Question:
The recursive function [tex]f(0) = 1[/tex], [tex]f(n) = f(n-1) + 2n[/tex] represents the nth term of a sequence. Determine the explicit function
Answer:
[tex]f(n) = n^2 + n+1[/tex]
Step-by-step explanation:
Given
[tex]f(0) = 1[/tex]
[tex]f(n) = f(n-1) + 2n[/tex]
Required
Write an explicit formula
Let n = 1
[tex]f(1) = f(1-1) + 2*1[/tex]
[tex]f(1) = f(0) + 2[/tex]
[tex]f(1) = 1 + 2 = 3[/tex]
Let n = 2
[tex]f(2) = f(2-1) + 2*2[/tex]
[tex]f(2) = f(1) + 4[/tex]
[tex]f(2) = 3 + 4 = 7[/tex]
Let n =3
[tex]f(3)=f(3-1) + 2 * 3[/tex]
[tex]f(3)=f(2) + 6[/tex]
[tex]f(3)=7+ 6 = 13[/tex]
Let n = 4
[tex]f(4) = f(4 - 1) + 2 * 4[/tex]
[tex]f(4) = f(3) + 8[/tex]
[tex]f(4) = 13+ 8 = 21[/tex]
So, we have:
[tex]f(1) = 3= 1 + 2 * 1=1+0*1*2*1[/tex]
[tex]f(2) = 7= 3 + 2 * 2=1+1*2+2*2[/tex]
[tex]f(3) = 13= 7 + 2 * 3= 1+2*3+2*3[/tex]
[tex]f(4) = 21 = 13 + 2 * 4= 1+3*4 +2 *4[/tex]
Following the above pattern:
[tex]f(n) = 1 + (n - 1) * n + 2 * n[/tex]
[tex]f(n) = 1 + n(n - 1) + 2n[/tex]
Open bracket
[tex]f(n) = 1 + n^2 - n + 2n[/tex]
[tex]f(n) = 1 + n^2 + n[/tex]
[tex]f(n) = n^2 + n+1[/tex]
PLEASE HELP I'LL GIVE BRAINLEST!!!! I HAVE 30 MINS!!!!
Which of these are characteristics of reptiles? Check all that apply. They undergo internal fertilization. Their urine is concentrated. They use their skin for gas exchange. They have two-chambered hearts. They are covered in scales.
Answer:
Answers Below. Have a wonderful day!
Step-by-step explanation:
They undergo internal fertilization: True Most reptiles undergo internal fertilization sexually when the sperm of a male reptile enters the cloaca of female reptiles, fertilizing the egg.
Their urine is concentrated: False Reptiles do not have the ability to produce liquid urine that is more concentrated than their own body fluid because they lack a structure in their nephron called the Loop of Henle.
They use their skin for gas exchange: False They cannot use their skin as an organ of gas exchange. Reptiles depend entirely on their lungs for this.
They have two-chambered hearts: False They have three-chambered hearts.
They are covered in scales: True All reptiles are covered in scales (snakes, lizards, turtles, etc.)
Answer:
1 and 5
Step-by-step explanation:
i did the test
Simplify the following
√9/25
√12/3
√15/3
Answer:
a)3/5
b)2
c)√5
...........
Answer:
√9/5 = 3/25 = 0.12
√12/3 = 1.15
√15/3 = 1.29
5. The value of a home increases by 7% each year. Explain why the value of the home doubles approximately once each decade.
Answer:
Step-by-step explanation:
2x=x(1.07)^t
2=(1.07)^t
t=log2/(log 1.07) ≈10.2 4 years
so it doubles in approximately in 10.2 years
To solve the problem we must know about Compounding.
What is compounding?Compounding is a process where the interest is credited to the initial amount and interest, on the whole, is charged again. and this continues for t period of time.
It is given by the formula,
[tex]A = P(1+r)^t[/tex]
where A is the value after t period of time,
P is the value of the asset at the beginning, and,
r is the rate of interest.
The value of the home doubles once each decade.
