Answers
Answer:
The sequence is:
[tex]\:\left\{a_{1,\:}a_2,\:a_3,\:a_4\right\}\:=\:\left\{-10,\:-23,\:-62,\:-179\right\}[/tex]
Step-by-step explanation:
Given the recursive function
[tex]a_n=3a_{n-1}+7[/tex]
As the first term is -10.
i.e.
[tex]a_1=-10[/tex]
Putting n = 2 to determine the 2nd term
[tex]a_n=3a_{n-1}+7[/tex]
[tex]a_2=3a_{2-1}+7[/tex]
[tex]a_2=3a_1+7[/tex]
[tex]= 3(-10)+7[/tex] ∵ [tex]a_1=-10[/tex]
[tex]= -23[/tex]
Putting n = 3 to determine the 3rd term
[tex]a_n=3a_{n-1}+7[/tex]
[tex]a_3=3a_{3-1}+7\:\:[/tex]
[tex]a_3=3a_2+7\:\:\:\:\:[/tex]
[tex]= 3(-23)+7[/tex] ∵ [tex]a_2=-23[/tex]
[tex]= -62[/tex]
Putting n = 4 to determine the 4th term
[tex]a_n=3a_{n-1}+7[/tex]
[tex]a_4=3a_{4-1}+7[/tex]
[tex]a_4=3a_3+7\:\:\:\:\:[/tex]
[tex]= 3(-62)+7[/tex] ∵ [tex]a_3=-62[/tex]
[tex]=-179[/tex]
Therefore, the sequence is:
[tex]\:\left\{a_{1,\:}a_2,\:a_3,\:a_4\right\}\:=\:\left\{-10,\:-23,\:-62,\:-179\right\}[/tex]
Related Questions
Each runner is carrying an 8 ounce bottle of water, a 2.1 ounce energy bar, and a 3 ounce energy drink. Write an expression in simplest form that represents the weight carried by y runners. Interpret the expression.
Answers
Answer:
13.1y
Step-by-step explanation:
;-; I'm sorry if I'm wrong
From 15 degrees to 21 degrees
Answers
Angle x is (2n + 12) and angle y is (3n + 18). Find the measure of angle x.
Answers
Answer: X and Y are supplementary angles. The sum of the supplementary angles is 180.
So, X + Y = 180
180 = 2n+12 + 3n + 18
180 = 5n + 30
5n = 150
n = 30
X = 2n+12
X = 2(30) + 12
X = 72
Y = 3n + 18
Y = 3(30) + 18
Y = 108
Step-by-step explanation:
Serial numbers for a product are to be made using 2 letters followed by 2 digits. The letters are to be taken from the first 6 letters of the alphabet, with no repeats. The digits are taken from the10 digits , with no repeats. How many serial numbers can be generated?
Answers
Answer:
0
Step-by-step explanation:
0
Every female rabbit has 5 baby rabbits. What is the constant of proportionality for the ratio of baby rabbits to female rabbits? one-fourth 5 4 one-fifth
Answers
Answer:
The constant of proportionality is for every i female rabbit there is 5 baby rabbits so the constant of proportionality is 1:5
Step-by-step explanation:
Answer:It is 1:5
Step-by-step explanation: One mother gives 5 bunnies, so you would multiply both. 1 mother, 5 bunnies, 1:5. Glad to help!
Shana bought 6.2 pounds of pecans and paid $56.00. About how much per pound did the pecans cost?
$5.00
$6.00
$8.00
$10.00
Answers
Explanation: round 6.2 down to 6, and round $56.00 up to $60.00 and then see which answer choice fits. 10 multiplied by 6 is 60 which would mean about 1 pound of pecans costs $10.00
Answer:
The correct answer is D
Which polynomial function has a leading coefficient of 1 and roots 2i and 3i with multiplicity 1?
O f(x) = (x – 21)(x - 31)
O f(x) = (x +21)(x + 31)
f(x) = (x-2)(x - 3)(x - 21(x-31)
f(x) = (x + 21)(x + 3/)(x - 2)(x - 31)
Answers
Answer:
D. f(x)= (x+2i) (x+3i) (x-2i) (x-3i)
Step-by-step explanation:
Correct on edge 2020
The polynomial with a leading coefficient of 1 and roots 2i and 3i with multiplicity 1 is
f(x) = (x – 2i)(x - 3i)
Option A is the correct answer.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
f(x) = (x - 2i)(x - 3i)
It has two roots of 2i and 3i with multiplicity 1.
x² - 3ix - 2ix - 6
x² - 5ix - 6
The leading coefficient is 1.
Thus,
f(x) = (x – 2i)(x - 3i) has a leading coefficient of 1 and roots 2i and 3i with multiplicity 1.
