Answers
Answer:
Recursive:
[tex]f(1)=4, f(n)=f(n-1)-4[/tex]
Explicit:
[tex]f(n)=4-4(n-1)[/tex]
And the 20th term f(20) is -72.
Step-by-step explanation:
We have the sequence:
4, 0, -4, -8...
Let’s find the recursive and explicit rule for the sequence.
Recursive Rule:
Let’s determine the factor by which the sequence is decreasing by. We see that each subsequent term is 4 less than the previous term. In other words, our common difference is -4.
So, this is a arithmetic sequence.
The standard format for an recursive rule for an arithmetic sequence is:
[tex]f(1)=a , f(n)=f(n-1)+(d)[/tex]
Where a is the initial term and d is our common difference.
From our sequence, we know that our initial term a is 4.
We also determined that our common difference is -4.
Substitute. Hence, our recursive rule is:
[tex]f(1)=4, f(n)=f(n-1)-4[/tex]
Explicit Rule:
The standard format for an explicit rule for an arithmetic sequence is:
[tex]f(n)=a+d(n-1)[/tex]
Where a is the initial term and d is the common difference. So, again, let’s substitute 4 for a and -4 for d. Hence, our explicit formula is:
[tex]f(n)=4-4(n-1)[/tex]
To find f(20), we can use the explicit formula. It is possible to use the recursive formula, but it gets tedious. Therefore, we will substitute 20 for n for our explicit formula:
[tex]f(20)=4-4(20-1)[/tex]
Evaluate:
[tex]\begin{aligned} f(20)&=4-4(19) \\ f(20)&=4-76 \\ f(20)&=-72 \end{aligned}[/tex]
Hence, our 20th term is -72.
Related Questions
2 More Problems! 20 points! AND BRAINLIEST TO CORRECT ANSWER!
Answers
Answer:
First Screen:
1 & 3
Second Screen::A
Step-by-step explanation:
HOPE THIS HELPS!!
The sum of 6 times a number and 8 is 3.
Answers
Answer:
8 times 3 plus 6
Step-by-step explanation:
Mr. Barnes hired a plumber to fix a leak. The total cost, in dollars, that the plumber charges for a job can be modeled by the function p(x)= 45+35x , where x represents the time, in hours, that the plumber used to complete the job. Mr. Barnes budgeted $220 to pay the plumber for the job. After how many hours will the cost of the job exceed Mr. Barnes's budget?
WILL PICK THE BRAINLEST.
Answers
Please answer quick, thank you for your time.
Add or subtract. Write in simplest form.
9 4/5 - 2 3/10
11 3/4 - 4 1/3
6 3/5 - 1 2/3
14 1/6 - 7 1/3
Answers
Answer:
7 1/2
7 5/12
4 14/15
6 5/6
Answer:
7 1/2
7 5/12
4 14/15
6 5/6
Step-by-step explanation:
I WILL GIVE BRAINLY
Enter values for x and y in the table to plot points in the graph.
Answers
Answer: positive
Y=0.04x-0.77
by-step explanation
Anyone know the answer?
Answers
Answer:7
Step-by-step explanation: The range is the value of the difference of the highest and lowest numbers. As I can see here, the highest is 9, while the lowest is 2, so 9-2=7
7 (4 + 9) help ols ok jjjj
Answers
I will give lots of points for this or.2
Answers
Answer:
Step-by-step explanation:
10+banna x orange
Answer:
Apple=10. Banana=6. Orange=6.
Step-by-step explanation:
Solve: -4(3-2x) = 6(3x + 3)
Step by step ?
Answers
Answer:
distribute the -4 to the 3 and -2x in the parentheses
-12+8x
distribute the 6 to the 3x and the 18
-12+8x = 18x+18
subtract 8x from both sides
-12= 10x+18
subtract 18 from both sides
-30= 10x
divide each side by 10
x= -3
What are three consecutive even integers whose sum is 66
Answers
Answer:
21,22,23
Step-by-step explanation: i love fried chicken look at my skin color
Answer:
Smallest integer: 20
Middle integer: 22
Largest integer: 24
Step-by-step explanation:
Denote the smallest integer as "x"; hence the next integer will be "x + 2", and the third will be "x + 4".
Using the information, set up an equation:
x + x + 2 + x + 4 = 66
Simplify
x + x + 2 + x + 4 = 66
3x + 6 = 66
Inverse operations
3x + 6 = 66
-6 -6
3x = 60
/3 /3
x = 20
Smallest integer: 20
Middle integer: 22
Largest integer: 24
If you have two points, you can only pick the first one to find the equation.
True
False
Answers
Answer:
well, it really depends but im pretty sure its false. you can start with either one and find the equation
Step-by-step explanation:
Passing through (5,7)
parallel to y = x + 6
Answers
Answer:
hil how are you doing
Step-by-step explanation:
This is pretty confusing please help!!!!!
Answers
___________ are reported in the business section of magazines or newspapers, as well as online.
Answers
Answer:
The stock market values
Step-by-step explanation:
PLS GIVE BRAINLIEST
It should be noted that the stock market values are reported in the business section of magazines or newspapers, as well as online.
