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. Craig read 3 books each week for 3 weeks. Joe read 4 books a week for 3 weeks. How many more books did Joe read? Choose the answer that has the correct expression and the correct answer to the question
4x3+4x4; Joe read 28 more books than Craig.
0 4x3 - 3x3; Joe read 27 more books than Craig.
3x3-4x 3; Joe read 3 more books than Craig.
0 4x3 - 3x3; Joe read 3 more books than Craig
Answers
Answer:
4*3 - 3*3;
Joe read 3 more books than Craig
Step-by-step explanation:
Given
Craig:
3 books weekly for 3 weeks
Joe:
4 books weekly for 4 weeks
Required
How many more books did Joe read.
First, we need to determine number of books Craig reads
If in a week, Craig reads 3 books
Then in 3 weeks, Craig reads 3 * 3 books
Next, we need to determine number of books Joe reads
If in a week, Joe reads 3 books
Then in 4 weeks, Joe reads 4 * 3 books
Next, we determine the difference;
[tex]Difference = 4 * 3 - 3 * 3[/tex]
[tex]Difference = 12 - 9[/tex]
[tex]Difference = 3[/tex]
Hence, Joe reads 3 more books
Option D answers the question.
What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (2, −1)? y = Negative one-thirdx − One-third y = Negative one-thirdx − Five-thirds y = 3x − 3 y = 3x − 7
Answers
Answer:
D, y = 3x − 7
Step-by-step explanation:
Edge 2020, mark as brainliest plz
Answer:
The Answer is D.
Step-by-step explanation:
Identify the most reasonable unit to measure the volume of a glass of orange juice.
Answers
Answer:
Liters
Step-by-step explanation:
Every recipient that has a volume of liquid in it,you mesure it in liters!
HELP it’s like 3:00 A.M and this is due at 3:20 A.M and my brain is completely dead.
Answers
Answer: Bigger X = 17 Smaller X = 1/3
Step-by-step explanation:
for the larger number
1x - 8 = 9 (equation)
X = 17 (the result)
for the smaller number
9x - 2 = 1 (equation)
X = 1/3 (the result)
Quadratic functions. Did I do it right?
Answers
Answer:
1) The graph is opening upwards
2) Axis of symmetry is x=-2
3) Vertex: (-2, 1) minimum y=1
4) y intercept is (0, 9)
5) domain: x|x ∈ R (All real numbers)
6) Range y|y ≥ 1
simplify I know I spelled it wrong
Answers
Answer:A
Step-by-step explanation:
Answer:
D ) 25t + 10
Step-by-step explanation:
Re-order terms so constants are on the left:
(5t+2) 5
5 (5t +2)
Distribute:
5 (5t +2)
25t +10
Answer:
25t +10
Mallory's mom gave her $25.00 to buy school supplies. Mallory needs to buy 5 notebooks and some mechanical pencils. If each notebook costs $2.19 and each mechanical pencil costs $1.50, how many mechanical pencils can Mallory buy using only the money her mom gave her?
Answers
Answer:
Mallory can buy 16 notebooks
Step-by-step explanation:
You divide 25.00 by 1.50 which is 16.6 repeating. so, she can only buy 16 notebooks
Answer:
she can buy 9 pencils
Step-by-step explanation:
line with a slope of 2 and passes through point (3, 5)
Answers
Answer:
i dont get what you are trying to say is their a graph u can show
Step-by-step explanation:
Answer:
y = 2x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 2, thus
y = 2x + c ← is the partial equation
To find c substitute (3, 5) into the partial equation
5 = 6 + c ⇒ c = 5 - 6 = - 1
y = 2x - 1 ← equation of line
For exercises 4-6, use the imaginary unit to write an equivalent expression for
the radicals.
Just number 4 and 6
Answers
6) 2(11i)
I’m pretty sure these are correct
solve the equation
pls help me
Answers
Whích best describes the range of the function f(x) = } 6)* after it has been reflected over the x-axis?
all real numbers
all real numbers less than 0
all real numbers greater than 0
O all real numbers less than or equal to 0
Answers
Answer:
c
Step-by-step explanation:
im right i took the test
A child tosses a baseball up into the air. On its way down, it gets caught in a tree for several seconds
before falling back down to the ground.
14
12
10
8
height (feet)
6
4
2
2
3 4 5 6 7 8 9 10
time (seconds)
Select the best description of the range of this function.
