Find the 4th term if the sequend in which a1 = 2 and a n+1 = -4a n + 2.

Answers

Answer 1
The given sequence is
[tex]a_{1}=2 \\ a_{n+1}=-4a_{n}+2[/tex]

Write the first 4 terms.
When n=1, obtain
a₁ = 2
When n=2, obtain
a₂ = -4a₁ + 2
    = -4(2) + 2 = -8 + 2
    = -6
When n=3, obtain
a₃ = -4a₂ + 2
    = -4(-6) + 2 = 24 + 2
    = 26
When n=4, obtain
a₄ = -4a₃ + 2
   = -4(26) + 2 = -104 + 2
   = -102

Answer:  a₄ = -102


Related Questions

Tanisha opened a bank account. She deposited $74.50 into her account every month for 10 months. She used $32.50 every month to pay for painting classes. After 10 months, she used 1 over 2 of the total money left in her account to go to a summer camp for painters. What is the total amount of money Tanisha spent to go to the summer camp?

Answers

She uses $210 because 74.50 x 10 = 745 and 32.50 x 10 = 325. Subtract the money she takes out every month on classes from the amount she puts in, 745 - 325 = 420. Then you would divide 420 by 2 because half of 420 is what she uses on the camp

Answer:

A

Step-by-step explanation:

19. if a vechicle was purchased for $32345. there's a 6% sales tax on automobile sales, how much tax will be added to the price of the car

Answers

the answer is 1,940 and 7 cents 

Need help asap with number 4

Answers

- What's being done to the problem ?

A radio active isotope decays according to the exponential decay equation where t is in days. Round to the thousandths place. For the half life: The half life is the solution (t) of the equation : a2=ae−7.571t a 2 = a e − 7.571 t

Answers

The decay function is
[tex]a(t)=a_{0} e^{-7.571t}[/tex]
where
a₀ = initial mass
t = time, days

At half life, a(t) = a₀/2, therefore the time required to achieve half life is given by the equation
[tex] \frac{a_{0}}{2} =a_{0} e^{-7.751t}\\ \frac{1}{2} =e^{-7.571t}[/tex]

Take natural log of each side.
ln(1/2) = -7.571 t

Divide each side by -7.571 to obtain
[tex]t= \frac{ln(1/2)}{-7.571} =0.0916[/tex]

Answer: 0.0192 days (nearest thousandth)

Solve for x: 4 over 5 x + 4 over 3 = 2x x = __________________ Write your answer as a fraction in simplest form. Use the "/" symbol for the fraction bar. Answer for Blank 1:

Answers

Let's see.

4x/5 + 4/3 = 2x

First we have to make each denominator the same, so I'll multiply 4x/5 by 3/3, 4/3 by 5/5, and 2x by 15/15

Now we have 12x/15 + 20/15 = 30x/15

With everything in the same denominator we can solve the new equation of
12x + 20 = 30x

20 = 18x

10 = 9x

X= 10/9
The answer question is x=10/9

The top base of a trapezoid is 18 inches and the bottom base is 22 inches. The height of the trapezoid is 8.5 inches. What is the area of the trapezoid

Answers

Final answer:

The area of the trapezoid with top base 18 inches, bottom base 22 inches, and height 8.5 inches is calculated using the formula (1/2) × (base1 + base2) × height, resulting in an area of 170 square inches.

Explanation:

To calculate the area of the trapezoid, you can use the formula for the area of a trapezoid, which is A = (1/2) × (base1 + base2) × height. In this case, the top base (base1) is 18 inches, the bottom base (base2) is 22 inches, and the height is 8.5 inches.

Using the formula, we get:

A = (1/2) × (18 inches + 22 inches) × 8.5 inches

A = (1/2) × 40 inches × 8.5 inches

A = 20 inches × 8.5 inches

A = 170 square inches

So, the area of the trapezoid is 170 square inches.

If angle DAB measures 34 degrees, what is the measure of arc DB

Answers

Arc DB will also measure 34 degrees.

Points D, E, and F are not in a line. To construct a circle through points D, E, and F, begin by drawing line segments ("DE" ) ̅ and ("EF" ) ̅. Then construct the perpendicular bisectors of ("DE" ) ̅ and ("EF" ) ̅, and name the point of intersection of the perpendicular bisectors O. How do you know that point O is the center of the circle that passes through the three points?

Answers

Final answer:

Point O is the center of the circle passing through points D, E, and F because it is equidistant from all these points. This is proven by the construction of the perpendicular bisectors of DE and EF and their intersection at point O.

Explanation:

The point O is the center of the circle that passes through the three points D, E, F because it is equally distanced from each of them. Here's why: When you draw perpendicular bisectors of lines DE and EF, you're effectively finding the midpoint of each line. Then, when these bisectors intersect at point O, point O is equidistant from points D and E (due to being on the bisector of DE), and from points E and F (due to being on the bisector of EF).

