Instructions: Identify the type of sequence and write the recursive rule.



Sequence: −11,−3,5,13,…

Type: Geometric or Arithmetic?

an=an−1 - ?

a1= ?

Answers

Answer 1

Answer:

[tex]a_n=a_{n-1}+8,n\geq 1[/tex]

[tex]a_1=-11[/tex]

Step-by-step explanation:

We are given that a sequence

-11,-3,5,13,...

[tex]a=a_1=-11[/tex]

[tex]a_2=-3[/tex]

[tex]a_3=5[/tex]

[tex]a_2-a_1=-3-(-11)=-3+11=8[/tex]

[tex]a_3-a_2=5-(-3)=5+3[/tex]

[tex]a_3-a_2=8[/tex]

Common difference between two consecutive terms is equal.

Hence, the sequence is Arithmetic.

Common difference, d=8

[tex]a_2=a_1+8=-3[/tex]

[tex]a_3=a_2+8=5[/tex]

[tex]a_4=a_3+8=13[/tex]

:

:

:

[tex]a_n=a_{n-1}+8, n\geq 1[/tex]

[tex]a_1=-11[/tex]


Related Questions

Can someone help me with this math homework please!

Answers

The rate of change is 4 due to the fact that each increase is on the graph is by a factor of 4 cm and each horizontal increase is 1 week, therefore we can also conclude that the plant grows 4cm in 1 week

Therefore the correct answers are
- The rate of change is 4
- The plant grows 4cm in 1 week

Divisibility rules with algebra

Answers

Answer:

D=8

Step-by-step explanation:

normal division rules

33 goes into 47 1 time

then it leaves 17D

if we divide 170 by 33, we get 5 and if we divide 179 by 33, we still get 5. So we have 17D-165. That leaves us with something that you multiply 33 with to have a 2 in the ones place so that you get a remainder of 2. (In order to get 2 in the remainder, we need a 2 in the ones place because 4-2=2. In order to get that we need to see which number multiplied with 33 would get us a number smaller than 179 but also has a 2 in the ones place. Theres only one number and thats 4. 33*4=132. So in order to get only 2 in the remainder, we need the rest to be subtracted. This means that 17D-165=134. This way we can see that D=8

What is the name for the marked angel ?

Answers

Answer:

A

Step-by-step explanation:

Answer:

The answer is <ead

please mark me brainliest

Please help out with this question..

Answers

Answer:

Step-by-step explanation:

C = 16 * 3 = 48

Let f(x) = 3x − 2 and g(x) = x + 1. Find (g ∘ f)(2).
Help plsssssssssssssssss

Answers

Answer:

(g ∘ f)(2) =5

Step-by-step explanation:

f(x) = 3x − 2

g(x) = x + 1

(g ∘ f)(2).

Find f(2) = 3(2) -2 = 6-2 = 4

Then find g(4) = 4+1 = 5

Can someone help me with this math homework please!

Answers

Answer:

4

Step-by-step explanation:

A line with 0 slope is parallel to x axis and it must have the same y coordinates

Answer:

4

Step-by-step explanation:

( 3, b ) and ( - 2, 4 )

x1 y1 x2 y2

Here,

x1 = y1 = 0

x2 = - 2

y2 = 4

Formula : -

Slope = ( y2 - y1 ) / ( x2 - x1 )

Slope = ( 4 - b ) / ( - 2 - 3 )

0 = ( 4 - b ) / - 5

4 - b = - 5 x 0

4 - b = 0

4 = b

b = 4

What is the measure of angle x? Please help asap! Khan academy question!

Answers

Answer:

38°

Step-by-step explanation:

90-58

I'm unsure if that's right but i think it is. otherwise 180-58 but angle x should be the rest of the angle in KAI

Answer:

[tex]\boxed{\boxed{\tt \angle x=32^{\circ}}}[/tex]

Step-by-step explanation:

From the diagram given, we know that ∠BAC and ∠IAK are vertical angles.