The range includes all numbers from 5 to 12.5.
The range includes all integers between 0 and 12.5.
The range includes all numbers from 0 to 8.5.
The range includes all numbers from 0 to 12.5.
Answers
Answer:
The range includes all numbers from 5 to 12.5.
Step-by-step explanation:
The range is along y- axis and the domain is along x- axis.
Range is given in heights and domain is given in time seconds.
It can depicted that for t= 0 secs the ball is at 5 feet and so on .
Therefore the range is given by numbers from 5 to 12.5.
Whereas the domain is given by numbers 0 t0 8.5 seconds
The range is the values of 'y' and the domain is the values of 'x'. So, the range of the includes all numbers between 5 and 12.5 and the domain includes all numbers between 0 and 8.5.
Given :
A child tosses a baseball up into the air. On its way down, it gets caught in a tree for several seconds before falling back down to the ground.
The graph attached below shows the given scenario that "A child tosses a baseball up into the air. On its way down, it gets caught in a tree for several seconds before falling back down to the ground".
The y-axis shows the height of the ball in feet from the ground and the x-axis shows the time in seconds.
The range is the values of 'y' and the domain is the values of 'x'. So, the range of the includes all numbers between 5 and 12.5 and the domain includes all numbers between 0 and 8.5.
Therefore, the correct option is A) The range includes all numbers from 5 to 12.5.
For more information, refer to the link given below:
https://brainly.com/question/11897796
A cheesecake recipe says, "Mix 12 oz of cream cheese with 15 oz of sugar. How many ounces of cream cheese are there for every ounce of sugar?_ How many ounces of sugar is that for every ounce of cream cheese?
Answers
ounces of sugar for every ounce of cream cheese = 15/12 = 5/4 ounces
Amanda’s dog eats 12\frac{1}{2}12 2 1 pounds of dog food in 3 weeks.
Answers
Answer:
y=mx+b
Step-by-step explanation:
What is the slope of y = -42 - 3?
Answers
PLEASE HELP ME!!!!!!!!!!!!!!!
You received a $150 gift certificate to a clothing store. The store sells T-shirts for $17 and dress shirts for $26. You want to spend no more than the amount of the gift certificate. You want to leave at most $8 of the gift certificate unspent. You need at least dress . What are all of the possible combinations of T-shirts and dress shirts you could buy?
seclect all that apply
A: 4 t-shirts and 3 dress shirts
B: 1 t-shirt and 5 dress shirts
C: 5 t-shirts and 2 dress shirts
D 2 t-shirts and 4 dress shirts
Answers
Answer:
d I think
Step-by-step explanation:
blablablablabal
Match the term with the definition. (5 points) Column A 1. Line : Line 2. Line Segment : Line Segment 3. Ray : Ray 4. Point : Point 5. Vertex : Vertex Column B a. a location, has no dimension b. the common endpoint of two segments or rays that form the "corner" of an angle c. an infinite number of points extending in opposite directions that has only one dimension d. part of a line that has two endpoints e. part of a line that has one endpoint and continues in one direction infinitely
Answers
Answer:
a. Point.
b. Vertex.
c. Line.
d. Line segment.
e. Ray.
Step-by-step explanation:
a. Point: a location, has no dimension. Also, a point doesn't have a size i.e no length, depth, breadth or height.
b. Vertex: is the common endpoint of two segments or rays that form the "corner" of an angle.
c. Line: is an infinite number of points extending in opposite directions that has only one dimension.
d. Line segment: is part of a line that has two endpoints.
e. Ray: is part of a line that has one endpoint and continues in one direction infinitely.
You buy a used car for $20,000. It depreciates at the rate of 21% per year. Find the value of the car for the given years.
A. 5 years.
B. 8 years.
Answers
Answer:
a is 840 ,b is 525
Step-by-step explanation:
At the end of each year, its value is down to 79%, which is 0.79 times its value at the start of the year. Keep this up for n years and the value is
V(n) = $20,000 (0.79)n,
where n is the number of years elapsed from when the value was $20,000. Just plug in n=5 and n=8, evaluate, and get your 2 answers.
Answer:
A. 5 years
Step-by-step explanation:
21% of 20,000 is 4200, mutiply that by 5 and get $20,000
what is the equation of the line in slope intercept form
Answers
Answer:
y=-5x
Step-by-step explanation:
Hi. ITS URGENT.
