10 points! I will thanks, rate, and give best answer!!



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

Answers

Answer 1
Answer: The fourth term is -102

----------------------------------------------

Explanation:

The term after the nth term is generated by this rule  [tex]a_{n+1} = -4(a_n) + 2[/tex] which means that we first
Step 1) multiply the nth term ( [tex]a_n[/tex] ) by -4
Step 2) Add the result of step 1 to the value 2 to get the next term in the sequence

Let's follow those steps above to generate the first four terms

The first term is [tex]a_1 = 2[/tex]. In short, the first term is 2

The second term is...
[tex]a_{n+1} = -4(a_n) + 2[/tex]
[tex]a_{1+1} = -4(a_1) + 2[/tex]
[tex]a_{2} = -4(2) + 2[/tex]
[tex]a_{2} = -8 + 2[/tex]
[tex]a_{2} = -6[/tex]
So the second term is -6

The third term is...
[tex]a_{n+1} = -4(a_n) + 2[/tex]
[tex]a_{2+1} = -4(a_2) + 2[/tex]
[tex]a_{3} = -4(-6) + 2[/tex]
[tex]a_{3} = 24 + 2[/tex]
[tex]a_{3} = 26[/tex]
The third term is 26

Finally, the fourth term is...
[tex]a_{n+1} = -4(a_n) + 2[/tex]
[tex]a_{3+1} = -4(a_3) + 2[/tex]
[tex]a_{4} = -4(26) + 2[/tex]
[tex]a_{4} = -104 + 2[/tex]
[tex]a_{4} = -102[/tex]
The fourth term is -102.

Related Questions

Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule. A(n) = –3 + (n – 1)(–2.2)

Answers

A(n) = a1 + (n - 1) * d
A(n) = -3 + (n - 1) * -2.2
n = term to find
a1 = first term = -3
d = common difference = -2.2

we can already see that the first term is -3 <==

4th term..
A(4) = -3 + (4 - 1) * -2.2
A(4) = -3 + 3(-2.2)
A(4) = -3 - 6.6
A(4) = - 9.6 <== 4th term

10th term...
A(10) = -3 + (10 - 1) * -2.2
A(10) = -3 + 9 * - 2.2
A(10) = -3 - 19.8
A(10) = - 22.8 <===10th term

Final answer:

The arithmetic sequence A(n) = –3 + (n – 1)(–2.2) yields the first, fourth, and tenth terms as -3, -9.6, and -22.8 respectively when n is substituted with the corresponding term number.

Explanation:

The arithmetic sequence described by the rule A(n) = –3 + (n – 1)(–2.2) can be used to find specific terms of the sequence. To find the first term, plug in n = 1 into the formula to get A(1) = -3 + (1 - 1)(-2.2) = -3. The fourth term can be found by plugging in n = 4 which yields A(4) = -3 + (4 - 1)(-2.2) = -9.6. The tenth term is calculated as A(10) = -3 + (10 - 1)(-2.2) = -22.8. Therefore, the first, fourth, and tenth terms are -3, -9.6, and -22.8 respectively.

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Joan likes to watch the birds in her yard.one morning,she notices that there are twice as many robins as blue jays.if she counted 21 blue jays and robins in all, how many blue jays did she count. Need help badly

Answers

21 divided by 3 = 7
14 robins 
7 blue jays

The football team has 30 more members than the basketball teams. If each group had 10 more members, the ratio of their membership would be 3.2. How many members are in each group? Write your answer as football x basketball y


****PLEASE HELP********

Answers

We start with football =basketball +30 of x=y+30
Add 10 so that 3/2=(f+10)/(y+10) 
Now let's use substitution to get 3/2=(y+30+10)/(y+10) or 3/2=(y+40)/(y+10) 
Now cross multiply so 3(y+10)=2(y+40) or 3y+30=2y+80. Solve to get y=50, meaning x must be 80.
Now let's check to make sure it would be 3/2 if each gets 10 new members. Football would then have 90 and basketball would have 60, so yes, it works!!

if the lines a and b in the diagram below are parallel why do angles 1 nd 8 measure 120 degree angles

A) Because they are alternate interior angles.
B) Because they are corresponding angles.
C) Because they are alternate exterior angles.
D) Because they are same-side interior angles.

