A recursive rule for a sequence is given. Find the first four terms of the sequence.
f(1) = 2
f(n) = 4. f(n – 1), where n is an integer and n > 2.
Answer:
So...
a0 = -2
a1 = (a0)2 - 4 = 4 - 4 = 0
a2 = (a1)2 - 4 = ((a0)2-4)2 - 4 =...= 02 - 4 = -4
For an+1, you may use the previous term (an) if you have just calculated it, rather than calculating it recursively again
a3 = (-4)2 - 4 = 12
The first four terms in the sequence are -2, 0, -4, 12.
Step-by-step explanation:
This recursive sequence is defined as follows:
a0 = -2 [the first term]
an+1 = an2 - 4 [for all other terms, n≥0; note that you cannot find a0 using this line]
Note that this is not "BASE" for a number base, but it is "SUB" for subscript, indicating the term. Sometimes, sequences are written with the first term being a1 and sometimes sequences are written with the first term being a0. This is because there are situations that make one or the other more convenient (for example, starting with elapsed time t=0 makes sense).
To find the value of later terms, a recursive definition requires that you find the value of the previous term, which requires that you find the value of the previous term, which requires that you find the value of the previous term, which requires that you find the value of the previous term, ... which requires that use the value of the first term.
That's why (joke) that the dictionary definition of "recursive" is "see recursive."
Steve's bedroom measures 12 feet by 13 feet. Ricardo's bedroom measures 8 feet by 14
feet. Assuming that both bedrooms are rectangular, whose room has the greater area?
Answer: Steve's bedroom has the greater area.
Step-by-step explanation: The formula for area is Area = Length x Width.
So all you have to do to figure this out is multiply the Width of the rooms by the length.
So Steve's room is 12ft X 13ft = 156ft
Ricardo's room is 8ft X 14ft = 112ft
156ft > 112ft
Steve's room has a greater area.
Which polynomial is in standard form?
N
O 26x5 + 12x7-8x3 + 6x
O 3x5 +x-6x2 + 5
11x5-6x2-9x+12
5x2 + 18x3 - 12x4 +4x7
Answer:
i am pretty sure it is D
Step-by-step explanation:
Answer:
Its C.) 11x^5 - 6x^2 - 9x + 12
Step-by-step explanation:
ejenuwitee
=D
=P
Which solution would make this equation have infinitely many solutions?
A.-18
B.-9
C.9
D.18
Answer: -18
Step-by-step explanation:
find m
right anwser gets brainliest
Answer:
The measure of <FDE is 18°
1. The temperature was very cold. Then the temperature doubled. Then the temperature dropped by 10 degrees. Then the temperature increased by 40 degrees. The temperature is now 16 degrees. What was the starting temperature?
Answer:
10,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
PLEASEEEEE HELLLPPP MEEE
Answer:
100
Step-by-step explanation:
solve x 3+3(x+2)=-24
Answer:
x=-11
Step-by-step explanation:
3+3x=6=-24
3x+9=-24
3x=-33
x=-11
Answer:
x = -11
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define Equation
3 + 3(x + 2) = -24
Step 2: Solve for x
Distribute 3: 3 + 3x + 6 = -24Combine like terms: 3x + 9 = -24Isolate x term: 3x = -33Isolate x: x = -11Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: 3 + 3(-11 + 2) = -24Add: 3 + 3(-9) = -24Multiply: 3 - 27 = -24Subtract: -24 = -24Here we see that -24 does indeed equal -24.
∴ x = -11 is the solution to the equation.
what is Evaluate 2. to the 2 power
Answer:
2^2 = 4
Step-by-step explanation:
2*2 = 4
Angela is planting flowers in her flowerbed. She wants the ratio of tulips to roses to be 5 to 2. If a total of 63 flowers are planted, how many tulips should there be?
Answer:
45 Tulips
Step-by-step explanation:
63/7=9
Tulips: Roses=5:2
Tulips=9x5=45
Roses=9x2=18
Please help i was crying :(
Also there is another one
“Subtract. Write Your answer in simplest form” which is: 6 3/4 - 2 3/20
Answer:
is it 4 3/5 it might be
Step-by-step explanation:
Solve the equation
(- 5 + 7)5x+ 4=16
The solutions are:
Answer:
x=2
Step-by-step explanation:
Answer:
x=1.2
Step-by-step explanation:
A typical tip in a restaurant is 15% of the total bill. If the bill is $160, what would the typical tip be?
