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]
whats 9- 3x=1+x
i need help
Answer:
9-2x=1
-2x=-8
x=4
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
x=2
Step-by-step explanation:
-3x-x=1-9
-4x=-8
x=-8/-4
x=2
plz mark as brainliest
LORD SOMEONE please help me!! ASAP I will give brainiest! Fr
the public school enrollment of a city is 13,500. Enrollment is declining at a rate of 4.5% per year. predict the enrollment in 5 years.
Answer:
16537.5
Step-by-step explanation:
4.5% of 13500 = 607.5
607.5 x 5 = 3037.5
3037.5 + 13500 = 16537.5
฿₤₦
I need help with my final!
Answer:
it is c
Step-by-step explanation:
Ronald is calculating the time required to fill the swimming pool at school. He found that it takes 11 minutes to fill the swimming pool with 99 gallons of water. At what rate does the swimming pool fill, in gallons per minute?
Answer:
[tex]11 \: minutes = 99 \: gallons \\ 1 \: minute = (\frac{1 \times 99}{11} ) \: gallons \\ = 9 \: gallos \: per \: minute[/tex]
What is the value for the lower quartile of the set?
Answer:
I believe its 4
Step-by-step explanation:
What is you favorite Fast Food restaurant and what do you like to get there?
(.Free .Points)
Please help me I do not have much time and pls no scam answers
please help me i will give brainliest
A 90 clockwise rotation and then a vertical reflection are applied to the scalene triangle. which figure represents the result of the transformation?(please help soon)
The figure that represent the rotation and reflection of the scalene triangle is given as follows:
Figure B.
What are the rotation rules?The five more known rotation rules are given as follows:
90° clockwise rotation: (x,y) -> (y,-x)90° counterclockwise rotation: (x,y) -> (-y,x)180° clockwise and counterclockwise rotation: (x, y) -> (-x,-y)270° clockwise rotation: (x,y) -> (-y,x)270° counterclockwise rotation: (x,y) -> (y,-x)A 90º clockwise rotation means that the scalene triangle is rotated right, and thus the figure would be given by option D.
After the vertical reflection, the orientation of the triangle would be changed, meaning that it would then be given by option B.
More can be learned about rotation rules at brainly.com/question/17042921
#SPJ1
will give brainiest if someone answers correctly
x=
Length=
Width=
According to question,
= 8x² + 6x - 2 = 228
= 8x² + 6x - 230 = 0
= 2(4x² + 3x - 115) = 0
= 2(4x² + 23x - 20x - 115) =0
= 2(x(4x +23) -5(x - 23) )= 0
= 2((x-5)(4x+23)) = 0
x = 5 , x = -23/4
let x = 5
so length 4x - 1
= 4 × 5 - 1
= 19 ft
width = 2x + 2
= 2 × 5 + 2
= 22 ft
_______
gosh! finally did it.. was too big -_-
Which expression represents these words?
7 more than the product of 9 and 8
Answer:
7 + (9 * 8)
Step-by-step explanation:
You don't need parenthesis unless it helps you understand.
The expression is represent as 7 + (9 x 8).
Here,
The condition is given as,
The expression is 7 more than the product of 9 and 8.
How to write an expression?
We write an expression by using numbers or variables and mathematical operators which are addition, subtraction, multiplication and division.
Now,
Product of 9 and 8 is written as 9 x 8.
Hence, 7 more than the product of 9 and 8 is written as;
⇒ 7 + (9 x 8)
The expression is represent as 7 + (9 x 8).
Learn more about to the write an expression visit:
https://brainly.in/question/17645770
#SPJ2
ITEMS
.
Paula purchased 8 erasers for $100.00. Calculate the cost of 12 erasers.
Answer:
$150
Step-by-step explanation:
100/8=12.5
12.5*12=150
maggie has a rectangular box with a length of 6 1/2 of 9 inches and hieght of 3 1/2 inches
what is the volume of the box
V = & x w x h
V = 6 1/2 x 9 x 3 1/2
V = 204 3/4
So answer is 204 3
4
NEED HELP ASAP
Find the approximate area of a triangle that has vertices at A(-4, 2), B(6, 4) and C(3,-1).
Answer:
I need more to the question so I can answer it
Step-by-step explanation:
Estimate −59.2345.678 by first rounding each number to the nearest whole number.
Answer:
-59
Step-by-step explanation:
2 is the first digit right after the decimal point. The digit after it is 3, Both digits would round down, therefore meaning that the whole number would still be -59
HELP DUE IN 15 MINS!
In parallelogram ABCD, AE = 2x - 10 and EC = 8x - 70. Find x.
x =??
Answer:
x = 10
Step-by-step explanation:
According to Midpoint of a segment theorem we can say that AE = EC
So,
2x - 10 = 8x - 70
=> First subtract 2x from each side of "="
-10 = 6x - 70
=> Now add 70 to both the sides.
60 = 6x
=> Lastly divide both sides of "=" by 6
10 = x
Hope this helps!
Consider the function g(x) = (x-e)^3e^-(x-e). Find all critical points and points of inflection (x, g(x)) of the function g.