Answers

The pairs of angles on opposite sides of the transversal but outside the two lines are called alternate exterior angles.

C) Because they are alternate exterior angles.

The curve y = x/(1 + x2) is called a serpentine. find an equation of the tangent line to this curve at the point (2, 0.40). (round the slope and y-intercept to two decimal places.) y =

Answers

Final answer:

The equation of the tangent line to the curve y = x/(1 + x2) at the point (2, 0.40) is given by y = -0.24x + 0.88, rounded to two decimal places.

Explanation:

The subject of the question refers to calculus, specifically the concept of finding the equation of a tangent line to a curve. This process typically involves finding the derivative of the function (which gives the slope of the tangent), and then using the point-slope form of the line equation.

The derivative of y = x/(1 + x2) can be found using the quotient rule for differentiation and is given by y' = (1 - x2)/(1 + x2)2. Evaluating this at x = 2 gives a slope of about -0.24 (rounded to two decimal places).

The equation of the line is usually written in the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept. Since we know that the line passes through the point (2, 0.40), we can substitute these values into the equation and solve for b. This yields a y-intercept of about 0.88 (rounded to two decimal places).

Therefore, the equation of the tangent line to the curve y = x/(1 + x2) at the point (2, 0.40) is approximately y = -0.24x + 0.88.

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Max is observing the velocity of a runner at different times. After one hour, the velocity of the runner is 5 km/h. After two hours, the velocity of the runner is 3 km/h.

Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used. (5 points)

Part B: How can you graph the equations obtained in Part A for the first 4 hours? (5 points)

Answers

You only have two observations to work the equation for the velocity.

You only can assume a linear relation.

Part a.

Calling x the independent variable (time in hours) and y the dependent variable (velocity in km/h) =>

x (time in hours)         y (velocity in km/h)

1                                  5
2                                  3

Now you use the linear relation:

slope: (3 - 5) km/h/ (2 - 1)h = - 2 km/1h^2 = - 2 km/h ^2

Equation:

y - 3 = slope * (x - 2)

=> y - 3 = - 2 ( x - 2)

=> y - 3 = - 2x + 4

=> y = 3 - 2x + 4

=> y = - 2x + 7

that is the slope-intercept form.

the standard form is y + 2x - 7 = 0

part B.

to draw the graph you can make a table with the points for the first four hours:

x (time in hours)            y (velocity in km/h)
                                        -2x + 7

1                                      -2(1) + 7 = 5

2                                      -2(2) + 7 = 3

3                                      -2(3) + 7 = 1

4                                     -2(4) + 7 = - 1

The graph, of course, is a straight line, because we started from that assumption.

Which of the following inequalities matches the graph?

graph of an inequality with a solid vertical line through the point negative 7, 0 and shading to the left of the line

Answers

x < = -7...solid vertical line means there is an equal sign in the problem...shading to the left or down means less then. A vertical line is represented by x = a number, and that number being the x value in ur set of points.

Of the 30 girls who tried out for lacrosse team 12 were selected. Of the 40 boys that tried out 16 were selected. Are the ratios of the number of students on the team to the number of students trying out the same for both boys and girls? Explain.

Answers

Girls;

Total number of girls who tried out = 30

Number of girls who got selected = 12

Ratio of girls on team to girls who tried out = [tex] \frac{12}{30} = \frac{2}{5} [/tex] = 2 : 5

Boys;

Total number of boys who tried out = 40

Number of boys who got selected = 16

Ratio of boys on team to boys who tried out = [tex] \frac{16}{40} = \frac{2}{5} [/tex] = 2 : 5

Hence, the ratios are the same.

