Answers
The relation between the linear and recursive functions are given as follows:
f(n) = -n < - > {-1,-2,-3,-4...}, where f(1) = 1 and f(n + 1) = f(n - 1) - 1 for n > 1.f(n) = 2n - 3 < - > {-1,1,3,5...}, where f(1) = -1 and f(n + 1) = f(n - 1) + 2 for n > 1.f(n) = -n + 5 < - > {4,3,2,1...}, where f(1) = 4 and f(n + 1) = f(n - 1) - 1 for n > 1.f(n) = 2n + 2 < - > {4,6,8,10...}, where f(1) = 4 and f(n + 1) = f(n - 1) + 2 for n > 1.What is a linear function and how does it relate to a recursive function?A linear function is modeled according to the following rule:
f(x) = mx + b
In which:
m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis, that is, when x = 0.Considering the concepts of a linear function, the recursive function is given as follows:
f(n) = f(n - 1) + m for n > 1. f(1) for n = 1. (numeric value of the linear function when x = 1).The linear function with first term -1 and slope -1 is given by:
f(n) = -n.
Hence:
f(n) = -n < - > {-1,-2,-3,-4...}, where f(1) = 1 and f(n + 1) = f(n - 1) - 1 for n > 1.
The linear function with first term -1 and slope 2 is given by:
f(n) = 2n - 3
Hence:
f(n) = 2n - 3 < - > {-1,1,3,5...}, where f(1) = -1 and f(n + 1) = f(n - 1) + 2 for n > 1.
The linear function with first term 4 and slope -1 is given by:
f(n) = -n + 5
Hence:
f(n) = -n + 5 < - > {4,3,2,1...}, where f(1) = 4 and f(n + 1) = f(n - 1) - 1 for n > 1.
The linear function with first term 4 and slope 2 is given by:
f(n) = 2n + 2
Hence:
f(n) = 2n + 2 < - > {4,6,8,10...}, where f(1) = 4 and f(n + 1) = f(n - 1) + 2 for n > 1.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
Related Questions
Two similar figures have sides in the ratio of 2:3. If a side of the smaller triangle has a length of 7, what is the length of
the corresponding side of the other triangle?
014
021
02
0 10/
Answers
Answer:
10 1/2
Step-by-step explanation:
The side of the smaller triangle has a length of 7, the larger triangle will be:
= (7 × 3)/2
= 10 1/2
APPLYING THE STA
How might this standard appear on a test?
Use proportional relationships to complete each question.
1) Fill the table. Round to the nearest cent.
Original
Cost
$24
$120
$60
Discount
Percentage
20%
15%
45%
Sale
Price
Sales Tax
Percentage
8.5%
7%
896
Sales Tax
Amount
Total
Cost
Answers
Answer:
Step-by-step explanation:
a
f(t)=4t-2 g(t)=2t+2 Find (3f-4g)(t)
Answers
Solving the Question
We're given:
[tex]f(t)=4t-2[/tex][tex]g(t)=2t+2[/tex][tex](3f-4g)(t)=?[/tex][tex](3f-4g)(t)[/tex] is the same as [tex]3f(t)-4g(t)[/tex]. Now, we can just plug in the functions as if they're variables in an equation.
[tex]3f(t)-4g(t)[/tex]
[tex]= 3(4t-2)-4(2t+2)\\= 12t-6-8t-8\\= 4t-14[/tex]
Answer[tex](3f-4g)(t)= 4t-14[/tex]
PLEASE HELP ME, IM BEGGING, IM ACTUALLY GOING TO CRY IF I GET THIS WRONG. A family camping in a national forest builds a temporary shelter with a tarp and a 4-foot pole. The bottom of the pole is even with the ground, and one corner is staked 5 feet from the bottom of the pole. What is the slope of the tarp from that corner to the top of the pole?
Answers
PLEASE HELPPP
Subject: Trigonometry
Answers
By using the trigonometric function of cosine, we conclude that the length of the hypotenuse is approximately equal to 7.2 units.