Answer:
The answer is "[tex]cirtical\ points \ (x,g(x))\equiv (e,0),(e+3,\frac{27}{e^3})[/tex]"
Step-by-step explanation:
Given:
[tex]g(x) = (x-e)^3e^{-(x-e)}[/tex]
Find critical points:
[tex]g(x) = (x-e)^3e^{(e-x)}[/tex]
differentiate the value with respect of x:
[tex]\to g'(x)= (x-e)^3 \frac{d}{dx}e^{e-r} +e^{e-r} \frac{d}{dx}(x-e)^3=(x-e)^2 e^{(e-x)} [-x+e+3][/tex]
critical points [tex]g'(x)=0[/tex]
[tex]\to (x-e)^2 e^{(e-x)} [e+3-x]=0\\\\\to e^{(e-x)}\neq 0 \\\\\to (x-e)^2=0\\\\ \to [e+3-x]=0\\\\\to x=e\\\\\to x=e+3\\\\\to x= e,e+3[/tex]
So,
The critical points of [tex](x,g(x))\equiv (e,0),(e+3,\frac{27}{e^3})[/tex]
Base your answers to the following questions on the food web below and on your knowledge of biology. Which organisms are carnivores? A. grass and trees B. mouse, rabbit, and cricket C. deer and mountain lion D. frog, snake, and hawk
Answer:
D
Step-by-step explanation:
what can 16 and 4 both be divided by
Answer:
4
Step-by-step explanation:
they can both be divided by 4
What information is missing in order to prove the following triangles are
congruent by SAS?*
Answer:
Two triangles are congruent if they meet one of the following criteria. : All three pairs of corresponding sides are equal. : Two pairs of corresponding sides and the corresponding angles between them are equal. ... and another pair of corresponding sides are equal in two right triangles.
lacy work 15 hours last week she was paid $127.50 what is your hourly pay
Given:
Lacy work 15 hours last week and she was paid $127.50.
To find:
The hourly pay of Lacy.
Solution:
We have,
15 hours pay = $127.50
To find the hourly pay of Lacy, we need to divide total pay by number of hours.
[tex]\text{Hourly pay}=\dfrac{\text{Total pay}}{\text{Number of hours}}[/tex]
[tex]\text{Hourly pay}=\dfrac{127.50}{15}[/tex]
[tex]\text{Hourly pay}=8.5[/tex]
Therefore, the hourly pay of Lacy is $8.50.
What is the area of the parallelogram with vertices at (0,1), (-1,2), (5,4) and (6,3)?
12 square units
10 square units
8 square units
16 square units
Answer:
d 16
Step-by-step explanation:
A rectangular piece of land is 1/4 miles long and a 1/2 mile wide what is the area of the piece of land in square miles
Answer:
1/8 square miles
Step-by-step explanation:
1/4 times 1/2 = 1/8
Solve 9x + 3 = -33 . PLEASE HELP ME IT WILL MAKE MY DAY
[tex] : \implies \sf 9x + 3 = - 33[/tex]
[tex] : \implies \sf 9x = - 33 - 3[/tex]
[tex] : \implies \sf 9x = - 36[/tex]
[tex] : \implies \sf x = \dfrac{ - 36}{9} = - 4[/tex]
[tex] \therefore \sf x = -4 [/tex]
How can -6 1/3 be expressed as the sum of it's integer and fractional parts?
I'm giving 20 points for this one
Answer:
bottom left: -6 + (-1/3)
Step-by-step explanation:
hope this helps :)
what is the answer to −9−(−4)=
Combine the like terms to create an equivalent expression: 5n + 6 +(-7n) - 9
Answer:
-2n - 3
Step-by-step explanation:
5n + 6 + (-7n) - 9
5n + 6 - 7n - 9
5n - 7n + 6 - 9
-2n - 3
For C it's y= 1.5x and D is y=2/3x
Answer:
y = 1.5x + 0 or y = 1.5x
Step-by-step explanation:
=> First lets find the slope:
Slope: Change in y / Change in x
Change in y = +15
Change in x = 10
Slope = 15/10 or 1.5
=> Now lets find the, y-intercept:
We know that y-intercept is the y-value when x = 0
So we can say:
y = 1.5x
y = 1.5(0)
y = 0
Therefore y-intercept = 0
Final equation: y = 1.5x + 0 or y = 1.5x
Hope this helps!
Calista worked all summer to save for spending money while she is away for college. She goes off to college with $3920 in her savings account. She wants to have at least $500 left in her account at the end of her 36-week school year. Write an inequality to represent this situation.
Answer:
3920 - 36x ≤ 500
Step-by-step explanation:
Calista worked all summer to save for spending money while she is away for college. She goes off to college with $3920 in her savings account. She wants to have at least $500 left in her account at the end of her 36-week school year. Write an inequality to represent this situation.
Let the amount of money spent in 36 weeks = x
At least = Less than or equal to = ≤
$3920 - 36x ≤ $500
Hence, the inequality to represent this situation is written as:
3920 - 36x ≤ 500
What is the mzb?
34°
76°
bº
Answer:
b^=118
the mzb is 42 we add each numbers by 42