*Vertical angles are two lines that intersect each other.*

So ∠BAC is equal to ∠IAK.

[tex]\tt \overline{KL} \perp \overline{FG}[/tex] so, ∠ABC =90°

(Interior angles in a triangle always add up to 180°).

[tex]\tt \angle BAC+\angle ABC+\angle BCA=180^{\circ}[/tex]

[tex]\tt 58+90+\angle BCA=180^{\circ}[/tex]

[tex]\tt \angle BCA=32^{\circ}[/tex]

∠BCA and ∠x are vertical angles, therefore they are congruent.

∠BCA and ∠x= 32°

______________________________________

Help Please!!!
Find volume of the sphere

Answers

Answer:

Step-by-step explanation:

Hey GurpTheDestoyer! Find the volume of the sphere. Round to the nearest whole number. Radius= 8 what is the volume? The Volume = 2,144.660585 cm3. Hope this helped! <3

Which of the following is true?
(A)The baby is male/female is determined by mother’s chromosome.
(B) The baby is male/female is determined by father’s chromosome.
(C) Pair of Mother’s chromosome is X-Y .
(D) Pair of Father’s chromosome is X-X .

Answers

Answer:

(B) The baby is male/female is determined by father’s chromosome.

Step-by-step explanation:

Men determine the sex of a baby depending on whether their sperm is carrying an X or Y chromosome.

Answer:

hi i hope it helps you

Step-by-step explanation:

please mark brainlist and like

thanks

and have a nice day.

ds
Given the velocity v =
dt
and the initial position of a body moving along a coordinate line, find the body's position at time t.
v = 9.8t + 12, s(0) = 20

Answers

Answer:

so the answer is I don't know

2.The school chess club is selling T-shirts for a profit of $4 each and baseball caps for a profit of $5 eac The club wants to sell 50 items and make a profit of $230. Calculate how many of each item the chess club needs

Answers

Step-by-step explanation

They sold $480 of tshirts, the ratio is 480;20, simplified to 24:1.

One shirt is $20, but $4 is the amount taken from 20 for the equipment.

Multiply $24 by the $4 taken for the equipment. (Equals $96)

They make 4/20 (1/5) of the the sales as a profit for equipment.

Multiply 1/5 by 480 and you will get $96 as the club's profits.

I hope this helped ya

The chess club needs 20 T-shirts and 30 baseball caps.

What is Profit?

Profit is a term that often refers to the financial gain that a company receives when revenue exceeds costs and expenses. A child at a lemonade stand, for example, spends one quarter to make one cup of lemonade. She then charges $2 for the drink. Her profit on a cup of lemonade is $1.75.

Given :

Total no. of items to be sold = 50

Total profit to be made = $230

Profit on each T-shirt = $4

Profit on each Baseball cap = $5

Let no. of t-shirts be x

Let no. of t-shirts be y

Forming equations according to given problem :

Eq 1 : x + y = 50

Eq 2 : 4x + 5y = 230

Multiplying Eq 1 with 4 we get : 4x + 4y = 200

Subtracting Eq 1 from Eq 2

Solving Eq1 and Eq2 we get x = 20 and y = 30.

Therefore, The chess club needs 20 T- shirts and 30 baseball caps.

To learn more about profits, refer to :

https://brainly.com/question/1078746

#SPJ2

can someone help me with this ? please and thank you

Answers

Answer:

(a), (c) and (d)

Step-by-step explanation:

Required

Which is linear

A linear function is represented as any of:

[tex]y = mx + b[/tex]

[tex]y - y_1= m(x - x_1)[/tex]

[tex](a)\ 8x - 3y = 2[/tex]

Rewrite as:

[tex]- 3y = -8x+2[/tex]

Divide by -3

[tex]y = \frac{8}{3}x - \frac{2}{3}[/tex] -- by comparison to [tex]y = mx + b[/tex], this is linear

[tex](b)\ y = |x - 4|-7[/tex]

This is an absolute function. It is not linear

[tex](c)\ y + 8=5(x - 4)[/tex]

By comparison to [tex]y - y_1= m(x - x_1)[/tex], this is linear

[tex](d)\ y = -7[/tex]

by comparison to [tex]y = mx + b[/tex], this is linear because [tex]m= 0[/tex]

Others are not linear

Express 0.00506 in standard form​

Answers

Answer:

[tex]5.06 x 10^{-3}[/tex]

Step-by-step explanation:

Move decimal 3 place to right.

