Mathematics High School

The explicit rule for a sequence is an=14-9n
What is the recursive rule for the sequence?

Answers

Answer 1
you have to add it then divide it 
Answer 2

The explicit rule for the sequence is [tex] a_{n}=14-9n [/tex]

Let us put n=1, we get

[tex] a_{1}=14-(9 \times 1)=5 [/tex]

Now let n=2,

[tex] a_{2}=14-(9 \times 2)=-4 [/tex]

Let n=3,

[tex] a_{3}=14-(9 \times 3)=-13 [/tex]

Similarly, in this manner we obtain a sequence as

5, -4, -13, -22,.....

Since we can clearly observe that the first term is '5' and common difference is '-9'.

So, we get recursive rule for the sequence as:

[tex] a_{n}=a_{n-1}-9 [/tex] , where [tex] a_{1}=5 [/tex].

Related Questions

help please!!!
In Angle ABC, C is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth.
a = 3, c = 19

A. M B. M C. M D M

Answers

we know that In right angle triangle c^2 = a^2 + b^2.
19^2 = 3^2 + b^2
b = (361 - 9)^1/2 = 18.761663039294
Now for angles
 sin(A) = a/c = 3/19
A = sin{-1}(3/19) = 9.0847202873911
A = 9.0847202873911
sin(B) = b/c = 18.761663039294 / 19
B = sin{-1}(18.761663039294 / 19) = 80.915279712614
B = 80.915279712614

In the right triangle shown, AC = BC = 7? What is AB?

Answers

Solve the right triangle shown in the figure
BC=2.7cm, AC=1.1cm, B wrong
so AB is the hypotenuse. It's an isocelels right traingle meaning the other two angles are 45 degrees. So AB = 7[tex] \sqrt{2} [/tex]. We know this because 45 45 is a special right triangle.

When calculating the successive discounts of 15% and 10% on a $100 item, _____. a. take 10% of $85 b. take 10% of $90 c. take 15% of $85 d. take 25% of $100

Answers

It would be a, take 10% of $85 as the $15 is taken off first then the next discount is attached to the new price

Answrer

Option (a) is correct .

i.e  take 10% of $85

Reason

As given

15% and 10% on a $100 item i.e first applied 15 % discount on $ 100 and than apply 10% discount .

15 % is written in the decimal form

[tex]= \frac{15}{100}[/tex]

= 0.15

Amount becomes when 15 % discount on$100 = 100 - 0.15 × 100

                                                                              = 100 - 15

                                                                              = $ 85

Now apply 10 % discount on $ 85.

10 % is written in the decimal form

[tex]= \frac{10}{100}[/tex]

= 0.1

Amount becomes when 15 % discount on$100 = 85- 0.1 × 85

                                                                              = 85 - 8.5

                                                                              = $ 76.5

Therefore the option (a) is correct about the  successive discounts of 15% and 10% on a $100 item is $76.5 .




There are three consecutive odd integers. Three times the largest is seven times the smallest. What are the integers?

Answers

Hello there!

This is how I would map out this problem...

First I would represent the smallest integer with the variable x. Since they are consecutive odd integers, add 2 to the middle integer and add 4 to the largest.

smallest: x
middle: x+2
largest: x+4

Now we need to find a way to solve for x. Since 3 times the largest is 7 times the smallest, we can set up an equation like this...
3(x+4)=7x

Now solve it!
3(x+4)=7x
3x+12=7x
12=4x
x=3

Now let's go back to our original data...
smallest: x
•Since the smallest is x, that means the smallest is going to be 3.
middle: x+2
•since the middle one is x+2, plug in 3 for x and we get 5.
largest: x+4
•since the largest is x+4, plug in 3 for x and we get 7.

This means the answer is...
Smallest: 3
Middle: 5
Largest: 7

I really hope this helps!
Best wishes :)

Porters family ordered 4 pizzas. They ate 2 3/8 of pizza how much pizza is left?