How to determine the length of the hypotenuse by trigonometric functions
Right triangles are triangles such that one of its internal angles is a right triangle. Fundamentally, trigonometric functions are relationships between two distinct sides of a right triangle.
The picture show that the length of one leg and the measure of the angle between that leg and the hypotenuse are known, but the length of the hypotenuse does not. By using concepts of trigonometric functions, we can find the length of the hypotenuse by using the cosine function:
cos θ = s / x
cos 33° = 6 / x
x = 6 / cos 33°
x = 6 / 0.839
x ≈ 7.154
The length of the hypotenuse is approximately equal to 7.2 units.
To learn more on trigonometric functions: https://brainly.com/question/14746686
#SPJ1
3(2x − 1) < 2(4 + 3x)
Answers
Answer:
Step-by-step explanation:
3(2x−1)<2(4+3x)
Step 1: Simplify both sides of the inequality.
6x−3<6x+8
Step 2: Subtract 6x from both sides.
6x−3−6x<6x+8−6x
−3<8
Step 3: Add 3 to both sides.
−3+3<8+3
0<11
any number below 11 is a solution.
1/6d + 2/3 = 1/4(d - 2)
Answers
distribute 1/4 to (d-2)
using a(b-c) = ab -ac
1/6d + 2/3 = 1/4d - 1/2
substract 2/3 from both sides
1/6d = 1/4d -7/6
subtract 1/4d both sides
-1/12d = -7/6
multiply both sudes by -12
d = 14
Need help on number 5!
Answers
And 2,4,5,6,7
last year springfeild middle school had 620 students. this yearz it jas 559 students. To the nearest tenth, what is the precent decrease
Answers
The percentage decrease is 9.83%.
The previous year Springfield middle school students were 620. This year it is 559 students.
Here we have to find the decrease in the percentage of students from the previous year.
The decrease in the students = 620- 559
= 61
Percentage decrease = (decrease/number of students last year)× 100
= (61/ 620 )× 100
= 0.09838 ×100
= 9.83%
Therefore the percentage decrease in the number of students from the previous year is 9.83%
To know more about the percentage refer to the link given below:
https://brainly.com/question/24877689
#SPJ9
can someone solve this?
Answers
Answer:
2L+2W
Step-by-step explanation:
U JUST MOVE THE 2 TO THE L AND MOVE THE 2W TO THE OTHER SIDE. I THINK MY ANSWER IS RIGHT BUT MAYBE WAIT FOR ANOTHER PERSON
Confirmed Solution:
[tex]p=2l+2w[/tex]
Hope this helps!
Answer the question in photo [ Brainliest + easy points ]
Answers
Answer:
TU = 27
Step-by-step explanation:
ST + TU = SU
(8x - 11) + (14x - 15) = 19x - 17
8x - 11 + 14x - 15 = 19x - 17
22x - 26 = 19x - 17
22x - 19x = 26 - 17
3x = 9
x = 3
TU = 14x - 15 = 14(3) - 15 = 27
If 3x6 = 15, then x =
Answers
Answer: + or - in between the 3x and 6? Can be either 7 or 3
Step-by-step explanation:
3x+6=15.
Subtract '6' on both sides.
3x=9.
Divide by '3'.
x=3
3x-6=15.
Add '-6' on both sides.
3x=21
Divide by '3'.
x=7
Again, it solely depends on your sign in between the first two numbers.
in a data set of 1,2,3,3,4,4,4,4,5,5,6,70 what is the standard deviation?
Answers
We need to know the concept of mean and standard deviation to solve the problem.The standard deviation of the data set is 18.36
The given dataset is 1,2,3,3,4,4,4,4,5,5,6,70, inorder to find the standard deviation of the data set we need to first find the mean of the dataset. Mean of a dataset means the average of the set of numbers. We divide the sum of all the numbers in the data set by the size of the set. We represent mean by μ.
μ=[tex]\frac{1+2+3+3+4+4+4+4+5+5+6+70}{12} =\frac{111}{12} =9.25[/tex]
Standard deviation measures the dispersion of a dataset relative to it's mean, the square of standard deviation is variance.
