. A sequence starts with 180, 120, …. If the sequence is arithmetic, create a recursive and explicit formula for the sequence. If the sequence is geometric, create a recursive and explicit formula for the sequence.
Answer:
Arithmetic Sequence
[tex]T_n = 240-60n[/tex] ---- Explicit
[tex]T_n = T_{n-1} - 60[/tex] --- Recursive
Geometric Sequence
[tex]T_n = 270* (\frac{2}{3})^n[/tex] ---- Explicit
[tex]T_n = T_{n-1} * \frac{2}{3}[/tex] ---- Recursive
Step-by-step explanation:
Given
[tex]180, 120,....[/tex]
(a) Assume it is an arithmetic sequence
The explicit formula is calculated using:
[tex]T_n = a + (n - 1)d[/tex]
Where
[tex]a = 180[/tex]
[tex]d = 120 - 180[/tex]
[tex]d = -60[/tex]
So, we have:
[tex]T_n = 180 + (n - 1)*-60[/tex]
[tex]T_n = 180 -60n + 60[/tex]
Rewrite
[tex]T_n = 180 + 60-60n[/tex]
[tex]T_n = 240-60n[/tex]
The recursive function is calculated using:
[tex]T_1 = 180[/tex]
[tex]T_2 = 120 = 180 - 60 = T_1 - 60[/tex]
[tex]T_3 = 60 = 120 - 60 = T_2 -60[/tex]
-
[tex]T_n = T_{n-1} - 60[/tex]
(b) Assume it is a geometric sequence
The explicit formula is calculated using:
[tex]T_n = ar^{n-1}[/tex]
Where
[tex]a = 180[/tex]
[tex]r = \frac{120}{180}[/tex]
[tex]r = \frac{2}{3}[/tex]
So, we have:
[tex]T_n = 180 * (\frac{2}{3})^{n-1}[/tex]
Split
[tex]T_n = 180 * (\frac{2}{3})^n \div (\frac{2}{3})^1[/tex]
[tex]T_n = 180 * (\frac{2}{3})^n \div (\frac{2}{3})[/tex]
Rewrite as:
[tex]T_n = 180 * (\frac{2}{3})^n * (\frac{3}{2})[/tex]
[tex]T_n = 180 * (\frac{3}{2})* (\frac{2}{3})^n[/tex]
[tex]T_n = 180 * \frac{3}{2}* (\frac{2}{3})^n[/tex]
[tex]T_n = 90 * 3* (\frac{2}{3})^n[/tex]
[tex]T_n = 270* (\frac{2}{3})^n[/tex]
The recursive function is calculated using:
[tex]T_1 = 180[/tex]
[tex]T_2 = 120 = 180 * \frac{2}{3} = T_1 * \frac{2}{3}[/tex]
[tex]T_3 = 80 = 120 * \frac{2}{3} = T_2 * \frac{2}{3}[/tex]
-
[tex]T_n = T_{n-1} * \frac{2}{3}[/tex]
suppose you want to pave the driveway below and blacktop costs $28 per square yard. how much would you spend to cover the driveway?
Answer:
$2576
Step-by-step explanation:
You need to get the areas of the squares, the little square the area is 8 yd since you multiply 4 times 2. The big rectangle we need our length times our width we get our width by subtracting 4 from 10 which means w=6, then we need our length, for that we add 12 and then 2 to account for the rest which means l=14, we multiply 14 times 6 which gives you 84 and add the area of the little square (8) so 84 plus 8= 92 multiply that times the cost per yard so (92)(28) and you get $2576
2.5 dividido en 45.5
Answer:
18.2
Step-by-step explanation:
45.5/2.5 = 18.2
which expression below has a value in between 0 and 1?
a) 5(^-2)*1
b) (3^2)^3
c) 1/2*2^3
3(^-2)*3^3
BRAINLEST TO THE PERSON WHO CAN ANSWER BOTH !
Answer:
Question 7: False, False, true
Question 8: B
Step-by-step explanation:
10
05
15
20
25
60
30
35
40
55
45
50
Which of the following represents the Inter-Quartile Range of data?
A. 26
B. 50
C. 56
D. 10
E. 16
The value that represents the Inter-Quartile Range of data is 26.
Option A is the correct answer.
What is the interquartile range?An interquartile range is a measure of the difference between the upper and lower quartiles of a dataset.
W can find the values of the upper and lower quartile and median from a box plot.
The middle line is the median and the first line is the lower quartile and the last line is the upper quartile.
The formula used is Upper quartile - Lower quartile.
We have,
From the boxplot, we can see that,
Third quartile = 46
First quartile = 20
Now,
Interquartile range
= Third quartile - First quartile
= 46 - 20
= 26
Thus,
The value that represents the Inter-Quartile Range of data is 26.