The population of a town is 500,000 in 1990. The population increases at a rate of 5% every five years. What will be the approximate population of the town in 2005?
A. 578,813
B. 587,712
C. 499,354
D. 512,945

Answers

A = P(1+r)^(t/5) A = 500000(1+0.05)^(15/5) A = 500000(1.05)^(15/5) A = 500000(1.05)^3 A = 500000*1.157625 A = 578812.5 Telling us that the population will be about 578,812 people in the year 2005

Which of the following equations has the solution x =  all real numbers? Select one: a. 4(3 - x) + 6x = 3x + 12 - x b. 4(3 - x) + 6x = 3x + 10 - x c. 4(3 - x) + 6x = 3x + 12 + 2x d. 4(3 - x) + 6x = x + 12 - 3x

Answers

a. 4(3-x) + 6x = 3x + 12 - x
    12 - 4x + 6x = 2x + 12
      2x + 12 = 2x + 12...infinite solutions <=== this one
    

b. 4(3 - x) + 6x = 3x + 10 - x
    12 - 4x + 6x = 2x + 10
    2x + 12 = 2x + 10...not this one...no solutions

c. 4(3 - x) + 6x = 3x + 12 + 2x
    12 - 4x + 6x = 5x + 12
     2x + 12 = 5x + 12....not this one...one solution

d. 4(3 - x) + 6x = x + 12 - 3x
    12 - 4x + 6x = -2x + 12
    2x + 12 = -2x + 12...not this one...one solution

The equation that has the solution x = all real numbers is given by option a) (4(3 - x) + 6x = 3x + 12 - x) and this can be determined by using the arithmetic operations.

Check all the options in order to determine which of the following equations has the solution x = all real numbers.

A) 4(3 - x) + 6x = 3x + 12 - x

Simplify the above equation separately that is:

LHS = 12 - 4x + 6x

       = 12 + 2x

RHS = 3x + 12 - x

       = 2x + 12

LHS = RHS means there is an infinite number of solutions.

B) 4(3 - x) + 6x = 3x + 10 - x

Simplify the above equation separately that is:

LHS = 12 - 4x + 6x

       = 12 + 2x

RHS = 2x + 10

LHS [tex]\neq[/tex] RHS means that there are no solutions.

C) 4(3 - x) + 6x = 3x + 12 + 2x

Simplify the above equation separately that is:

LHS = 12 - 4x + 6x

       = 12 + 2x

RHS = 5x + 12

LHS [tex]\neq[/tex] RHS means that there are no solutions.

D) 4(3 - x) + 6x = x + 12 - 3x

Simplify the above equation separately that is:

LHS = 12 + 2x

RHS = 12 - 2x

LHS [tex]\neq[/tex] RHS means that there are no solutions.

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Enter the degree of the polynomial below

7x^7+10x^4+4x^3-5x^11-10x^6-6x^7

A. 11
B. 10
C. 6
D. 7

Answers

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

Rewriting the expression we have
[tex] 7x^{7} + 10x^{4}+ 4x^{3}-5 x^{11} -10 x^{6} -6 x^{7} [/tex]

We can see that the highest power is 11, hence the degree of the polynomial is 11

Correct answer: A

Assuming that n 1 , rewrite the compound interest equation B t 900 1.185 t in the general form.

Answers

[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\\ t=year \end{cases}[/tex]

[tex]\bf 1.185\implies 1+0.185\qquad\quad and\quad n=1 \\\\\\ A=P\left(1+\frac{r}{n}\right)^{nt}\implies A=P\left(1+0.185\right)^{nt}\implies A=P\left(1+\frac{0.185}{1}\right)^{1\cdot t}[/tex]

so, the percentage of the rate is 0.185, what's that as a percentage? well, 0.185 * 100, 18.5%.

Read the following statement: All prime numbers are odd. Which of the following choices is a counterexample to the statement?
1
17
2
7

Answers

All prime numbers are odd.
A counter-example is one that will prove this statement to be false.

ur answer is : 2....it is 2 because 2 is a prime number and it is even...in fact, it is the only even number that is a prime number.


The choice which is a counterexample to the statement is 2.

What are prime numbers?

"It is a number that is divisible only by itself and 1 "

For given question,

We have been given a statement 'All prime numbers are odd. '

We need to select a counterexample to given statement.

Consider a number 2.

2 is divisible only by itself and 1

This means, 2 is a prime number.

We know that 2 is an even number.

Therefore, the choice which is a counterexample to the statement is 2.