Answer:
24$
Step-by-step explanation:
15%=0.15
160*0.15=24
How many blueberries on the on cake roof
Answer:
say what
Step-by-step explanation:
Three equal squares are superimposed as indicated in the figure. The areas of the overlapping zones are 2 cm², 5 cm², and 8 cm², respectively. The total area of the non-overlapping area of the squares is 117 cm². What is the length of the side of each square?
Answer: The square side lengths are 1 cm, 5 cm, and 11 cm.
===========================================================
Explanation:
Refer to the diagram below.
Define the following areas
A,B,C = non-overlapped regionsD,E,F = overlapped regionsIt doesn't really matter how you set up the labels, or what letters you pick, as long as you stay consistent.
We're told that "The areas of the overlapping zones are 2 cm², 5 cm², and 8 cm²", so let's make
D = 2E = 5F = 8Furthermore, we are told that "The total area of the non-overlapping area of the squares is 117 cm²" which means A+B+C = 117
---------------------------------------
Refer to the diagram. For now, focus on the upper right square. It has regions A, E, and F. The area of this square is A+E+F
Similarly, the area of the left-most square is D+B+E
The area of the bottom-most square is C+F+D
Add up the expressions we found and we get
(A+E+F)+(D+B+E)+(C+F+D) = A+B+C+2D+2E+2F
This represents the sum of all three square areas even if we peeled the squares apart to not overlap.
----------------------------------------
Let's plug in A+B+C = 117
We get
A+B+C+2D+2E+2F
117+2D+2E+2F
Now plug in D = 2, E = 5, and F = 8
117+2(2)+2(5)+2(8)
117+4+10+16
117+30
147
The sum of the three square areas is 147 square cm.
----------------------------------------
Now we have to do a bit of trial and error. We're looking for ways to break up 147 such that it is a sum of three squares.
In other words, we want to find integers m,n,p such that m^2+n^2+p^2 = 147
Let's try subtracting off 121
147-121 = 26
I picked 121 since it's the largest perfect square just smaller than 147
Repeat this process, but do so for 25 since 25 is smaller than 26
26-25 = 1
We can see that
1 + 25 + 121 = 147
1^2 + 5^2 + 11^2 = 147
One solution is m = 1, n = 5, p = 11. There may be other solutions. Keep in mind that m,n,p are positive whole numbers.
So we got a bit lucky with our trial and error process. If we didn't find such a triple, we'd have to try other possible combos of squares until we get the right match.
Because 1^2 + 5^2 + 11^2 = 147, this means the squares' side lengths are 1, 5, and 11.
You earn 90% on a quiz. If you earned 36 points, how many points was the quiz worth?
Answer:
36/90%=40
Step-by-step explanation:
40 points in total
how much change did she receive?
What is the simple interest earned when the principal is $500 at a rate of 10% held in the ban for 8 months?
S.I= PRT /100
where,
P = price $500
R = rate 10%
T = time =8months
= $500*10*8/100
= $40,000/100
S.I = $400
Find an ordered pair (x,y) that is a solution to the equation
3x-y=6
Answer:
2,0
Step-by-step explanation:
Help please! I need an explanation but I dont understand this!!!!!!!
Answer:
its to small
Step-by-step explanation:
I NEED HELP W 36
pls pls pls pls help help!
Answer:
1
Step-by-step explanation:
When you substitute the inside of f(g(2)), you get g(x)=2-4. Then you substitute that answer of -2 and plug it into f(x)=2x+5. Since f(-2)=2(-2)+5 equals to 1, that should be your answer.
What is the area of a rectangle with a length of 1/3 yards and width of 3/4 yard?
Answer:
1/4 yards squared
Step-by-step explanation:
Area of a rectangle equals length times width.
1/3 x 3/4 = 3/12, or 1/4
Answer:
It would be 1/4 and if not try 3/12
Step-by-step explanation:
I hope this helped
Find the slope of the line graphed below.
Answer:
-3/5
Step-by-step explanation:
So first, you have to find out the two points :
(-1,-1), and (4,-4)
Next, you have to put into this formula:
y1-y2/x1-x2
The y values in our points are -4 and -1, and our x values are 4 and -1. Lets now substitute:
-4-(-1)/4-(-1)
Now simplify: -4+1/4+1, and solve and you will get -3/5 as the slope
If you liked it, please give me a good rating and please mark me as the brainliest... Thanks!
Hope you do well on your assignment!