Given to us
As it is given that the value of a home increases by 7% each year, therefore, the value of the home is compounding every year.
We know the formula of compounding,
[tex]A = P(1+r)^t[/tex]
Why does the value doubles?Now, let's assume a house whose value is 'P' today, therefore, substitute the value of the house in the formula of compounding,
[tex]A = P(1+r)^t[/tex]
Substitute the rate at which the value is increasing,
[tex]A = P(1+0.07)^t[/tex]
We know that in a decade there are 10 years,
[tex]A = P(1.07)^{10}[/tex]
[tex]A = 1.967P\approx 2P[/tex]
As we can see that the value of the home is almost 2 times the 'P' therefore, twice the value of the home at the beginning.
Hence, the value of the home doubles once each decade.
Learn more about Compounding:
https://brainly.com/question/25857212
Last week, Jen started a new job at the mall. She worked 36 hours over 4 workdays of equal length. She makes $8 an hour. How much did she make for each day of work?
Answer:
1652
Step-by-step explanation:
because 36x4=144 and 144x8=1652
Answer:
1652
Step-by-step explanation:
YO 10 or 22 points can somebody pls help me I’m stuck. Solve each inequality for x then graph your answer on a number line. Remember when you divide by a negative you have to switch the inequality symbol. Pls pls help me :(
Answer:
x<5
Step-by-step explanation:
−2(x−7)>4
Step 1: Simplify both sides of the inequality.
−2x+14>4
Step 2: Subtract 14 from both sides.
−2x+14−14>4−14
−2x>−10
Step 3: Divide both sides by -2.
−2x ÷ −2 > −10 ÷ −2
x<5
Multiply the following Polynomial Expressions.
( 2x – 6) ( 3x2 + 4x - 2)
Answer:
24
Step-by-step explanation:
???? 0.243 + 70.3 =
Answer:
70.243
Step-by-step explanation:
hope this helps you!!
Answer:
0.243 + 70.3 = 70.543
I hope This Helps^^Find the number of sides of a regular polygon if one interior angle is 120 degrees A3 B4 C5 D6
Answer:
n = 6
Step-by-step explanation
Number of sides = 360/Measure of exterior
Measure of exterior = 180 - interior angle
Exterior angle = 180 - 120
Exterior angle = 60 degrees
Substitute into the formula
number of sides = 360/60
number of sides = 6
Hence the number of sides required is 6
Gabriel has 15 ⅝ pounds of clay. He will use 7/10 pound to make each bowl. After making 8 bowls, Gabriel wonders how many more bowls he can make. How many more bowls can how make?
Answer:
14
Step-by-step explanation:
The total amount of bowls he can make given the pounds of clay and the pound needed to make a bowl = [tex]15\frac{5}{8}[/tex] ÷ [tex]\frac{7}{10}[/tex]
= [tex]\frac{125}{8}[/tex] ÷ [tex]\frac{7}{10}[/tex]
= [tex]\frac{125}{8}[/tex] ×[tex]\frac{10}{7}[/tex] = 22.32
Number of bowls he can more more = total amount of bowls that can be made - number of bowls already made
22.32 - 8 = 14.32 bowls
Rounding off to the nearest whole number gives 14
which pair of adjacent angles is complementary?
(the picture is below)
Answer:
C)
Step-by-step explanation:
The sum of the 2 angles add up to 90 degrees.
Hope this helps! Have a nice day! Plz mark as brainliest!!!
-XxDeathshotxX
Someone please help me with this question
How many different 5-digit PIN codes are there that only include the digits 7, 2, 4, 6, 9 and 3?
Answer:
720
Step-by-step explanation:
6*5*4*3*2=720
To purchase $14,500 worth of restaurant equipment for his business, Hans made a down payment of $1800 and took out a business loan for the rest. After years of paying monthly payments of $562.88. , he finally paid off the loan.