I need help with No 5 and 7 (see image)
Please show workings
Answers
Answer:
5. a^3 + b^3 = (a+b)^3 - 3ab(a+b)
Step-by-step explanation:
(a+b)^3
= (a+b) (a+b) (a+b)
={(a+b) (a+b)} (a+b)
={a(a+b) + b(a+b)} (a+b)
=(a^2 + ab + ab + b^2) (a+b)
=(a^2 + b^2 + 2ab) (a+b)
=a^2(a+b) + b^2(a+b) + 2ab(a+b)
=a^3 + a^2b + ab^2 + b^3 + 2a^2b + 2ab^2
=a^3 + b^3 + 3a^2b + 3ab^2
=a^3 + b^3 + 3ab(a+b)
(a+b)^3 = a^3 + b^3 + 3ab(a+b)
(a+b)^3 - 3ab(a+b) = a^3 + b^3
a^3 + b^3 = (a+b)^3 - 3ab(a+b)
Hope this helped!
Answer:
I am just giving the expansion, so that you can substitute the values and solve it
What is 2/3 divided by 1/2 ?
A. 3/4
B. 4/3
C. 1/3
D. 1/4
Answers
Answer:
B. 4/3 is your answer dear.
Step-by-step explanation:
Solve
2/3 * 2/1
coz it is reciprocal .
you'll get 4/3
Hope you got it.
plz answer its due today!!
Answers
Answer:
-5/8
Step-by-step explanation:
Let p(x) = -2x - 9. If p(x) = -19, find x.
Answers
Answer:
x=5
Step-by-step explanation:
Step 1: Flip the equation.
−2x−9=−19
Step 2: Add 9 to both sides.
−2x−9+9=−19+9
−2x=−10
Step 3: Divide both sides by -2.
Exact Form:
x = 9/17
Decimal Form:
x = 0.52941176…
Edit: "but what are the steps to get 9/17"
1. Move all terms containing x to the left side of the equation.
2. Divide each term by −17 and simplify.
i need some help with this
Answers
Answer:
d
Step-by-step explanation:
hope this is right
I WILL GIVE YOU BRAINLIEST Simplify the expression using the distributive property.
4(3x + 2)
A. 7x + 8
B.12x + 2
C. 7x + 6
D.12x + 8
SHOW YOUR WORK PLZSSSSSSS
Answers
D
Like the other person said
Delia measured a doorway to be 1 meter wide. Which of these is a nearly equivalent measurement? A 15 miles B 10.5 yards C 3.3 feet D 98.7 inches
Answers
Answer:
c
Step-by-step explanation:
I need help with this Show work on each one
Answers
Answer:
first one is 1
Second is -2/3
Ghosts are still one of the greatest frights. The number of scares a ghost will get is modeled with the equation
`y=5x+2`. Skeletons, on the other hand, have become rather common and no one is scared of them anymore. In fact, they often are scared themselves more than they scare anyone else. If the equation for skeletons is perpendicular to the equation for ghosts and passes through the point (10, -4), what is the equation for skeletons?
Answers
Answer:
i don't know the answer but i really want the points
Step-by-step explanation:
Solve plzzz ASAP due today
Answers
Answer:
#3- x=2.73
#4- x=8
Step-by-step explanation:
Answer: X = 3 / X = 8
Step-by-step explanation:
3. (Angles add up to 180)
30x + 4 + 86 = 180
30x + 90 = 180
subtract 90 from both sides
30x = 90
Now divide by 30
x = 3
Check your work ( input 3 to the equation)
30(3) + 4 + 84
90+ 90 = 180 it works :)
4. (Angles are adjacent to each other so there equal)
10x - 3 = 77
add 3 to both sides
10x = 80
divide it by 10
x = 8
Check your work ( input 8 to the equation )
10(8) -3 = 77
80 - 3 = 77
77 = 77
Which expression could be used to determine the cost of a $50 video game after a 20 percent discount?
50 dollars (0.20)
50 dollars minus left-bracket (50 dollars) (0.08) right-bracket
50 dollars minus 0.80
50 dollars (0.80). please a b c or d?
Answers
Answer:
d
Step-by-step explanation:
to find a discount you would multiply 50(0.20) whatever amount you get you would subtract that from 50
this is the same as 50(0.80)