The formula for standard deviation is :
σ=[tex]\sqrt{\frac{(1-9.25)^{2}+(2-9.25)^{2} +...+(70-9.25)^{2} }{12} } =\sqrt{\frac{68.0625+52.5625+78.125+110.25+36.125+10.5625+3690.5625}{12} } \\=\sqrt{\frac{4046.25}{12} } =\sqrt{337.1875} =18.36[/tex]
Thus we found the standard deviation of the data set to be 18.36
Learn more about standard deviation from here:
https://brainly.com/question/27393915
#SPJ9
Please help with problem 18
Algebra 1
Answers
The value of x is -1 and the values on both sides are the same, hence the equation has infinite number of solution
Solving Linear equationLinear equations are equation that has a leading degree os 1. Given the equations below:
-x +4 = x + 6
Collect the like terms
-x - x = 6 - 4
-2x =2
Divide both sides by -2
-2x/-2 = 2/2
x = -1
For the expression
5n + 7 =. 7(n+1) - 2n
5n + 7 = 7n + 7 - 2n
simplify
5n - 5n = 7 - 7
0n = 0
Since the values on both sides are the same, hence the equation has infinite number of solution
Learn more on linear equation here: https://brainly.com/question/1884491
#SPJ1
(a) two lawn car companies are competing for a landscaping contract. company a charges $250 monthly consulting fee plus $10 per square foot of landscaping, whereas company b charges a $90 monthly consulting fee plus $12 per square foot of landscaping. for how many square feet of landscaping will the two companies charge the same amount?
Answers
Total charge by company A for 80 sq.feet = 250+10(80)= $1050
Total charge by company B for 80 sq.feet = 90+12(90)=$1170
Let x be the no.of square feet for landscaping
Company A
Monthly consulting fee = $250
Cost of landscaping of 1 sq.feet = $10
Cost of landscaping of x sq.feet = $10x
So, Total charge by company A = 250+10x ---1
Company B
Monthly consulting fee = $90
Cost of landscaping of 1 sq.feet = $12
Cost of landscaping of x sq.feet = $12x
So, Total charge by company B = 90+12x ---2
Now we are supposed to find how many square feet of landscaping will the two companies charge the same amount
So, Equate 1 and 2
250+10x = 90+12x
160=2x
80=x
So, the two companies charge the same amount for 80 sq.feet
Total charge by company A for 80 sq.feet = 250+10(80)= $1050
Total charge by company B for 80 sq.feet = 90+12(90)=$1170
learn more of square foot here
https://brainly.com/question/11109636
#SPJ4
Absolute Value
-2 l3dl =4
Answers
Answer -2|3d| = 4
Step-by-step explanation:
no solution
What is 1.83 as a fraction?
Answers
Answer:
183/100
Step-by-step explanation:
hope this works :)
Answer:
183/100 as a fraction of 1.83
Which choice is equivalent to the quotient below?
√32
√√2
OA. √24
√2
OB.
C. 2
OD. 4
Answers
The answer would be D. 4
because you would multiply the numerator and denominator by the conjugate.
What is the acceleration in this graph?
Answers
Answer:
70 m / 40 seconds = 7/4 m/s or 1.75 m/s
Step-by-step explanation:
the line stops at 0.7 time = 40 seconds
70 m / 40 seconds = 7/4 m/s or 1.75 m/s
HELP.............................! !
Answers
I hope it helps:)
Answer:
It would be 28.69.
Explanation:
4.99 x [tex]5 \frac{3}{4}[/tex] = 28.6925
Because of the kind of number (28.6925), you will have to round up.
To round up the number has to be a 5 or higher. Well, you have a 9 and then a 2. A 2 can't round up a 9, so you just end up discarding the 2 and the 5 at the end of the number.
Henceforth, you are left with 28.69.
-----------------------------------------------
Hope this makes sense and is correct!
