If f(1)=3 and f(n)=-2f(n-1)+ 1, then f(5)=

Answers

Answer 1

Answer: Our function is $f(n)=-2f(n-1)+1$ .
We want to find f(5).
Let's substitute 5 for n.
f(5) = -2f(5-1) + 1
f(5) = -2f(4) + 1
We need to know f(4).
f(4) = -2f(4-1) + 1
f(4) = -2f(3) + 1
We need to know f(3).
f(3) = -2f(3-1) + 1
f(3) = -2f(2) + 1
We need to know f(2).
f(2) = -2f(2-1) + 1
f(2) = -2f(1) + 1
We know that f(1) = 3
f(2) = -2(3) + 1
f(2) = -6 + 1
f(2) = -5
Now we can use f(2) = -5 to find f(3)...
f(3) = -2(-5) + 1
f(3) = 10 + 1
f(3) = 11
Now we can use f(3) = 11 to find f(4)...
f(4) = -2(11) + 1
f(4) = -22 + 1
f(4) = -21
Now we can use f(4) = -21 t find f(5)!
f(5) = -2(-21) + 1
f(5) = 42 + 1
f(5) = 43

Answer 2

Answer: $f(1)=3\ and\ f(n)=-2f(n-1)+1\nf(2)=-2f(2-1)+1=-2f(1)+1=-2(3)+1=-6+1=\boxed{-5}\nf(3)=-2f(3-1)+1=-2f(2)+1=-2\boxed{(-5)}+1=10+1=\boxed{11}\nf(4)=-2f(4-1)+1=-2f(3)+1=-2\fbox{11}+1=-22+1=\fbox{-21}\nf(5)=-2f(5-1)+1=-2f(4)+1=-2\fbox{(-21)}+1=42+1=\boxed{\boxed{43}}$

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What is the equation of a line, in general form, that passes through point (1, -2) and has a slope of 1/3. 3x - y - 7 = 0
x - 3y + 7 = 0
x - 3y - 7 = 0

Answers

Hello,

y+2=1/3*(x-1) ==>3y+6=x-1==>x-3y-7=0

Answer C

Mike has 21 pounds of tomatoes and 9 pounds of mixed peppers from his garden that he will use to make salsa and tomato sauce. The graph represents the system of equations shown.A system of equations. x plus 5 y equals 21. x plus y equals 9.

The variable x represents the number of batches of salsa that can be made and y represents the number of batches of tomato sauce that can be made.

A coordinate grid showing Garden Produce with Batches of Salsa on the x axis and Batches of Tomato Sauce on the y axis and two lines. The first line passes through (0, 9) and (6, 3). The second line passes through (1, 4) and (6, 3).

Which statement is true about the graph?

Mike can make 3 batches of salsa and 6 batches of tomato sauce using all of his garden produce.
Mike can make 3 batches of salsa and 3 batches of tomato sauce using all of his garden produce.
Mike can make 6 batches of salsa and 3 batches of tomato sauce using all of his garden produce.
Mike can make 6 batches of salsa and 9 batches of tomato sauce using all of his garden produce.

Answers

Answer:

C)Mike can make 6 batches of salsa and 3 batches of tomato sauce using all of his garden produce.

Step-by-step explanation:

Tomas learned that the product of the polynomials (a + b)(a2 – ab + b2) was a special pattern that would result in a sum of cubes, a3 + b3. His teacher put four products on the board and asked the class to identify which product would result in a sum of cubes if a = 2x and b = 1.Which product should Tomas choose?

(2x + 1)(2x2 + 2x – 1)
(2x + 1)(4x3 + 2x – 1)
(2x + 1)(4x2 – 2x + 1)
(2x + 1)(2x2 – 2x + 1)

Answers

This is a simple substitution problem. Clearly the answer here is (2x + 1)(4x2 – 2x + 1). We just have to replace a with 2x and b with 1. The tricky part here is the first term in the second group of terms. 2x is to be squared. Common mistake here is raising the x with 2 and not including the coefficient.

The product that Tomas should choose given that the pattern resulted in a sum of cube is (2x + 1)(4x² – 2x + 1)

Data obtained from the question

Polynomial => (a + b)(a² – ab + b²)
a = 2x
b = 1
Product =?

How to determine the product

(a + b)(a² – ab + b²)

But

a = 2x

b = 1

Substituting the value of a and b, we have

(a + b)(a² – ab + b²)

(2x + 1)[(2x)² – (2x × 1) + 1²]

(2x + 1)(4x² – 2x + 1)

Thus, the product that Tomas should choose is (2x + 1)(4x² – 2x + 1)

Learn more about polynomial:

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Hey! Im counting on you guys!Ken drove 174 miles in 3 hours. The equation y = 57x represents the distance in miles, y, Brenda drove in x hours. Determine who had the faster driving speed and by how much.

Please form your answers like so:
Of the two drivers, (...) had the faster driving speed by (...) mile(s) per hour.

Answers

Answer:

Ken is faster by 1 mile per hour

Step-by-step explanation:

Ken's speed

174/3 = 58 mph

Brenda's speed

57 mph as per formula

Comparing the values, we see that

Ken is faster by 58 - 57 = 1 mile per hour

Answer:

To find Ken's speed divide total distance by total time:

174 miles / 3 hours = 58 miles per hour.

In the equation for Brenda, the 57 is the miles per hour because you would multiply that by x ( hours) to get total miles (y).

Ken had the faster driving speed.

Step-by-step explanation:

NEED HELP ASAP WILL MARK BRAINLIEST!!!!!!!!!What is the solution to the system of equations

-4x - 5y - z = 18
-2x - 5y -2z=12
-2x + 5y +2z=4

A) (4,0,2)
B) (-4,0,-2)
C) (-4,2,0)
D) (-4,0,2)

Answers

Answer:

Step-by-step explanation:

When we have multiple answers, we can check each to find the solution. Each ordered pair is written as (x,y,z). We substitute each into the equations to find which satisfy all equations and which do not.

A) (4,0,2)

-4(4)-5(0)-(2)=18

-16-0-2=18

$-18\neq18$

Not a solution

B) (-4,0,-2)

-4(-4)-5(0)-(-2)=18

16-0+2=18

18=18 is true. We now try the other equations.

-2(-4)-5(0)-2(-2)=12

8-0+4=12

12=12

We try the last equation.

-2(-4)+5(0)+2(-2)=4

8+0+-4=4

4=4

We no longer need to try C or D because a system of equations only has one solution. B is the solution.

The number of tickets sold to a charity basketball games is a function of the price charged with rule n=4,000-50p

Answers

Answer:

the function n=4,000-50p represents the number of tickets sold for a charity basketball game as a function of the price charged. The constant term 4,000 represents the maximum number of tickets sold at a price of zero, and the coefficient of -50p indicates the rate at which the number of tickets sold decreases with an increase in price.

hope this helps a little

Step-by-step explanation:

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