Learn more about polynomials here:
https://brainly.com/question/2284746
#SPJ2
Calculate the slope of the line through the two points given:
a. (-3, 5) and (3, -4)
b. Without graphing the line, is the line slanted up or slanted down (from left to right)? How do
you know?
Answers
True or False? 6 ab and 4 ba are like terms
Answers
WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST!
Answers
The other equations goes up or goes down by fraction and exponential.
Number C does not cross (0,0) and in order to be proportional, it needs to be linear and cross the point of origin
A rectangular garden has a perimeter of 320 feet. The length of the garden is 8 feet longer than the width. What is the width of the garden? (hint: substitution method)
Answers
What is the value of 1/3 + 3/4
Answers
Answer:
13/12 or 1 1/12
Step-by-step explanation:
find the common denominator
Bri opened a lemonade stand on her street. It costs her $11.00 to buy the supplies each day, and she sells lemonade for $2.00 a cup. If she wants to make at least $75.00 in profits (sales - expenses) each day, what is the minimum number of cups of lemonade Bri needs to sell? Input your answer as a whole number.
Answers
Answer:
Bri would need to sell a minimum of 43 cups of lemonade.
Step-by-step explanation:
Item 10
Convert 514% to a decimal.
Enter you answer in the box below.
Answers
Answer:
5.14
Step-by-step explanation:
Which of the following is equivalent to sec2θ−1sec2θ for all values of θ for which sec2θ−1sec2θ is defined?
Answers
Answer:
[tex]2 sin^2 \theta[/tex]
Step-by-step explanation:
According to the scenario, the following information is given:
[tex]= \frac{sec^2 \theta - 1 }{sec^2 \theta}[/tex]
[tex]= (\frac{1}{\frac{cos^2\theta}{\frac{1}{cos^2\theta} }} - 1)[/tex]
[tex]= 1 - cos^2\theta\\\\= 1 - (1 - 2 sin^2 \theta)\\\\= 2 sin^2 \theta[/tex]
Therefore for the given equation, the answer is [tex]2 sin^2 \theta[/tex]
Question 11
Exit Ticket - This Thanksgiving, Grandma is looking for a DEAL on pies.
She knows that her family would eat either sweet potato pie or pumpkin pie. She has to make a
choice of buying pies. Which is better a better deal for Grandma?
A. 5 Sweet Potato Pies for $15.65
B. 6 Pumpkin Pies for $23.50
Answers
Answer:
A
Step-by-step explanation:
Because the cost per pie is less.
⦁ Explain how geologists determine the relative age of sedimentary rock layers in the Grand Canyon using Steno's Principle of Superposition? (5 points. Answer in at least 2 complete sentences.)
⦁ Explain why sedimentary rock layers of the North and South Rim(side) of the Grand Canyon are the same age, using Steno’s Principle of Lateral Continuity. (5 points. Answer in at least 2 complete sentences)
Answers
Answer:
go on PH release sum stress
Step-by-step explanation:
What is the slope of the line passing through the points (-3, 4) and (2, – 1)?
A = - 1
B = -5/3
C = 1
D = 3/5
Answers
Answer:
-1
Step-by-step explanation:
Slope (m) =y2-y1 / x2-x1
= - 1-4/2-(-3)
= - 5/2+3
= - 5/5
- 1
which pairs of ratios could form a proportion 6/9, 10/5
Answers
Answer:
for 6/9, 2/3 and 12/18 would work. For 10/5, 2/1 and 4/2 would work
Toru takes his dog to be groomed. The fee to groom the dog is $75 plus 6.75% tax. Is $80 enough to pay for the service? explain
Answers
Write the slope intercept form of the equation of each line plz
Answers
Answer: B. y = -13/6x + 8
Step-by-step explanation:
13x + 6y = 48 subtract 13x from both sides
-13x -13x
6y = -13x + 48 Divide both sides by 6
y = -13/6x + 8
Answer:
The answer is B. y = -13/6x+8
Step-by-step explanation:
3 Rapididentity
Find the value of x.
(3x + 1)(x + 19)
s
Answers
=3x^2+ 58x+19
Please show how to find the answer to (-0.6)-(7.6)=?
Answers
Answer:
-8.2
Step-by-step explanation:
(-0.6) - (7.6)
-0.6 -7.6 = -8.2
When there are two negatives, you add them together to get your negative answer.
=(-0.6)-(7.6)
-0.6 + -7.6
= -8.2
Calculating the Sales Tax at Store B Store A Store B How much sales tax will be charged at Store B? Computer Repair $1,200 $1,350 Sales Tax 6% 7% Gratuity 15% 15% Shipping Free 2% of total price
I'll mark brainleiest whoever answers.