Learn more about the interquartile range here:
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It takes Jada 20 minutes to walk to school. It takes Andre 80% as long to walk to
school.
How long does it take Andre to walk to school?
Answer:
16
Step-by-step explanation:
The length of the hypotenuse of a 30°-60°-90° triangle is 11. What is the perimeter?
O
A. 11 33
- + 3
2 2
B. 33 11
+
2 2
C. 11 + 33 3
D. 33 + 11 5
Answer:
B
Step-by-step explanation:
Using pythagoras theorem
PLease answer!!! 30 points!!!
Answer:
a
Step-by-step explanation:
They make a right angle. A right angle adds up to 90.
Answer:
C.Step-by-step explanation:
Hopes this helps. Mark as brainlest plz!Which is equivalent to 3 X 3 X 3 X 3 X 3 A 3x5 B 3^3 C 5^3 D 3^5
Answer:
2x+5x-6
Step-by-step explanation:
Debbie has at most $60 to spend on clothes. She wants to buy a pair of jeans for $22 and the rest on t-shirts. Write an inequality that represents the relationship between the amount of money Debbie has and how much she can spend on t-shirts.
Answer:
22+8x less then or equal to 60
Step-by-step explanation:
Debbie has at most $60 to spend
Then it will be <=60
Now she has to spend 22 dollars on jeans so 22 will be add to the initial amount for sure.
And
Let x be the number of t-shirts
Then the cost of x t-shirts will be 8x
Putting this in to inequality will be:
The inequality to find the maximum number of t-shirts is:
Which angles are vertical angles?
Answer:
It would be Angles GFC and EFH.
Think of it like I'm drawing a capital X. Would you consider the top and bottom parts of the X to be the same? Or would you consider the top and left parts to be the same?
The correct answer for this would be that the top and bottom parts of X are the same size. Now, remember that whenever two lines are making an X. this is because the two angles only touch each other in the center point and don't share a side.
Find the interquartile range (IQR) of the data in the dot plot below. goals luis's lacrosse
Answer:
3.5
Step-by-step explanation:
The interquartile range is the difference between the third and first quartile
IQR = Q3 - Q1
From the dot plot given :
The data, X could be culled :
X = 43, 44, 44, 44, 45, 45, 47, 48, 48
n = 9
Q3 = 3/4(n + 1)th term
Q3 = 3/4(10) = 7.5th term = (47 + 48) / 2 = 47.5
Q1 = 1/4(n + 1)th term
Q1 = 1/4(10) = 2.5th term = (44 + 44) / 2 = 44
Q3 - Q1 = 47.5 - 44 = 3.5
Answer:
3.5
Step-by-step explanation:
smart
Rosa says 4x and -6x are like terms, so they can be combined. Tiffany says 5a and 5b are like terms, so they can be combined. Is Rosa correct? Is Tiffany correct? Why or why not?
please help =)
Answer:
Rosa is correct, it's the variable that determines if something has like terms, not the coefficients.
Step-by-step explanation:
A cylinder has a base radius of 3m and a height of 17m. What is its volume in cubic m, to the nearest tenths place?
Answer:
V= 480.7 m cubed
The volume of the cylinder nearest to tenths place is 480 m^3.
What is cylinder?A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface.
For the given situation,
The formula for volume of the cylinder is [tex]V=\pi r^{2} h[/tex]
Radius of the cylinder,r = 3 m
Height of the cylinder, h = 17 m
The value of π = 3.14
On substituting the above values,
[tex]V=(3.14) (3^{2})(17)[/tex]
⇒ [tex]V=480.42[/tex] ≈ 480
Hence we can conclude that the volume of the cylinder is 480 m^3.
Learn more about volume of cylinders here
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Adam wants to buy a new computer that costs $510. He earns $8.50 per hour working for his aunt. Enter an equation using the variable x that can be used to solve for the number of hours Adam must work to buy
the computer.
Pls help
Answer:
x = number of hours to work
x = 510/8.5
x = 60 hours
Step-by-step explanation:
A color wheel is divided into 6 equal pieces. Select all of the true statements about the pieces of the color wheelA color wheel is divided into 6 equal pieces. Select all of the true statements about the pieces of the color wheel
Answer:
sidekick egocentric Jayco
Read the excerpt from Martin Luther King Jr.’s "I Have a Dream” speech.
We can never be satisfied as long as the Negro is the victim of the unspeakable horrors of police brutality. We can never be satisfied as long as our bodies, heavy with the fatigue of travel, cannot gain lodging in the motels of the highways and the hotels of the cities. We cannot be satisfied as long as the Negro's basic mobility is from a smaller ghetto to a larger one.
Why does King repeat the phrase "we can never be satisfied”? Select 3 options.
to inspire listeners
to demand action
to explain racial differences
to show negativity
to rally emotional support
to accept current treatment
PLZZ HELP I HAVE A TIMER
Answer:
1. To Inspire Listeners
2. To Demand Action
5. To Rally Emotional Support
Step-by-step explanation:
I just took the test:)
Calculate the population
data set;
mean for the following
40, 50, 55, 78,58,60,73, 35, 43, 48.