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Which expression can be used to determine the average rate of change in f(x) over the interval [2,9]
a) f(9-2)
b) f(9)-f(2)
c) f(9-2)/9-2
c) f(9)-f(2)/9-2

Answers

The correct answer is the second c or what I assume you meant to be d
f(9)-f(2)/9-2

Answer:

D. f(9-2)/9-2   on Edg2020

Step-by-step explanation:

Hope this helps!!! Have a great day!!!    : )

The table and the graph below each show a different relationship between the same two variables, x and y:

How much more would the value of y be on the graph than its value in the table when x = 12?
Please just help me understand, do not give me the answer! thank you

Answers

Notice how both the table and the graph are lines. Moreover, they pass through the origin, so you could find y = a * x in each case, then substitute x=12, and compare each value. It says how much more, so the correct thing is to subtract. If it were how many times, then divide. Is that all you need? You don;t want the solution

How to solve (8.76 x 109)(6.52 x 10-3)/13.27 x 105?

Answers

use PEMDAS:
P = parenthesis
E = exponents
M = multiplication
D = division
A = addition
S = subtraction


First, start with the parenthesis:
(8.76 * 109)(6.52 * 10 - 3) / 13.27 * 105
(954.84)*(62.2) / 13.27 * 105

Then do ALL multiplication:
59,391.048 / 1,393.35

Now do all division:
42.62

So, your final answer is 42.62

What is the value of x 20 35 60 70

Answers

x+40 =3x (vertical angles)
2x = 40
x = 20

answer  is A. 20 (first choice)

Answer:

Value of x is:

20

Step-by-step explanation:

Clearly, the two angles are vertically opposite

and vertically opposite angles are always equal

So, x+40=3x

Subtracting both sides by x, we get

x+40-x=3x-x

i.e. 40= 2x

Dividing both sides by 2, we get

x = 20

Hence, Value of x is:

20

Evaluate 5x + (-2x 2) for x = 3.

Answers

5x + (-2x^2) for x = 3
5(3)+ (-2(3^2)) = 15 - 18 = -3

hope it helps
The answer to the expression is -3.

What is the equation of the quadratic graph with a focus of (1, 1) and a directrix of y = −1?


f(x) = − one fourth (x − 1)2 + 1

f(x) = − one fourth (x − 1)2

f(x) = one fourth (x − 1)2 + 1

f(x) = one fourth (x − 1)2

Answers

alright,
directix is y=something so it opens down or up

we use
(x-h)²=4p(y-k)
the vertex is (h,k)
and p is distance from focus to vertex
if focus is above directix, p is positive
if focus is below directix, p is negative

so we gts

focus=(1,1)
directix is y=-1
1>-1
focus is above

oh, vertex is in middle of focus and directix
so
beteeen (1,1) and y=-1 is, hmm
that is a distance of 2 vertically
2/2=1
1 down from (1,1) is (1,0)
vertex is (1,0)
p=1

so
(x-1)²=4(1)(y-0)
solving for y to get into f(x)=something form
(x-1)²=4y
y=1/4(x-1)²
f(x)=1/4(x-1)²

4th option

If g is the variable, which mathematical sentence expresses the information below? "The number of gallons of gas in the tank plus 7 more adds up to 12 gallons."

Answers

An equation for the sentence would be g + 7 = 12, where g is the unknown number of gallons.

Answer: [tex]g+7=12[/tex]

Step-by-step explanation:

The given statement : The number of gallons of gas in the tank plus 7 more adds up to 12 gallons.

Given variable : 'g'

if g represents the number of gallons of gas in the tank, then for the given statement we have the following expression:-

[tex]g+7=12[/tex]

Hence, the mathematical sentence expresses the given information :-

[tex]g+7=12[/tex]

Let u = <-9,4>, v = <8, -5>. Find u - v.

Answers

I am guessing vectors :)

(-17, 9)

or in polar form

√370, -27°53'50"

To find the difference between vectors u and v, subtract corresponding components.

Given vectors u = <-9,4> and v = <8, -5>, to find the difference u - v, subtract corresponding components:

Subtract the x-components: -9 - 8 = -17

Subtract the y-components: 4 - (-5) = 9

Therefore, u - v = <-17, 9>.