By definition, the center of a circle is a point that is equidistant from all points on the circle's circumference. Hence, because points D, E, and F are on the circumference and are equidistant from O, O is the center of the circle passing through points D, E, and F.

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Final answer:

Point O is the center of the circle passing through points D, E, and F because it is equidistant from the vertices of triangle DEF, which is confirmed by the properties of the perpendicular bisectors of line segments DE and EF that intersect at point O.

Explanation:

To determine that point O is the center of the circle passing through points D, E, and F, we use the properties of perpendicular bisectors in a triangle. When we draw the line segments DE and EF, we are essentially drawing two sides of the triangle DEF. Constructing the perpendicular bisectors of these sides involves finding the midpoint of each side and then drawing a line that is perpendicular to that side at its midpoint.

The point where these two perpendicular bisectors intersect, point O, is equidistant from the vertices of the triangle (D, E, and F). This is because the perpendicular bisector of a line segment has the property that every point on the bisector is equidistant from the two endpoints of the segment. In the case of triangle DEF, point O is equidistant from D and E, since it lies on the bisector of DE, and is also equidistant from E and F, since it lies on the bisector of EF.

Since point O is equidistant from all three vertices of the triangle, it can serve as the circle's center, with the radii to the vertices being equal. This circle that we have created by using this method is also known as the circumcircle of triangle DEF, and point O is referred to as the circumcenter.

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Which statement is true for the equation 3x − 3x − 2 = −2?

It has no solution.
It has one solution.
It has two solutions.
It has infinitely many solutions.

Answers

Hey. This equation has infinite many solutions.
3x - 3x - 2 = - 2
3x - 3x = 0
3x = 3x
This equals to each other meaning infinite solutions

The equation will have infinitely many solutions.

What is an equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

This equation has infinitely many solutions.

3x - 3x - 2 = - 2

3x - 3x = 0

3x = 3x

This equals each other meaning infinite solutions.

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A ball is dropped from a height of 5 ft and bounces to 60% of its previous height on each subsequent bounce. Which statement is true regarding the vertical distance the ball has traveled when it hits the ground for the fourth time?

A) 10.88 ft vertical distance traveled total
B) 16.76 ft vertical distance traveled total
C) 18.06 ft vertical distance traveled total
D) 21.76 ft vertical distance traveled total

Answers

Answer:

the answer is 16.76 ft option B

Step-by-step explanation:

The vertical distance the ball has traveled when it hits the ground for the fourth time is 16.76m.

What is the percentage?

The Percentage is the value per hundred.

Distance traveled by the ball when it hits the ground first time =5m

After the first hit, it bounces to 60% of its previous height

60% of 5m =3m

This means ball goes 3m up and then 3m down before hitting for the second time.

So, the vertical distance traveled by the ball till the second hit=5+3+3 =11m

After the second hit, it bounces to 60% of its previous height

60% of 3m =1.8m

This means ball goes 1.8m up and then 1.8m down before hitting for the third time.

So, the vertical distance traveled by the ball till the third hit=11+1.8+1.8 = 14.6m

After the third hit, it bounces to 60% of its previous height

60% of 1.8m =1.08m

This means ball goes 1.08m up and then 1.08m down.

So, the vertical distance traveled by the ball till the fourth hit=14.6+1.08+1.08 = 16.76m

Hence, the vertical distance the ball has traveled when it hits the ground for the fourth time is 16.76m.

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The taxable earnings column of a payroll register records

Answers

The taxable earning column of a payroll register records those wages which are subject to taxation. There are several earnings which would not be taxed, as such you need to be able to differentiate between the two, while providing the end user with a easily read format of the moneys.

Final answer:

The taxable earnings column of a payroll register records the amount of earnings that are subject to taxes.

Explanation:

The taxable earnings column of a payroll register records the amount of earnings that are subject to taxes. In payroll, taxable earnings refer to the portion of an employee's wages or salary that is subject to various taxes, such as income tax and Social Security tax.

For example, if an employee earns $1,000 per week and the income tax rate is 20%, the taxable earnings would be $800 ($1,000 - $200).

It's important to note that not all earnings may be taxable. Some types of income, such as certain reimbursements or non-taxable fringe benefits, may be excluded from taxable earnings.

Find the area of a circle, in terms of pi, if the radius is 20 ft.