A stock market is also known as the equity market. It can also be called the share market. It's the aggregation of buyers and sellers of stocks.The buyers and sellers represent the ownership claims on businesses. The stock market values are reported in the business section of magazines or newspapers, as well as online.Learn more about stock market on:
https://brainly.com/question/24239991
Has this app helped u
Answers
Answer:
Discoveries and scientific and technical inventions do not influence the behavior of people, but their lives do
Step-by-step explanation: what app and ok
En la casa de la familia de Trevor viven 6 personas (incluyendo a Trevor) y hay 3 baños. En el último mes, cada
persona se bañó durante un promedio de 480 minutos y utilizó un promedio de 72 litros de agua al bañarse
(en todo el mes). El agua cuesta 0.20 dólares por litro.
¿Cuánto dinero gastó la familia de Trevor en total en agua al bañarse el mes pasado?
dólares.
Answers
Answer:
La familia de Trevor gastó 86.4 dólares al bañarse en todo el mes.
Step-by-step explanation:
El costo del agua viene dado por:
[tex] C = \$0.20/L [/tex] (1)
Y cada persona de la familia de Trevor gasto en promedio 72 litros de agua. Si la familia tiene 6 integrantes (incluido Trevor) entonces:
[tex] A = 72 L*6 = 432 L [/tex] (2)
Entonces, toda la familia usó 432 litros de agua en promedio en todo el mes.
Para saber el dinero total gastado por la familia debemos multiplicar la ecuación (1) y la ecuacion (2):
[tex] C = \$0.20/L*432 L = \$86.4 [/tex]
Por lo tanto, la familia de Trevor gastó 86.4 dólares al bañarse en todo el mes.
Espero que te sea de utilidad!
Usando proporciones, hay que la familia de Trevor gastó 86.4 dólares en total en agua al bañarse el mes pasado.
En la casa, hay 6 personas.Cada persona utilizó un promedio de 72 litros de agua.Por eso, en todo, 6 x 72 = 432 litros de agua fueron usados.
Cada litro cuesta $0.2. De esa forma, el total de dinero gasto es de:
T = 0.2 x 432 = 86.4.La familia de Trevor gastó 86.4 dólares en total en agua al bañarse el mes pasado.
Un problema similar es dado en https://brainly.com/question/20453191
A store sells ice cream with assorted toppings. They charge $3.00 for an ice cream, plus 50 cents per ounce of toppings.
How much does an ice cream cost with 4 ounces of toppings?-------()
How much does an ice cream cost with 11 ounces of toppings?----()
If Elena's ice cream cost $3.50 more than Jada's ice cream, how much more did Elena's toppings weigh?-------()
Answers
Answer:
1st question: $2.00 2nd question: $5.50 3rd question: 7 oz.
Step-by-step explanation:
4 x 50= 2 = $2.00
11 x 50= 550 = $5.50
7 x 50= 350 = $3.50
I WILL MARK BRAINIEST
Answers
Answer:
X=32°
Y=122°
Z=58°
Step-by-step explanation:
X+73°+75°=180° (interior angles of a triangle adopts to 180°)
X=180°-148°
X=32°
32°+Y+26°=180°(interior angles of a triangle adopts to 180°)
Y=180°-58°
Y=122°
Y+Z=180(angle on straight line adopts to 180°)
Z=180°-122°
Z=58°
Answer:
x=32, y=122, z=58
Step-by-step explanation:
[tex]Lets\ consider\ the\ quadrilateral\\Angle\ 1=73\\Angle\ 2=75\\Let\ angle\ 3\ be\ w\\\ We\ observe\ that,\\26+w=180 [Linear\ Pair]\\w=180-26\\w=154\\Hence,\\w+z+73+75=360[Angle\ Sum\ Property\ of\ A\ Quadrilateral]\\z+154+73+75=360\\z+302=360\\z=58[/tex]
[tex]We\ now\ observe\ that,\\Angle\ z\ and\ Angle\ y\ form\ a\ linear\ pair\ and\ hence\ are\ supplementary.\\z+y=180\\58+y=180\\y=122[/tex]
[tex]Hence,\\As\ y,26\ and\ x\ form\ a\ triangle, \\Through\ Angle\ Sum\ Property\ of\ a\ triangle\ they\ are\ supplementary \\Hence,\\26+x+y=180\\26+x+122=180\\x+148=180\\x=32[/tex]
12 + 4x – 4 = 12x – 9 – 8x
Answers
Answer:
No solution
Step-by-step explanation:
Basically the simplified equation is 17 = 0, which is wrong so there is no solution.
can someone help me with this?
Answers
Answer:
either b or d
Step-by-step explanation:
id go with d
what is the value of this expression below when x=3 and y =8
6x+10y ? PLEASE DONT WASTE MY TIME
Answers
Answer:
98
Step-by-step explanation:
6(3)+10(8)
=18+80
=98
PLS GIVE BRAINLIEST
18x + 18
1
18 1
12
+18 Substitute.
+ 18
Multiply.