God bless! :)
Find the slope of the following lines
Explain how you got the answer
Answers
From the given graph, the slope of the given line is [tex]m=\frac{-4}{3}[/tex]
Given,
The points
[tex](x_{1},y_{1})=(-2,3)[/tex]
[tex](x_{2},y_{2})=(1,-1)[/tex]
The slope of the line m= [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Substitute the values in the equation
[tex]m=\frac{(-1)-(3)}{1-(-2)} \\m=\frac{-1-3}{1+2}\\ m=\frac{-4}{3}[/tex]
Hence, the slope of the given line is [tex]m=\frac{-4}{3}[/tex]
Learn more about slope of the line here
brainly.com/question/14511992
#SPJ1
a company has a competition to win a car. each contestant needs to pick a positive integer. if there’s at least one unique choice, the person who made the smallest unique choice wins the car. if there are no unique choices, the company keeps the car and there’s no repeat of the competition. it turns out that there are only three contestants, and you’re one of them. everyone knows before picking their numbers that there are only three contestants. how should you make your choice?
Answers
Each participant selects 'a' with a probability of (1/2)^a;
the lowest particular wonderful integer (LUPI) recreation is a recreation that, relying on who you ask and while 12 months you ask it, has either been pretty thoroughly studied or no longer studied in any respect. There seem to be a few wonderful solutions; for instance, one symmetric mixed method is as follows if all integers are approved:
What is probability explain?
probability is a measure of the chance of an event to arise. Many activities can't be expected with total fact. we will predict handiest the chance of an event to occur i.e. how possibly they are to happen, using it
probability is the department of mathematics regarding numerical descriptions of ways probably an event is to occur, or how in all likelihood it is that a proposition is genuine. The opportunity of an occasion is various among zero and 1, where, more or less speakme, zero indicates impossibility of the event and 1 suggests truth
To learn more about probability this; visit: https://brainly.com/question/14210034
#SPJ4
Please help with 2. And 3. I took a picture
Answers
Answer:
Step-by-step explanation:
its ratio
he spaces are usually stocked with standard office [marker for question 26] equipment, such as photocopiers, printers, and fax machines.
Answers
"The spaces are usually stocked with standard office [26] equipment,
such as photocopiers, printers, and fax machines." Option A: No Change, i.e., no sentence correction is needed.
What is sentence correction?Sentence correction or sentence improvement is a type of grammatical practice where a sentence is given with a word or a phrase that requires grammatical changes or improvement.
Now,
When giving particular examples of something you're describing, we utilize the phrase "such as."Unless the example comes right at the end of the sentence, use a comma before "such as" and after your examples if they are not crucial to the truth of your sentence. A comma should only be used before "such as," not after it, as the examples of office equipment are near the end of the phrase while being crucial to its content. As a result, Option A is correct and no correction is necessary.To learn more about sentence correction, refer to the link: https://brainly.com/question/14632568
#SPJ4
the mass of the combined coins is 75 grams. Each penny has
Stephanie adds pennies, nickels and quarters to a scale until
a mass of 2.5 grams, each nickel has a mass of 5 grams and each quarter has a mass of 5.7 grams.
Create an equation to model this situation, where x is the number of pennies, y is the number of nickels and z is the
that the mass of the combined coins is exactly 75 grams.
number of quarters that Stephanie can put on the scale so
Answers
The required equation is 2.5x + 5y + 5.7z = 75.
What is mass?Mass is measured in terms of weight of body. Gram, kilogram, and pounds are some of the standard mass units to measure.
Given that,
Pennies, nickels, and quarters are added to a scale by Stephanie until the combined weight of the coins is 75 grams.
Number of pennies = x
Each pennies has a mass = 2.5 grams
Mass of x pennies = 2.5x grams
Number of nickels = y
Each nickels has a mass = 5 grams
Mass of y nickels = 5y grams
Number of Quarters = z
Each Quarter has a mass = 5.7 grams
Mass of z Quarters = 5.7z grams
Total Mass = Mass of x Pennies + mass of y nickels + mass of z quarters
= 2.5x + 5y + 5.7z grams
Total Mass = 75 grams
Equation both is 2.5x + 5y + 5.7z = 75
The required equation is 2.5x + 5y + 5.7z = 75.