Because the decimal was moved to right, the exponent is negative.

Find square root of 0.0324

Answers

Answer:

0.18

Step-by-step explanation:

△ABCis reflected to form​​ ​△A′B′C′​. The vertices of △ABC are A(3, 1), B(1, 5), and C(6, 9). The vertices of △A′B′C′ are A′(−1, −3), B′(−5, −1), and C′(−9, −6). Which reflection results in the transformation of ​△ABC​​ to ​△A′B′C′​​? Reflection across the x-axis reflection across the y-axis reflection across y = x reflection across y=−x I NEED HELP PLS The answer choies are: A. Reflection across the x-axis B. Reflection across the y-axis C. Reflection across y = x D. Reflection across y=−x

Answers

Answer:  D) reflection across y = -x

Explanation:

When we reflect over y = x, we basically swap x and y. So for instance, the point (3,1) becomes (1,3).

When reflecting over y = -x, we will do the same thing but we'll make each coordinate swap in sign from positive to negative (or vice versa). The rule for reflecting over y = -x is [tex](x,y) \to (-y,-x)[/tex]

So if we apply that rule to point A(3,1) then it becomes A ' (-1, -3).

Similarly, B(1,5) moves to B ' (-5, -1)

Finally, C(6,9) becomes C ' (-9, -6)

Please hurry I will mark you brainliest

What is the equation of the line with a slope of -3 and a y-intercept of 4?

Answers

Answer:

y = -3x+4

Step-by-step explanation:

The slope intercept form of an equation is

y = mx+b where m is the slope and b is the y intercept

y = -3x+4

De los 30 balones de un colegio, dos quintos son de fútbol, un tercio de baloncesto y el resto de voleibol. ¿Cuántos balones de voleibol hay en el colegio? ayuda es para hoy ;(​

Answers

Answer:

Number of Volleyballs = 8 balls

Step-by-step explanation:

Given:

Total number of balls = 30 balls

Fraction of soccer ball = 2/5 balls

Fraction of basketball = 1/3 balls

Rest are Volleyballs

Find:

Number of Volleyballs

Computation:

Number of Volleyballs = Total number of balls - Total number soccer balls - Total number of basketballs  

Number of Volleyballs = 30 - (30)(2/5) - (30)(1/3)

Number of Volleyballs = 30 - 12 - 10

Number of Volleyballs = 30 - 22

Number of Volleyballs = 8 balls

If the discriminant of an equation is zero, which of the following is true of the equation?​

Answers

[tex]\sf Your \: question \: is \: incomplete. \: [/tex]

______________________

[tex]\sf \: I \: believe \: this \: is \: the \: answer \: you \: wanted[/tex] ⟹

[tex]\sf If \: the \: discriminant \: of \: an \: equation \: is \: zero, \: then \\ \sf \: the \: equation \: will \: have \:\underline{ 1 \: real \: solution \: with \: real \: and \: equal \: roots}.[/tex]

[tex]\boxed{ \sf{Explanation}} [/tex]

[tex]\sf If \: discriminant \: of \: quadratic \: equation \: ax^{2} + bx + c \: \\ \sf is \: b^{2} - 4ac = 0 \: then \: it \: will \: have \\ \sf↦\underline{1 \: real \: solution \: with \: real \: and \: equal \: roots.} [/tex]

Answer:

see explanation

Step-by-step explanation:

If b² - 4ac = 0

Then the roots are real and equal

A number is equal to three times the smaller number also the sum of the smaller number and four is the larger number situation is graft on the coordinate plane below where X represents the smaller number and Y represents the larger number which two equations represent the situation