Answers
Answer:
18 x+18
Step-by-step explanation:
did you get a number that it is equals to caz i dont understand how you are suppose to work out 18× +18
Write an expression that represents the given statements (use N to represent “a number”):
a) Two times a number plus three
b) Four less than a number
c) A number minus 5, then multiplied by 6
Answers
b) n - 4
c) (n - 5) 6
Suppose that you need to buy some chicken for dinner tonight. You found an ad showing that a store across town has chicken on sale for $2.99 per pound. Your usual neighborhood store sells the same chicken for $3.79 per pound. You are considering whether it is worth the drive to purchase the chicken from the store across town. Information you will need:________
A. You need to purchase 3 pounds of chicken
B. Your neighborhood store is 2.1 miles away and takes about 8 minutes to get there
C. The store across town is 8.6 miles away and takes about 24 minutes to get there
D. Your car averages about 22 miles per gallon in the city Gas is $3.05 per gallon
Answers
Answer:
C). The store across town is 8.6 miles away and takes about 24 minutes to get there.
D). Your car averages about 22 miles per gallon in the city Gas is $3.05 per gallon.
Step-by-step explanation:
The information regarding the distance of the store across town from the house, the time required to reach there, the average of the car, and the cost of gas per gallon would assist in calculating if the extra drive is worth buying chicken from the city store.
Cost of chicken in the city store - $2.99 per pound
Average of the car in 1 gallon = 22miles
so, the average of the car in 1 mile = 1/22
Cost of traveling 8.6miles = 8/22 * $3.05
= 24.40/22
Additional cost = $ 1.109
Total cost of buying chicken from the city store = $2.99 + $1.10
= $4.09
Hence, it is not worth to buy the chicken from the store across the town as it is costlier in comparison to $3.79 in nearby store.
Whoever answers this I will mark you Brainliest or else I’ll report you
Answers
Answer:
Uhh ok
Step-by-step explanation:
Answer:
yea
Step-by-step explanation:
ok the answer is ok
I need help finding the domain
Answers
Answer: [-11,4]
Step-by-step explanation:
yes in brackets
Answer:
(-11, 4)
Step-by-step explanation:
The domain is the x values that the equation/line covers.
The line starts at -11 and ends at 4. We use parenthesis instead of brackets since the circles are open and not closed.
(-5)-6 find the different
Answers
Answer:
-11
Step-by-step explanation:
−5−6
=−5−6
=−5+−6
=−11
Hope this Helps!
solve for x.
a) 9[tex]9^{3x+4}[/tex] = [tex]27^{4x+3}[/tex]
b) [tex]4^{3x}[/tex] = [tex]2^{x+1}[/tex]
(include steps pleez)
Answers
Answer:
Question a)
[tex]9^{3x+4}=27^{4x+3}[/tex]
[tex]x=-0.166[/tex]
Question b)
[tex]4^{3x}=2^{x+1}[/tex]
[tex]x=0.2[/tex]
Step-by-step explanation:
Question a)
Given the expression
[tex]9^{3x+4}=27^{4x+3}[/tex]
Taking log on both sides
[tex]log\left(9^{3x+4}\right)=log\left(27^{4x+3}\right)[/tex]
[tex]\left(3x+4\right)\cdot \left(log\left(9\right)\right)\:=\left(4x+3\right)\cdot \left(log\left(27\right)\right)[/tex]
[tex]3x+4=\left(\frac{log\left(27\right)}{log\left(9\right)}\right)\cdot \left(4x+3\right)[/tex]
[tex]3x+4=1.5\times \left(4x+3\right)[/tex]
[tex]3x+4=6x+4.5[/tex]
[tex]3x=6x+0.5[/tex]
[tex]\frac{-3x}{-3}=\frac{0.5}{-3}[/tex]
[tex]x=-0.166[/tex]
Therefore, the value of x:
[tex]x=-0.166[/tex]
Question b)
Similarly, we can solve the 'b' expression
Given the expression
[tex]4^{3x}=2^{x+1}[/tex]
Taking log on both sides
[tex]log\left(4^{3x}\right)=log\left(2^{x+1}\right)[/tex]
[tex]3x\cdot \left(log\left(4\right)\right)=\left(x+1\right)\cdot \left(log\left(2\right)\right)[/tex]
[tex]3x=\left(\frac{log\left(2\right)}{log\left(4\right)}\right)\cdot \left(x+1\right)[/tex]
[tex]3x=0.5\times \left(x+1\right)[/tex]
[tex]3x=0.5x+0.5[/tex]
[tex]2.5x=0.5[/tex]
Divide both sides by 2.5
[tex]\frac{2.5x}{2.5}=\frac{0.5}{2.5}[/tex]
[tex]x=0.2[/tex]
Therefore, the value of x = 0.2
45% of 720 feet
Plzzz heelllp
Answers
Answer:
324 feet
Step-by-step explanation:
Brainliest pls
Answer:
324
Step-by-step explanation:
You can either do 0.45·720 or make 45% into a fraction (45/100) and cross cancel with 720.
at a candy store you get 7 giant lollipops for $16.12 how much would it cost to buy 6 lollipops?
Answers
Answer:
$13.80
Step-by-step explanation:
Divide $16.12 by 7 which equals 2.30, then multiply 2.30 by 6 to get ^^