Answers

area of circle= π·r² so, π·20²= π·400≡ 1256.637061

If a 12-student class averaged 90 on a test, and a 20-student class averaged 80 on the test, then all 32 students averaged

Answers

let the marks of the students in class 1 be

[tex]m_1, m_2, ....., m_1_2[/tex]

the average of these 12 marks is 90, so 

[tex]\frac{m_1+ m_2+ .....+ m_1_2}{12}=90 [/tex]

which means

[tex]m_1+ m_2+ .....+ m_1_2=90*12=1080[/tex]


similarly, let [tex]n_1, n_2, ....., n_2_0[/tex] be the marks of the students in the second class, 

so [tex] \frac{n_1+ n_2+ ..... n_2_0}{20}=80 [/tex]

which means [tex]n_1+ n_2+ ..... n_2_0=80*20=1600[/tex]


The 32 students averaged:

[tex] \frac{(m_1+ m_2+ .....+ m_1_2)+(n_1+ n_2+ ..... n_2_0)}{12+20}= \frac{1080+1600}{32}= \frac{2680}{32}= 83.75[/tex]
The formula to find the average of a data is given as follow
Mean = The sum of the data value ÷ Number of data

We would need the sum of 32 values to work out the mean score of 32 students. We will work out separately by finding the sum of scores of 12 students and sum of scores of 20 students

90 = Sum of data ÷ 12
Sum of data = 90×12 = 1080 scores

80 = Sum of data ÷ 20
Sum of data = 80×20 = 1600 scores

The sum of data of 32 students is 1080+1600 = 2680 scores
Mean = 2680÷32 = 83.75 

If a Rubik’s Cube has a volume of 384 cubic centimeters, how long is one side of the cube?

Answers

The answer is:  "7.268 cm" .
________________________
Explanation:
________________________
Since the formula for the volume, "V", of a cube, is:

V = s³ ;

in which:  "s" = side length of a cube;

Given:  "V = 384 cm³ " ;  Plug this value into the formula; to solve for "s" ;

V = s³ ;

↔  s³ = V ; 

     s³ = V ; 

     s³ = 384 cm³ ;

Take the "cubic root" of EACH SIDE of the equation; to isolate "s" on one side of the equation ; & to solve for "s" ; 
_________________________________________________
   ∛(s³) = ∛ (384 cm³) ;

     s =   7.2684823713285586  cm

Round to:  7.268 cm .
__________________________________________________

50% of all cakes. Jenny baked that week were party cakes. 1-5 we're fruit cakes, and the remainder were sponge cakes. What percentage of cakes were sponge cakes

Answers

I think by 1-5 you mean 1/5??

1/5 = 0.20 = 20%

50% + 20% = 70%

100-70 = 30

 so 30% were sponge cakes

Waylon played defense in 12 soccer games. This was 60% of the total number of games he played. How many games did Waylon play?

Answers

Assume he played x games in total.

So x * 60% = 12

->x = 12 / 60% = 20
g(60/100)=12

60g=1200

g=1200/60

g=20 games

Quadrilateral ABCD is a rhombus. Suppose measure of angle A decreases. Which of the following changes would also need to happen in order for ABCD to still be a rhombus?

Answers

Final answer:

If angle A of a rhombus decreases, angle C must also decrease and the side length of the rhombus must remain the same for it to still be a rhombus.

Explanation:

When angle A of a rhombus decreases, there are two changes that need to happen in order for the rhombus to still be a rhombus.

The opposite angle, angle C, must also decrease by the same amount in order to maintain the opposite angles of a rhombus being equal. The side length of the rhombus must remain the same, as all sides of a rhombus are congruent.

Therefore, if angle A decreases, angle C must also decrease by the same amount, and the side length of the rhombus must remain the same in order for ABCD to still be a rhombus.

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Reflection across the x-asis?

Answers

so you would reflect it across the x axis (the one that goes left and right). The points would have new coordinates, but it should make the same shape...hope this helps!

Calculate 40^13 (mod85)

Answers

I pretty sure the answer is 134217728000000000000/17

Find the sum of the three expressions and choose the correct answer.
-2u 3 v + 5uv - 1

7u 3 v - 2u 2 v 2

5u 2 v 2 - uv + 6


The answer choices are.....
A. 5u3v + 3u2v2 + 4uv + 5

B. -5u3v - 3u2v2 + 4uv + 7

C. 5u3v - 3u2v2 + 4uv - 5

Answers

[tex](-2u^3v + 5uv - 1) +(7u^3v - 2u^2v^2) +(5u^2v^2 - uv + 6)=\\\\ -2u^3v + 5uv - 1 +7u^3v - 2u^2v^2 +5u^2v^2 - uv + 6= \\ \\ (7u^3v-2u^3v)+(5u^2v^2-2u^2v^2)+(5uv-uv)+(6-1)=\\\\ \boxed{5u^3v+3u^2v^2+4uv+5}[/tex]
The answer will be 5u3v + 3u2v2 + 4uv + 5

help please thank you

Answers

To multiply by 6/7, we multiply by 6 and divide by 7. 1 +3/4= (1*4)/4+3/4
= 4/4+3/4=7/4.  (7/4)*6=42/4. to divide by 7, we multiply 7 to the denominator to get 42/28, simplifying it to 3/2 or 1+1/2 tons

Which point represents a solution to the system y ≤ (1)/(5)x y > 4x-3 select all that apply
(5,1)
(0,0)
(-2,-3)
(2,5)

can you help me with this question and explain how you got the answer please and thank you ! this is very important !!!!!!!!!