Answers

Answer:

this question is missing needed information

The triangle below is isosceles. Find the length of side x in simplest radical form with
a rational denominator.
x
V10
21:32
Submit Answer
Answer: =
s
attempt 1 out of 2
CAN SOMEONE HELP ME PLS

Answers

Answer:

x=2*sqrt(5)

Step-by-step explanation:

Since the triangle is isosceles, the other side (not x) is sqrt(10). Using Pythagoras, we have 10+10=x^2, x=2*sqrt(5)

order the set of irrational numbers from least to greatest

Answers

Answer:

answer is A

hope it helps please mark as brainliest answer and give me thanks

#Dhruv here

The angle between the top of a building and a point 80 feet away from the base (on level ground) is 70° . To the nearest foot, how tall is the building?

Answers

Answer: 220 feet tall

Step-by-step explanation:

1. Draw!

2. Use trigonometric ratios to solve for the height (Remember SOH CAH TOA)

Answer:

The building is 220 ft tall

Step-by-step explanation:

2X. (3x - 2y + 4z) con proceso porfavor, ayuda

Answers

[tex]\bf \large \rightarrow \: \: 2x \: ( \: 3x \: - \: 2y \: + \: 4z \: )[/tex]

[tex]\bf \large \rightarrow \: \:6 {x}^{2} \: - \: 6y \: + \: 8x z[/tex]

Espero que te sea de ayuda.

Can someone please just help me fill in those three boxes I’ve been struggling

Answers

7+ square root of 143 = 18.96 and 7- square root of 143 = -4.96

I also believe that 18.96 also makes sense for the last blank because the question makes it seem like it has to be a positive number.

In an A.P the term is -10 and the 15th term is 11 and the last term is 41. Find the sum of all terms in this progression.​

Answers

Answer:  542.5

This is equivalent to the fraction 1085/2

===============================================================

Explanation:

AP stands for "arithmetic progression", which is another name for "arithmetic sequence"

a1 = -10 is the first term

the 15th term happens when n = 15, so

an = a1 + d*(n-1)

a15 = -10 + d(15-1)

a15 = 14d-10

Set this equal to 11 (the stated 15th term) and solve for d

a15 = 11

14d-10 = 11

14d = 11+10

14d = 21

d = 21/14

d = 3/2

d = 1.5 is the common difference

Let's find the nth term

an = a1 + d(n-1)

an = -10 + 1.5(n-1)

an = -10 + 1.5n - 1.5

an = 1.5n - 11.5

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

The last term is 41, so we'll replace the 'an' with that and solve for n

an = 1.5n - 11.5

41 = 1.5n - 11.5

41+11.5 = 1.5n

52.5 = 1.5n

1.5n = 52.5

n = (52.5)/(1.5)

n = 35

So the 35th term is 41.

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

We're summing n = 35 terms from a1 = -10 to an = 41

S = sum of the first n terms of arithmetic progression

S = (n/2)*(a1 + an)

S = (35/2)*(-10+41)

S = 542.5

The 35 terms add up to 542.5 which is the final answer

As an improper fraction, this converts to 1085/2

PLEASE NEED HELP ASAP WILL MARK BRAINLIEST Question 2 of 10
Before radar and sonar, sailors would climb to the top of their ships to watch
for land or changes in weather. If the lookout at the top of the mast can see
an island five miles away, about how tall is the mast? Round your answer to
the nearest whole number if necessary. Use the formula for the relationship
between height (h) and visibility, how far you can see, (d):

O A. 30 feet
O B. 11 feet
O C. 36 feet
O D. 61 feet

Answers

Answer:

36

Step-by-step explanation:

Answer:

36 feet

Step-by-step explanation:

I can confirm that 36 feet is the correct answer. as seen below, I was able to get 100%

the graph of a linear function is given below

Answers

Answer:

The "zero" is where it crosses the x axis which is -2 in this graph

Step-by-step explanation:

Can someone help me with this task please? !!