Answers
Answer:it’s 94.50
Step-by-step explanation: 7% of 1350 is 94.50 on edge
Why does the efficient market hypothesis reduce the demand for financial advisors?
Answers
Part of a financial advisor's job is to allocate money in the best available asset or security (eg: stocks and bonds). So they look at market data and use mathematical models to help judge on where to put money. Their goal is to so called "beat the market", meaning they want to earn the best return compared to other players in the market. Doing so will allow them to "buy low, sell high" which is a common cliche in finance. Though it's a very good rule to follow of course.
The efficient market hypothesis says that whatever the stock price is currently, it reflects everything about that company. In other words, there are no hidden facts that may surprise investors to drastically change the price of the stock. All information is completely transparent. What this means is that anyone can determine where to put their money without the need for a financial advisor.
I don't think demand would be completely wiped out since even if in a 100% transparent environment, people would still prefer to have others manage their money or not want to deal with complicated math formulas. However, demand would be reduced to some degree. In reality, there are always hidden factors that don't fully contribute to the cost of a security, which is why the efficient market hypothesis isn't fully applicable in every situation. So this is likely why financial advisors are in demand and are paid well.
Given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solution. Show why this is true by solving the system of equations given. Justify the reason for each step. Hint: use addition property of equality and multiplication property of equality in your answers 5x + 2y = 7 3x - y = 2 A. To solve the system using elimination, first multiply the bottom equation by 2. Write the new system of equations B. Why is this multiplication allowed? C. What variable will be eliminated when the equations are combined after the multiplication? D. Next, add the equations together. Your answer should be a single equation with one variable. E. Why can you add the equations? F. Solve the equation for x. G. Substitute x back into one of the equations to solve for y. H. What is the solution to the system of equations?
Answers
Answer:
Explained below.
Step-by-step explanation:
The system of two equations is:
[tex]5x+2y=7...(i)\\\\3x-y=2...(ii)[/tex]
Step A:
To solve the system using elimination, first multiply the bottom equation by 2. Write the new system of equations.
[tex]5x+2y=7\\\\6x-2y=4[/tex]
Step B:
The multiplication is performed to simplify the elimination process.
Step C:
The variable that will be eliminated when the equations are combined after the multiplication is y.
Step D:
Next, add the equations together. Your answer should be a single equation with one variable.
[tex]5x+2y=7\\ +\\6x-2y=4\\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\\\11x=11[/tex]
Step E:
We can add the equation because both the equation are in the same format, i.e. ax + by = c.
Step F:
Solve the equation for x.
11x = 11
x = 1
Step G:
Substitute x back into one of the equations to solve for y.
[tex]5x+2y=7\\\\(5\times 1)+2y=7\\\\5+2y=7\\\\2y=7-5\\\\2y=2\\\\y=1[/tex]
Step H:
The solution to the system of equations is: (x, y) = (1, 1).
Henry can write 5 pages of his novel in 3 hours. At this rate how many pages can Henry right in 8 hours?
Answers
Answer:
Henry can write 13 pages in 8 hours.
Step-by-step explanation:
Choose the product. -7p 3(4p 2 + 3p - 1)
Answers
Answer:
14p -3
Step-by-step explanation:
-7p 3(4p 2+3p - 1)
3x4= 12p
3x3=9p
12+9= 21
21-7=14p
3x2=6
3x-3=-9
-9 +6= -3
= 14p -3
hope this helps :)
Find the area of a compound shape
Can you please explain
Answers
Answer:
[tex]A=292.53~m^2[/tex]
Step-by-step explanation:
Area of a Compound Shape
The shape shown in the image is made of two shapes: Half a circle of radius 8 m and a triangle of base 24 m and height 16 m.
The area of a circle of radius r is:
[tex]A_c = \pi r^2[/tex]
The area of a triangle of base b and height h is:
[tex]\displaystyle A_t=\frac{b.h}{2}[/tex]
Calculate the area of the circle:
[tex]A_c = \pi 8^2[/tex]
[tex]A_c = 64\pi[/tex]
Area of half the circle:
[tex]A_c/2 = 32\pi~m^2[/tex]
Area of the triangle:
[tex]\displaystyle A_t=\frac{24\cdot 16}{2}[/tex]
[tex]A_t=192~m^2[/tex]
The area of the shaded shape is:
[tex]A=32\pi~m^2+192~m^2[/tex]
Substituting the value of pi:
[tex]\mathbf{A=292.53~m^2}[/tex]
On your first day in business, 126 people come to eat. They spend about $52 each. About how much money did you earn on your first day?
Answers
Answer:
You erned about $6,552
Step-by-step explanation: