,2 ,and 3
A carpenter sands 1/2 of a dresser in 3/4 hour ,how long does it take the carpenter to sand 1 dresser
Answer:
1.5 hours = 1 hour 30 mins
Step-by-step explanation:
3/4 = 0.75
0.75 x 2 = 1.5
Evaluate - 3x + 2y when x = 2 and y = 3
Answer:
the answer is 0
Step-by-step explanation:
Answer:
0
Step-by-step explanation:
-3x + 2y
-3(2) + 2(3) ## Substitution
-6 + 6 ## Distributive
0 ## Addition
find the linear relationships
Answer:
everytime the x goes up by 3, the y goes down by 3
Step-by-step explanation:
this is the question
Answer:(1,1)
Step-by-step explanation:
Its asking where both linear and curve lines are being hit,
(fxg)(0)= 1,1
Which of these is the standard form of the following function?
f(x) = -9(x + 5)2 + 4
f(x) = 9x2 − 90x − 221
f(x) = -9x2 − 90x − 221
f(x) = 9x2 − 180x + 221
f(x) = -9x2 − 180x − 221
Answer:
the answer is B) -9x2 -90x -221
-7n=35
what does n equal and show your steps and ur solution plz thx
reply or answer asap
Answer:
n = - 5
Step-by-step explanation:
The expression is given as ;
-7n = 35
Divide both sides by -7
-7n/-7 = 35/-7
n= -5
The value of n is -5
Allie bought some DVDs for $14.99 each. Which expression below represents Allie’s cost for d DVDs? A. 14.99 + d B. 14.99 + 14.99d C. 14.99 ÷ d D. 14.99d
Answer:
D. 14.99d
Step-by-step explanation:
d represents the number of DVD's she purchased, and 14.99 was the cost for each DVD. Answer D is multiplying the variable d and the coefficient 14.99. When multiplying variables, there is no need to place a multiplication sign.
Answer:
C. 14.99 divided by d
Step-by-step explanation:
the answer is c because you don't know how many DVDs he bought so by dividing the answer you can then know the price of each DVD they bought.
How do I find the rule of a linear table ?
Answer:
start by checking that it's a linear relationship that's occurring by having a look at the difference in our X in each step against the difference in our Y in each step.
Step-by-step explanation:
bro 8.1 • 10-8 is greater than 9.2
Answer:
Your statement is true
Step-by-step explanation:
:|
CAN YOU PLSSSSSSSSSSSSSSSSSSS HELP ME WITH THIS
There are 15 students not going on the field trip. That is 6% of all
of the 6th graders, How many 6th graders are there?
Answer:
250
Step-by-step explanation:
15=6%
?=1%
15/6=2.5
2.5=1%
1%=1/100
2.5 x 100=
250
What is the answer to this question?
Answer:
Step-by-step explanation:
X=-6
Step-by-step explanation:
x= -6
......................
3.(06.01)
What is the value of the expression 5^2 +2^2? (2 points)
Answer:
29
Step-by-step explanation:
5^2=25
2^2=4
25+4=29
Answer: 29 is the final answer
Step-by-step explanation: Have a nice day - Lily ^_^
If anyone willing to help, I'll be glad :)
Answer:
22
Step-by-step explanation:
Since its a parallelogram, opposite sides are congruent. Therefore:
BC = AD
a - 1.5 = 20.5
+1.5 +1.5
a = 22
Answer:
a=22
Step-by-step explanation:
a-1. 5 =20. 5 ( opposite side of parallelogram are equal )
or, a=20. 5+1. 5
or, a=22
you can do it from another side too.
2a-20. 8 = a + 1. 2 ( opposite side of parallelogram are equal )
or, 2a - a = 1. 2 + 20. 8
or, a = 22
Hope it will help you ☺✌
Find the measure of each interior angle.
Answer:
d) m<J = 115, m<K = 130, m<M = 50, m<N = 65
Step-by-step explanation:
The sum of interior angles in this rectangle is equal to 360
if we add all the given angles 7x + 10 = 360 subtract 10 from both sides
7x = 350 divide both sides by 7
x = 50 to find the measure of each angle replace x with 50
Find the ratio (red to blue) of the perimeters of the similar triangles. Write your answer in simplest form.
Answer:
I think the answer is 9/2
Solve 3-4/7 with steps pls
In ASTU, S = 3.8 inches, t = 9.8 inches and u=9.6 inches. Find the measure of ZU to
the nearest 10th of a degree.
Answer: 75.8
Step-by-step explanation:
DO THESE ON A PIECE OF PAPER! PLEASE HELP! QUICK!!DO ALL OF THEM!!!
Answer:
i cant sseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
the picture
Answer:
Step-by-step explanation:
It will be a little slanted so i am sorry.
I am struggling with math right now this will help out a lot
Answer:
A car bought every 10 seconds? If that is even true
Step-by-step explanation:
I'm confused on this, so please help for 10 points.
Answer:
third one
Step-by-step explanation:
Answer: it would be the third option, (2/5)^4
Step-by-step explanation:
sure thing! so, when all of those fractions in parenthesis, it means they are all going to be multiplied. and, this gets easy! that third option means that all of them are getting multiplied 4 times, which is exactly what the original problem means. hope this helps!
Which expressions are equal to 4y + 8 + 4y + 8?
Answer:
8y + 16
Step-by-step explanation:
Put the like variables together
Your doctor told you to eat 25 25 grams of fiber each day. You had 4 4 grams of fiber for breakfast. What percent of the 25 25 grams of fiber have you eaten so far?
Answer: 16%
Step-by-step explanation:
Grams of fiber recommended by doctor = 25 grams
Grams of fiber had for breakfast = 4
Percentage of gram ate = Grams had for breakfast / Grams recommended by doctor × 100
= 4/25 × 100
= 4 × 4
= 16%
Answer: 16%
Step-by-step explanation:
A mine worker is in a tunnel 25 feet below the ground. He descends another 13 feet. What is his final position? i already know that part of the answer is -25 -
but is it -25 - 13 or -25 - -13
Answer: -25 - 13
This simplifies to -38
So the worker's final position is 38 feet below the ground.
A diagram is shown below.
==========================================================
Explanation:
Draw a vertical number line. Plot 0 on it to indicate the ground level, or surface level. Then plot -25 on it, which is below 0. This is 25 feet below the ground.
To move 13 further feet downward, we will subtract 13 from -25. Subtracting a positive means we move downward.
For example, start at the 30th of a building. This is marked as +30 or just 30 on the vertical number line. Subtract off 13 to go down 13 floors and we have 30-13 = 17. So after going down 13 floors, we're at the 17th floor now.
Going back to the problem at hand, we start at -25 and subtract off 13 to get the final answer -25 - 13
The answer is not -25 - -13 and it is not -25 - (-13). This is because the two negatives cancel to be a positive. So -25 - (-13) becomes -25+13. Here we're starting at -25 but then going up 13 feet. Instead we want to go down 13 feet.
------------------------------------
After we determine the expression is -25 - 13 we will effectively add the positive versions of those numbers like so
25+13 = 38
But the final answer is negative because we're starting underground and moving further underground.
We can write it like this
-25 - 13 = -(25+13) = -(38) = -38
Therefore, if the worker starts off 25 feet underground, and moves 13 feet downward, then the worker ends up 38 feet underground. Again, use the vertical number line to help see this.
Check out the diagram below.
Anyone know the correct answer?!
Answer: Lower-right corner [tex]3^7 \times \frac{1}{3^4}[/tex]
Explanation:
We use the rule that
[tex]a^{-b} = \frac{1}{a^b}[/tex]
The negative exponent tells us to apply the reciprocal if we want the exponent to be positive.
In this case, a = 3 and b = 4
So,
[tex]a^{-b} = \frac{1}{a^b}\\\\3^{-4} = \frac{1}{3^4}[/tex]
which is why overall,
[tex]3^7\times 3^{-4} = 3^7 \times \frac{1}{3^4}[/tex]