Answer:
I think it’s 11.8
Step-by-step explanation:
What is sec 0 when cot 0 = -4V2? 0 (1,0) [?] [ ] Rationalize the denominator if necessary. sec 0 =
Answer:
[tex]Sec~ 0=\frac{\sqrt{66} }{8}[/tex]
Step-by-step explanation:
[tex]Cot~0=-4\sqrt{2}[/tex]
[tex]Sec~0=\sqrt{33}/4\sqrt{2}[/tex]
[tex]=\sqrt{33}/4\sqrt{2} *4\sqrt{2} /4\sqrt{2}[/tex]
[tex]=4\sqrt{66} /32[/tex]
[tex]= \sqrt{66}/8[/tex]
᪥༄᪥༄᪥༄᪥༄᪥༄᪥༄
hope it helps...
have a great day!!!
How to find the central angle
Answer:
x = 50
Step-by-step explanation:
Note that the 3 interior angles must sum up to 180 degrees:
50 + x + 80 =180, or
50 + x = 100, or
x = 50
Find the magnitude and directon of F +ū.
Answer:
Step-by-step explanation:
The only time the word 'incorrectly' isn't spelled incorrectly is when it's spelled incorrectly. (⊙_ ⊙)
ahaha good one
Step-by-step explanation:
...........
Q7. What would be the best next step in solving the following equation for x?
8x - 4 = 10
Answer:
The next step would be adding -4 to the other side since it would cancel out -4
Step-by-step explanation:
What is the slope of a line parallel to the line whose equation is 15x+9y=-16215x+9y=−162. Fully simplify your answer.
Answer:
-5/3
Step-by-step explanation:
Any line parallel to the given line will have the same slope as the given equation;
Given the equation 15x+9y=-162
Rewrite in standard from y = mx+b
15x+9y=-162
9y = -15x - 162
y = -15/9 x - 162/9
y = -5/3 x - 18
This gives the required equation;
Since mx = -5/3 x
m = -5/3
Hence the slope of the line parallel to the given line is -5/3
Which table has a constant of proportionality between y and x of 12?
Will give brainliest if correct
Answer:
Table A
Step-by-step explanation:
If you do delta method (Change in y and x)
For example, 120-24
______ = 96/8
10-2
Then you divide both the numerator and denominator by the denominator (which is 8) and that gets us to 12 as our answer. Do the same method for all of the numbers in table A.
Ps: I hope that I was helpful, and you are welcome.
I AM GIVING OUT BRAINLIST
Step-by-step explanation:
18.706 → 19
18.706 → 18.71
18.706 = 19
18.706 = 18.71
Help please with this math ;-; I beg of you
Answer:
49 - 9π
Step-by-step explanation:
Area of white portion = area of triangle - area of circle
To find the area of the triangle:
The area of a triangle can be calculated using this formula
[tex]A=\frac{bh}{2}[/tex] where b = base length and h = height
The height given is 7m and the base length given is 14m
That being said we plug in the given values into the formula
[tex]\frac{14*7}{2} \\14*7=98\\\frac{98}{2} =49[/tex]
Hence, the area of the triangle is 49 sq meters.
To find the area of circle
( note that the area is in terms of pi; shown by the answer choices. )
Formula for area of a circle = [tex]A=\pi r^2[/tex]
We are given the diameter ( 6m )
However, we need the radius
To convert diameter to radius we divide by 2
6/2 = 3 so the radius = 3m
Now we plug in 3 into the formula
[tex]A=\pi 3^2\\3^2=9\\A=9\pi[/tex]
Remember we do not apply pi because the answer should be in terms of pi.
Now we subtract the two
Area of white portion = 49 - 9π
Hence, the answer is A
Answer:
49 - 9π
Step-by-step explanation:
Hope this helps
Find the area of a circle with diameter 8 in.
Use the value 3.14 for n, and do not round your answer.
Be sure to include the correct unit in your answer.
Answer:
Step-by-step explanation:
50.27 should be the area of a circle that has a radius of 4 in.
Which equation matches the graph?
f( x) = x3 + 2
f( x) = ( x + 2) 3
f( x) = ( x - 2) 3
f( x) = x3 – 2
f( x) = x3
Answer:
D. f(x) = x³ - 2Step-by-step explanation:
The graph is the translation of the parent function 2 units down.
The parent function is f(x) = x³.
The translation is f(x) - 2
The function is:
f(x) = x³ - 2Correct choice is D
Answer:
Option D
Step-by-step explanation:
The parent function is y=x³
y=x³Translate 2 units down
y=x³-2This is showing on graph
Option D is correct