Answers

Answer:

we need to get your brain thinking in this way. that you begin to understand how to do these things.

airways to say that your brain is not working that way, is not a valid excuse. we need to change that. your brain needs to get used to this way of thinking.

so, please, please, PLEASE go through the explanations below and tell me, where exactly in these explanations you stopped understanding what I was saying. so that I can better explain to you what is happening.

1. (0, -2)

2. 4

3. a geometric sequence. the common ratio is -2.0

4. the third option

5. the fourth option

Step-by-step explanation:

1. as x increases, y decreases. until, suddenly after x=0, this tendency reverses, and with increasing x also y increases. so, this is a turning point.

2. look at the line. it only starts with x>0 (it looks like x is around 1).

"input" is all the values of x the function has a defined result for (y = result values).

so, as there is no line for negative x, we can eliminate the first 2 answers.

x=0 is no valid answer either (as mentioned above, the line only starts well after x=0).

in the answer options the only x value having an y value above or below this x value is x=4.

3. look at the difference between 2 numbers next to each other in the sequence.

2.4 to -4.8

-4.8 to 9.6

and so on.

what do we need to do to get from the left to the right ?

we need to multiply by -2.

so, the relationship between "sequence item n" (an) to "sequence item n-1" (an-1) is a ratio, a multiplication factor :

an/an-1 = -2

4. it is completely simple. a function can be many things. on an x/y coordinate grid it can have gaps, it can have sharp direction changes,...

but there us one thing a function can never have : multiple different y values for one x value.

in the first graph x=2 has two different y values (-1 and -3). so, it is not clear what the result for x=2 would be. and that means, it is not a function.

in the second graph x=4 has two different y values.

in the third graph all is OK.

in the fourth graph x=-2 has two different y values.

so, only the third option is a function.

5. this function calculates the height of the thrown rock after t seconds of flight.

therefore, only the fourth answer makes sense.

How do I simplify this? With steps please :)

Answers

Answer:

[tex]{ \tt{ = \frac{ {p}^{2} + 8p + 16 }{ {p}^{2} - 16 } }} \\ \\ = { \tt{ \frac{ {(x + 4)}^{2} }{(x - 4)(x + 4)} }} \\ \\ = { \tt{ \frac{(x + 4)}{(x - 4)} }}[/tex]

Two thousand numbers are selected randomly; 960 were even numbers. At the 0.10 level of significance, determine whether the proportion of odd numbers is significantly different from 50%.

Answers

Answer:

The p-value of the test is 0.0734 < 0.1, which means that there is significant evidence, at the 0.1 level of significance, to conclude that the proportion of odd numbers is significantly different from 50%.

Step-by-step explanation:

Test if the proportion of odd numbers is significantly different from 50%.

At the null hypothesis, we test if the proportion is of 0.5, that is:

[tex]H_0: p = 0.5[/tex]

At the alternative hypothesis, we test if the proportion differs from 0.5, that is:

[tex]H_1: p \neq 0.5[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.5 is tested at the null hypothesis:

This means that [tex]\mu = 0.5, \sigma = \sqrt{0.5(1-0.5)} = 0.5[/tex]

Two thousand numbers are selected randomly; 960 were even numbers.

This means that [tex]n = 2000, X = \frac{960}{2000} = 0.48[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.48 - 0.5}{\frac{0.5}{\sqrt{2000}}}[/tex]

[tex]z = -1.79[/tex]

P-value of the test and decision:

The p-value of the test is the probability that the sample proportion differs from 0.5 by at least |0.48-0.5| = 0.02, which is P(|z|<1.79), which is 2 multiplied by the p-value of z = -1.79.

Looking at the z-table, z = -1.79 has a p-value of 0.0367

2*0.0367 = 0.0734

The p-value of the test is 0.0734 < 0.1, which means that there is significant evidence, at the 0.1 level of significance, to conclude that the proportion of odd numbers is significantly different from 50%.

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