Which function represents g(x), a reflection of f(x) =2/5 (10)x across the x-axis? g(x) =-2/5 (10)x g(x) =-2/5(1/10)^x g(x) =2/5(1/10)^-x g(x) =2/5 (10)-x

Answers

all values of f(x)  will change from positive to negative if you reflect in x-axis.

So the first choice is the correct one.

Answer:

A. [tex]g(x)=-\frac{2}{5}(10)^x[/tex].

Step-by-step explanation:

We are given the function [tex]f(x)=\frac{2}{5}(10)^x[/tex].

Now, g(x) is obtained by reflecting the function f(x) over x-axis.

Reflection of f(x) over x-axis changes f(x) to -f(x).

So, we get,

[tex]g(x)=-f(x)[/tex]

i.e. [tex]g(x)=-\frac{2}{5}(10)^x[/tex]

Thus, the reflected function is [tex]g(x)=-\frac{2}{5}(10)^x[/tex].

So, option A is correct.

Write 14/42 in simplest form

Answers

7/6!!!!!!!!!!!!!!!!!!!!!!
7/6 should be your answer

What is the following product

Answers

The answer is choice C. The work is shown in the attached image. 

Use the distributive property to remove the parentheses.
-5(5v-4x-1)

Answers

-5(5v-4x-1)

You need to multiply all the variables in the parentheses by -5.
(-5*5v) - (-5*4x) - (-5*1)

-25x + 20x + 5
= -5*5v -5*-4x -5*-1

=  - 25v + 20x + 5

The foodservice department has been asked to prepare a special luncheon for the grandway hospital board of directors on tuesday. there will be 25 board members at the luncheon. there are 125 portions of vegetable lasagna needed for the hospital's lunch service that day. the standardized vegetable lasagna recipe yields 125 portions and requires 21 lb of ricotta cheese. how much ricotta cheese must chef carl order to meet production needs?

Answers

125/21 = 150/x
cross multiply
125x = 3150
x = 3150/125
x = 25.2 lbs....rounded up = 26 lbs <==

My past due bill is $585.00, and I just made payment arrangements for the next 3 months to keep my account from being suspended. My normal monthly bill is $50.00 per month. How much will I need to pay each month?"

Answers

585/3 = 195 + 50 = $245

Answer:

$245

Step-by-step explanation:

Given : My past due bill is $585.00, and I just made payment arrangements for the next 3 months to keep my account from being suspended. My normal monthly bill is $50.00 per month.

To Find:  How much will I need to pay each month?"

Solution:

Past due bill = $585

Now  just made payment arrangements for the next 3 months to keep my account from being suspended

So, Payment each month of past bill = [tex]\frac{585}{3}=195[/tex]

My normal monthly bill is $50.00 per month.

So, I need to pay per month = $50+$195= $245

Thus ,I need to pay $245 per month .

For a fixed amount of gas at a constant temperature, the volume of the gas is inversely proportional to its pressure. The function v=18000/p relates the volume in cubic inches and pressure in pounds per square inch of a gas. What is the volume when the pressure is 900 pounds per square inch?

Answers

Answer:

Volume of the gas is 20 cubic inches.

Step-by-step explanation:

Inverse proportion: Let x and y be two quantities are said to be inverse proportion or inversely proportional if one quantity increases at the same rate the other decreases.

[tex]x \propto \frac{1}{y}[/tex] or

[tex]x = \frac{k}{y}[/tex] ⇒[tex]k =xy[/tex]   where k is constant.

Since, it is given that the volume of gas is inversely propotional to its pressure.

Given the function:  

[tex]v = \frac{18000}{p}[/tex]           ......[1] ; where volume in cubic inches and pressure in pounds per square.

To find the volume in cubic inches.

The pressure (p) = 900 pounds per square inch.

Substitute the value of p in [1];

[tex]v = \frac{18000}{900}= 20 in^3[/tex]

Therefore, the volume(v) = 20 cubic inches when the pressure is 900 pounds per square inch.

The volume when the pressure is 900 pounds per square inch is [tex]20 in^3.[/tex]

What is proportionality?

proportionality can be explained as equality between two ratios, it gives relationship that is always in the same ratio.