To know more about Mass visit:
https://brainly.com/question/19694949
#SPJ9
Lengths (mm)
Frequency
200 - 209
1
210 - 219
16
220 - 229
71
230 239
108
240 - 249
83
250 - 259
18
260 269
3
What is the lower class boundary for the first class?
class boundary =
Enter an integer or decimal number
Answers
Answer:
270 9764
359
548
69
80
554
331
594
850
667
216
8674
213
253
5
3
64
7
45
692
213
649
8574
6646
549
837
849
In a week, a man received a paycheck for $826.60. The withholding for taxes was $91.40. If he worked 34 hours in that week, what is his hourly pay rate?
Answers
The hourly rate will be $21.6
Percentages and taxesTaxes are money charged from the good bought or sold. Given the following parameters
Amount received = $826.60
Tax paid = $91.40
Balance = 826 - $91.40
Balance = $734.6
This shows that the man collected $734.6 for a 34 hours work. The hourly rate will be;
Hourly rate= $734.6/34
Hourly rate= $21.6
Hence the hourly rate will be $21.6
Learn more on unit rate here: https://brainly.com/question/4895463
#SPJ1
potatoes cost janice $1 per pound, and she has $5.00 that she could possibly spend on potatoes or other items. suppose she feels that the first pound of potatoes is worth $1.50, the second pound is worth $1.14, the third pound is worth $1.05, and all subsequent pounds are worth $0.30 per pount.
Answers
A . 3 pounds of potatoes
B . 2 pounds of potatoes
A . Janice will purchase potatoes until the value of potatoes is less than the cost of potatoes. Janice has $5.00 to spend on potatoes and the cost of potatoes is $1.00.
By assuming that the First pounce of potatoes is worth $1.50. which is greater than $1.00. If the second pound is worth $1.14, then Janice will purchase these as well, since the value is more than $1.00. If the remaining pounds are worth $0.30 then Janice will not purchase these because the value is less than the cost.
Thus Janice will purchase 3 pounds of potatoes for the Total cost of $3.00
B. Now assume Janica has only $2.00 to spend on potatoes. She will purchase the first pound which is $1.50 and the second pound which is $1.14. She now spends her entire amount of money on potatoes. If she want to purchase she could not do that.
Thus Janice will purchase 2 pounds of potatoes at a total cost of $2.00
To know more about the Solution refer to the given link below:
https://brainly.com/question/24127539
#SPJ4
The complete question is:
Potatoes cost Janice $1 per pound, and she has $5.00 that she could possibly spend on potatoes or other items. If she feels that the first pound of potatoes is worth $1.50, the second pound is worth $1.14, the third pound is worth $1.05, and all subsequent pounds are worth $0.30 per pound, how many pounds of potatoes will she purchase? How many pounds will she purchase if she has only $2 to spend?
The price of a CD decreased from $18 to $12. What is the percent of decreased?
Answers
Percentage decrease = Difference/Original price*100
[tex] = \frac{18 - 12}{18} \times 100 = \frac{600}{18} = 33.33\%[/tex]
Hope this helps :)
WILL GIVE BRAINLIST TO BEST ANSWER JUST PLEASE HELP!!!!!!
A plumber earns $75 for a repair job, plus an additional $45 per hour he works. On Tuesday, he completed 2 repair jobs and earned a total of at least $465.
Part A: Write an inequality that can be used to determine h, the numbers of hours the plumber worked Tuesday.
Answers
Answer:
He worked 7 hours
Step-by-step explanation:
X= Number of jobs, H= Hours worked T= Total money made
firstly we have to arrange this into a formula, which will allow you to insert any a value of one variable and find the other variable
this equation is 75x + 45h = T
from this question we know that he worked 2 jobs and made a total of 456$
Adding these into the equation we get:
(75*2) + 45h = 465
solving to find h by isolating the variable, the final answer will be
h = 7