Which of the following ratios is not equivalent to the rest: *
6 to 8
54 : 72
36 : 56
3 to 4
Answer:
36:56
Step-by-step explanation:
Answer: C 34:55
Step-by-step explanation:
start with 6:8 that’s the first one multiply by 9 on each side you get 54:72 so that’s the same and then 6:8 divide by 2 and you get 3:4 but for 36:56 you’d have to multiply by 6 and that would give you 36:48 not 36:56
Can anyone help me out solving this?
Answer: 25
Step-by-step explanation: When you divide exponents with the same base, you can subtract the exponents. It becomes 5^4-2, which is 5^2, which is 25
Point k lies at (-3,4). Point k is reflected over the y-axis and then translated 7
units down to produce K'. Which rule could have been used to produce K' from K?
K(x, y) +K'(x,y-7)
K(x,y) →K'(-x, y-7)
K(x,y) →K'(x, -y-7)
K(x,y) → K'(-x-7.-y-7)
Answer:
b
Step-by-step explanation:
Answer:B
Step-by-step explanation:
Tina is taking picture of her friends. if she sets a tripod level on the ground, will the bottom of each of the legs of tripod be coplanar
Answer:
Yes
Step-by-step explanation:
Can you help me with this question please
Answer:
34
Step-by-step explanation:
Answer:
34 just subtract
Step-by-step explanation:
PLEASEEEE HELPP !
A company sells bottles of vitamin capsules. The graph and table show the linear relationship between the cost per capsule in cents and the number of bottles ordered. What is the slope of the line that models this situation?
Answer:
[tex] slope (m) = -5 [/tex]
Step-by-step explanation:
The slope can be calculated using two points, (2, 60) and (4, 50) as shown below:
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} [/tex], where,
[tex] (2, 60) = (x_1, y_1) [/tex]
[tex] (4, 50) = (x_2, y_2) [/tex]
Plug in the values into the equation
[tex] slope (m) = \frac{50 - 60}{4 - 2} [/tex]
[tex] slope (m) = \frac{-10}{2} [/tex]
[tex] slope (m) = -5 [/tex]
Answer:
x=6
Step-by-step explanation:
The sum of three numbers $x$ ,$y$, $z$ is 165. When the smallest number $x$ is multiplied by 7, the result is $n$. The value $n$ is obtained by subtracting 9 from the largest number $y$. This number $n$ also results by adding 9 to the third number $z$. What is the product of the three numbers?
Just take the $ out
You're given
x + y + z = 165
7x = n
n = y - 9
n = 9 + z
and you want to find xyz.
Solve the last three equations for x, y, and z :
7x = n → x = n/7
n = y - 9 → y = n + 9
n = 9 + z → z = n - 9
Substitute x, y, and z into the first equation and solve for n :
n/7 + (n + 9) + (n - 9) = 165
n/7 + 2n = 165
n + 14n = 1155
15n = 1155
n = 77
Now solve for x, y, and z :
x = 77/7 = 11
y = 77 + 9 = 86
z = 77 - 9 = 68
Then the product is
xyz = 11 • 86 • 68 = 64,328
The product of the three numbers is 8,192,040. The sum of three numbers x, y, z is 165: x + y + z = 165
The problem states:
1. When the smallest number x is multiplied by 7, the result is n: 7x = n
2. The value n is obtained by subtracting 9 from the largest number y: n = y - 9
3. The value n is also obtained by adding 9 to the third number z: n = z + 9
Now, let's proceed to find the values of x, y, z, and n:
From equation (2), we can express x in terms of n:
x = n/7
Now, substitute the value of x in equation (1):
(n/7) + y + z = 165
From equation (3), we can express y in terms of n:
y = n + 9
Now, substitute the value of y in the equation above:
(n/7) + (n + 9) + z = 165
From equation (4), we can express z in terms of n:
z = n - 9
Now, substitute the value of z in the equation above:
(n/7) + (n + 9) + (n - 9) = 165
Combine the terms with n:
3n/7 = 165
To isolate n, multiply both sides by 7/3:
n = 165 * (7/3)
n = 385
Now, we have the value of n, which is 385. To find the values of x, y, and z, substitute n back into the respective equations:
x = n/7 = 385/7
≈ 55
y = n + 9 = 385 + 9
= 394
z = n - 9 = 385 - 9
= 376
Now, we have the values of x, y, z, and n:
x = 55,
y = 394,
z = 376,
n = 385
To find the product of the three numbers, simply multiply them:
Product = x * y * z
= 55 * 394 * 376
≈ 8,192,040
So, the product of the three numbers is 8,192,040.
To know more about three numbers:
https://brainly.com/question/30269736
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