We were given the function as[tex]v= \frac{18000}{p}[/tex]

But the pressure is given as pressure (p) = 900 pounds per square inch.

We can get volume, if we substitute "p" as;

[tex]v=\frac{18000}{p}[/tex]

[tex]V= \frac{18000}{900} =20 in^3.[/tex]

Hence, the volume when the pressure is 900 pounds per square inch is [tex]20 in^3.[/tex]

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Solve and check the inequality
|8m+4|<12

Answers

This is the concept of algebra, to solve the inequality we proceed as follows;
|8m+4|<12
given that the absolute value is represented by positive and negative values, we shall have:
-(8m+4)<12
-8m-4<12
-8m<12+4
-8m<16
thus;
m>16/(-8)
m>-2

also:
8m+4<12
8m<12-4
8m<8
m<8/8
m<1
hence the answer is -2<m<1

HELP! Algebra!
The following two-way table shows the number of students of a school who have a cell phone and/or have a part-time job:


Based on the table, how many students have both a cell phone and a part-time job?
Answers:
A- 10
B- 40
C- 50
D- 100

Answers

The table shows that of those who have a part time job, 40 students have a cell phone, and 10 do not.  The correct answer is B, or 40.  40 students out of 100 have both a cell phone and a part-time job.

The number of students have both a cell phone and a part-time job is 40.

The correct option is (B)

What is algebra?

Algebra is a branch of mathematics that deals with symbols or variables and uses arithmetic operations (+, –, ×, ÷) to find the unknown quantities represented by these variables.

Given table shows that,

The students having whether having cell phones or not and whether the students are having part time job or not.

As we can see from the Column I shows students having cellphones and the first row shows students having part time job. which is 40.

Hence, the students have both a cell phone and a part-time job is 40.

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From a deck of 52 cards, one card is drawn at random. Match the following subsets with their correct probabilities. 1.P(face card) 2.P(seven of hearts) 3.P(no black) 4.P(king) 5.P(diamond) Sustainability is the long-term well-being of the natural environment and the mutually beneficial interactions among _____. Two cars leave the same location at the same time but one car is heading north and the other is heading south. After 3 hours, the cars are 360 miles apart. If the car heading north is traveling 10 miles per hour slower than the car heading south, what are the two speeds of the cars? SHOW THE EQUATION When referring to the percent daily value of important nutrients which the following are considered correct?A 5% is a considered lowB 8% is it considered lowC 20% is it considered highD both A and C The graph shows f(x) = 1/2 and its translation, g(x).Which describes the translation of f(x) to g(x)? What is the length of the hypotenuse of the triangle? The baker pays $0.80 per pound for sugar and $1.25 per pound for butter. Write an expression that shows how much the baker will spend if he buys 6 pounds of butter and 20 pounds of sugar. A company uses a variable percentage markup of 35% .if the total cost of a product is $15,what is its selling price Which term refers to markings on a map that run in an east and west direction and measure distance north and south of the equator? Question 1 options: lines of latitude bench marks lines of longitude contour interval Which carbohydrate can be used by the body as an immediate source of energy? glucose cellulose chitin glycogen Prove that if m, d, and k are integers and d > 0, then (m + dk) mod d = m modd. Discuss the growing concerns for over credibility of online medical resources A 68-year-old male has a 20 pack year smoking history. he quit smoking 10 years ago. to screen for cardiovascular disease the nurse practitioner should order: True or false: the difference between the lower limit of a confidence interval and the point estimate used in constructing the confidence interval is called the sampling error. Please fill the answer:) The hot plates on an electric stove change ______ energy into ______ and a small amount of _____energy. how does henry david thoreau feel about standard us institutions such as postal service and the press What is pm pn equal to? I draw a card 50 times from a standard 52 deck and gets a heart 8 times what's the probability that I draw a heart on the next draw what did robert lee do when he heard five forks had been taken Teens usually don't realize how addictive nicotine is, which is one reason why __________ percent of adults began smoking in their teens. A. 75 B. 25 C. 50 D. 90 Steam Workshop Downloader