Answer:
hello your question is incomplete below is the complete question
To purchase $14,500 worth of restaurant equipment for his business, Hans made a down payment of $1800 and took out a business loan for the rest. After 2 years of paying monthly payments of $562.88. , he finally paid off the loan. What was the total amount Dean ended up paying for the equipment ( including the down payment and monthly payments )
answer: $15309.12
Step-by-step explanation:
Initial cost of equipment = $14500
Down payment = $1800
cost of equipment = 14500 - 1800 = $12700
Monthly payment = $562.88
Therefore payment made after 2 years = ( 562.88 * 24 ) = $13509.12
Total amount paid by Dean for the equipment
= down payment + monthly payments
= $1800 + $13509.12
= $15309.12
You are organizing a school banquet. You spend $82 on decorations. Dinner will cost $13 for each person that attends. In the equation y=13x+82, y is the total cost of the banquet for x people. Complete the solution (69,?) to find the cost for 69 people.
Answer:
(69,979)
Step-by-step explanation:
In the coordinates, x is represented as 69. We can now insert this into the equation.
y = 13x + 82
Now to insert x.
y = 13(69) + 82
Now we can multiply 13 by 69.
13*69 = 897
Now fix the equation.
y = 897 + 82
Now add to get our y.
897 + 82 = 979
Substitute into the equation.
y = 979
And there is our answer. We now need to put this into the coordinates.
And we get our final answer of (69,979).
Hope this helps. Have a nice day.
last year, 15 dogs entered the local dog show. this year, 27 entered. what is the percent increase?
Answer:
80%
Step-by-step explanation:
What is the measure of an angle that is the complement of angle M?
A.
10°
B.
60°
C.
90°
D.
None of the above
E.
45°
Answer:
the measure of an angle that is the complement of angle M=90-75=15
non of the above
Factor completely: 2x^3-12x^2+18x
Answer:
2x(x - 3)²
Step-by-step explanation:
We can simplify this a lot by first factoring 2x out of each term:
2x³ - 12x² + 18x
= 2x(x² - 6 + 9)
We can then factor the trinomial fairly easily, as it's a perfect square:
= 2x(x - 3)²
Evaluate 2x-y if x=-3 and y= -7
Answer:
1
Step-by-step explanation:
Substitute x with -3 and y with -7
2(-3)-(-7)
Multiply
-6-(-7)
Signs are both negative, turn into positive sign
-6+7
Add
1
Answer:
1
Step-by-step explanation:
x = - 3 and y = - 7
2x-y =?
Now
2*(-3)-(-7)
-6 +7. (sign of negative when multiplied it turns into positive)
1. Answer
help me find the value of x!
Find the solution to the equation.
7m = 112
Answer:
m= 16
Step-by-step explanation:
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Answer:
- [tex]3x^{2}[/tex] - 40x - 100
Step-by-step explanation:
f (x ) . g ( x )
( 3x - 10 ) ( 10 - x )
30x - [tex]3x^{2}[/tex] - 100 + 10x
Simplify the like terms.
40x - 100 - [tex]3x^{2}[/tex]
= - [tex]3x^{2}[/tex] - 40x - 100
Answer:
your answer is D
Grant walks 4/5 of a mile in 1/4 hour. What is his ratio of miles to hours in simplest form?
Answer:
You can always ask the tutor they give the correct answer :))
Lannister checks out 6 set of books from the library each set has the same number of books she reads 7 of the books and she has 11 books left to read how many books are in each sets
Answer:
3
Step-by-step explanation:
Lannister checks out 6 sets of book
Each set had the same number of books
She reads 7 books and has 11 more to go
Therefore the number of books in each set can be calculated as follows
= 11+7
= 18
18/6
= 3
Hence there are 3 books in each set
2{x+8}+5{x-1}=60 answer
Answer:
x=7
Step-by-step explanation:
2{x+8}+5{x-1}=60
Distribute
2x+16+5x-5 = 60
Combine like terms
7x +11 = 60
Subtract 11 from each side
7x+11-11 = 60-11
7x = 49
Divide each side by 7
7x/7 = 49/7
x = 7
explain the error .
help me plll
Answer:
Correct solution in steps
5 - 2(a + 7) + 10a = The first operation is parenthesis5 - 2(a) - 2(7) + 10a = The second operation is simplification5 - 2a - 14 + 10a = Next operation is collecting like terms(10a - 2a) + (5 - 14) = Next operation is simplification8a + (-9) = 8a - 9The error in the given solution was the first step: (5 - 2)
2(12 - y) = 23- (2y - 1) is there a solution for this?