Answers

The system is 

i) [tex]y \leq \frac{1}{5} x[/tex]
ii) [tex]y\ \textgreater \ 4x-3[/tex]

The solutions to this system, are all points (x, y) for which BOTH these 2 inequalities hold.

Check the points separately: 

(5, 1)
i) [tex]1 \leq \frac{1}{5} *5=1[/tex] True
ii) [tex]1\ \textgreater \ 4*5-3=20-3=17[/tex] Not True

(0, 0)
i) [tex]0 \leq \frac{1}{5} *0=0[/tex] True
ii) [tex]0\ \textgreater \ 4*0-3=-3[/tex] True

(-2, -3)
i) [tex]-3 \leq \frac{1}{5} (-2)= \frac{-2}{5}= -0.4[/tex] True
ii) [tex]-3\ \textgreater \ 4(-2)-3=-8-3=-11[/tex] True

(2, 5)
i) [tex]5 \leq \frac{1}{5}*2= \frac{2}{5} =0.4[/tex] Not True
ii)[tex]5\ \textgreater \ 4*2-3=8-3=5[/tex] Not True


Answer: (0, 0) and (-2, -3)

Write an equation of the line that has a slope of 5 and y-intercepts 3 in slope-intercept form.

Answers

The slope intercept form of a line is:

y=mx+b, where m=slope and b=y-intercept

We are told that m=5 and b=3 so

y=5x+3

PLEASE HELP!!!! Show steps and explain how to get the answer please

Solve 5x-16=4(x-8)-3x

Answers

5x-16 = 4(x-8)-3x

first expand what is in parenthesis

4(x-8) = 4x-32

 so now you have 5x-16 = 4x-32-3x

subtract 3x from 4x on the right side of equation 4x-3x = x

5x-16 = x -32

subtract 1x from each side to get

4x-16 = -32

add 16 to both sides to get 4x=-16

x = -16/4 = -4

x=-4

5x-16=4(x-8)-3x
[distribute the 4]
5x-16=4x-32-3x
[combine like terms]
5x-16=x-32
[subtract x and add 16 to both sides]
5x-x=-32+16
[combine like terms]
4x=-16
[divide by 4]
x=-4

What is the degree of 6x5 - 4x2 + 2x3 - 3 + x?

Answers

Answer:

55555555555555555555

Step-by-step explanation:

The degree is 5.

what is degree of polynomial?

The degree of a polynomial is the highest power of the variable in a polynomial expression.

Given function:

6x5 - 4x2 + 2x3 - 3 + x

as, the function have powers 2, 3  and 5.

Among which the highest power is 5.

So, degree of the polynomial is highest power of the variable present in an equation.

Hence, the degree of polynomial is 5.

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What is an equation that equals 58 explain!

Answers

equation? like any equation?    That could be any like x+y=58 or 4x+5y=58 or any...........

Some equations that equal 58 include: 58x, 29 + 29, and y + 58x.

For example, 58x is equal to 58 because you can change x to 1, and 58 times 1 is 58. Therefore, it is equal to 58.

Let me know if this was helpful and remember to brainliest!

Raul has $640 saved, and jaime has $320 saved. They each begin a new job on the same day and save all of their money. Raul earns $180 per day and jaime earns $200 per day. In how many days will they have an equal amount of money

Answers

Hi there , solution is in the figure attached with...hope it helps u

In 16 days will they have an equal amount of money.

What is Algebra?

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Raul has $640 saved, and jaime has $320 saved.

Raul earns $180 per day and jaime earns $200 per day.

let the be number of days they both have same amount

640 + 180x = 320 + 200x

320 = 20x

x= 16

Hence, 16 days will they have an equal amount of money.

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10 times the sum of half a number and 6 is 8

Answers

x=1 cause 10•1/2x+6=8 so we first use one and then the rest will be answered

Which expression is the result of the perimeter of rectangle b minus the perimeter of rectangle a

Answers

Retangle B perimeter = 2(3x+5) + 2(2x-2)
                                      6x + 10 + 4x - 4
                                      10x + 6

Retangle A perimeter = 2(2x+8) + 2(x-1)
                                      4x + 16 + 2x - 2
                                      6x + 14


(10x + 6) - (6x + 14) =
10x + 6 - 6x - 14 =
4x - 8    ←  answer

Jose made 33 of the 88 baskets for basketball team.What percent did he no make?

Answers

It is 62.5% miss rate.
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