Answer:
Step-by-step explanation:
Short Answer: No
2(12 - y) = 23- (2y - 1) Remove the Brackets on both sides
24 - 2y = 23 - 2y + 1 Combine like terms on the right
24 - 2y = 24 - 2y No matter what you do, the 2ys are going to cancel. When they do, the question goes with them.
You get 24 = 24 Which is true but not relevant.
The other answer you could use is there are an infinite number of answers.
Equality will be maintained, but there is no single answer that works.
Answer:
This equation is an identity, all real numbers are solutions.
Step-by-step explanation:
Simplifying
2(12 + -1y) = 23 + -1(2y + -1)
(12 * 2 + -1y * 2) = 23 + -1(2y + -1)
(24 + -2y) = 23 + -1(2y + -1)
Reorder the terms:
24 + -2y = 23 + -1(-1 + 2y)
24 + -2y = 23 + (-1 * -1 + 2y * -1)
24 + -2y = 23 + (1 + -2y)
Combine like terms: 23 + 1 = 24
24 + -2y = 24 + -2y
Add '-24' to each side of the equation.
24 + -24 + -2y = 24 + -24 + -2y
Combine like terms: 24 + -24 = 0
0 + -2y = 24 + -24 + -2y
-2y = 24 + -24 + -2y
Combine like terms: 24 + -24 = 0
-2y = 0 + -2y
-2y = -2y
Add '2y' to each side of the equation.
-2y + 2y = -2y + 2y
Combine like terms: -2y + 2y = 0
0 = -2y + 2y
Combine like terms: -2y + 2y = 0
0 = 0
Solving
0 = 0
Anything raised to a power of zero is always:
Answer:
1
Step-by-step explanation:
u cant really multiply anything so it 1
Please answer. Thanksss
Answer:
1. no
2. no
3. yes
4.yes
Step-by-step explanation:
hope this helped
Answer:
No, No, Yes, Yes
Step-by-step explanation:
We can simply substitute the pairs as x and y in the equation:
(5, 0)
7*5 + 5*0 = 35 + 0 = 35
[tex]35 \ne 9[/tex]
(-4, -3)
7*(-4) + 5*(-3) = -28 - 15 = -43
[tex]-43 \ne 9[/tex]
(2, -1)
7*2 + 5*(-1) = 14 - 5 = 9
[tex]9 =9[/tex]
(-3, 6)
7*(-3) + 5*6 = -21 + 30 = 9
[tex]9 = 9[/tex]
The diagram shows a circle contained in a square. What is the simplified ratio of the area of the circle to the area of the square?
Answer:
π/4Step-by-step explanation:
We have a = 2r
Area of square:
A₁ = a² = 4r²Area of circle:
A₂ = πr²Ratio:
A₂/A₁ = πr²/4r² = π/4Answer:
π/4
Step-by-step explanation:
Hope this helps
what's the domain and range function for y=(x-12)^2+11
Answer:y = x 2 − 12 x The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined. Interval Notation: ( − ∞ , ∞ ) Set-Builder Notation: { x | x ∈ R } The range is the set of all valid y values. Use the graph to find the range. Interval Notation: [ − 36 , ∞ ) Set-Builder Notation: { y | y ≥ − 36 } Determine the domain and range. Domain: ( − ∞ , ∞ ) , { x | x ∈ R } Range: [ − 36 , ∞ ) , { y | y ≥ − 36 }
Step-by-step explanation:
Answer:
Step-by-step explanation:
There is no restriction upon x so the domain is all real numbers
x=(-oo, +oo)
y has a minimum value when x=12 and y=11. Any other value of x increases the value of y. So the range is all real numbers greater than or equal to 11.
y=[11, +oo)