Answers

1 and 5/8 i would guess but is the pizza in 12th or is it just 8th's 

PLEASE HELP ME ON THIS QUESTION

THX~ BRANiLiEST AVAILABLE

PLZ EXPLAIN IF U COULD

Answers

The answer is NOT A nor B, because they're both decreasing.
D's answer shows that the graph is only increasing by 1/2, and C shows that the  graph will increase at a normal rate.

The answer is C.

Find the length of the side labeled x round to the nearest 10th

Answers

Trig problem here. We have 2 right triangles, the one on the left and on the right. They share one side. To find the length of this side, look at the left triangle. The hypotenuse is 44 and theta is 25, and since cos(theta)=adjacent/hypotenuse, cos(25)=adjacent/44 therefore the sidelength is 44cos(25). We are looking for x and now have an angle and a side for the righthand side right triangle so because tan(theta)=opposite/adjacent, tan(34)=opposite/(44cos(25)) therefore the opposite side is 44*cos(25)*tan(34)
You can solve for x by using trigonometry. However, only the angle opposite to x has been given. In order to get another length, find the altitude of the triangle. Use the length of the left side given to set up an equation like this. Let "y" equal the altitude temporarily.
Cos. 25 = y/44
Cos. 25 x 44 = y
0.9063 x 44 = y
39.8772 = y

Now that we have the altitude you can set up another equation for x.
Tan. 34 = x/39.8772
Tan. 34 x 39.8772 = x
0.6745 x 39.8772 = x
26.8971714 = x

Final Answer: x is approximately 26.9



A car dealership has seven cars in the lot. Unfortunately, the keys to the cars have been mixed up. The manager randomly grabs a key and tries to start a car salesman also randomly picks a different key and tries to start another car. What is the probability that both cars start?

Answers

To determine The probability of both of these occurring, you would multiply the probability of each together. So, there is a 1/7 chance of the first salesman getting the right key, and 1/6 chance of the second salesman getting the right key. 1/7 x 1/6= 1/42 chance of both occurring.

what is the solution of this equation x + 6 =24

Answers

If you are looking for x then it is X = 18
the answer is 18 because you had to subtract 6 by 24 and you get 18.

 x=18

Please help! I'm very confused. 20 points.

Answers

1) Use the distributive property to eliminate parentheses.
.. 3(6x) -3(5) -7(3x) -7(10) = 0
.. 18x -15 -21x -70 = 0 . . . . . . finish multiplying terms
.. -3x -85 = 0 . . . . . . . . . . . . . collect like terms
.. -85 = 3x . . . . . . . . . . . . . . . .add 3x
.. -85/3 = x . . . . . . . . . . . . . . .divide by 3
.. -28 1/3 = x . . . . . . . . . . . . . write as mixed number


2) 5 -(6 +9x) = 9 -(4x -1)
.. 5 -6 -9x = 9 -4x +1 . . . . . eliminate parentheses using the distributive property
.. -1 -9x = 10 -4x . . . . . . . . . collect like terms
.. -1 = 10 +5x . . . . . . . . . . . . add 9x
.. -11 = 5x . . . . . . . . . . . . . . . subtract 10
.. -11/5 = x . . . . . . . . . . . . . . divide by 5
.. -2 1/5 = x . . . . . . . . . . . . . write as mixed number

A ball is thrown straight up with a initial velocity of 56 feet per second . The height , h , of the ball t seconds after it is thrown is given by the formula h(t)=56t-16t^2 . What is the maximum height of the ball?

Answers

Formula: H(t) = 56t – 16t^2  

H(t) = - 16t^2 + 56t

A.      What is the height of the ball after 1 second? H (1) = 56(1) – 16(1) ^2 = 40 pt.

B.      What is the maximum height? X = - (56)/2(- 16) = 1.75 sec h (1.75) = 56(1.75) – 16(1.75) ^2 h (1.75) = 49ft.

C.      After how many seconds will it return to the ground? – 16t^2 + 56t = 0   - 8t =0 t = 0

-          8t (2 + - 7) = 0     2t – 7 = 0  t = 7/2   Ans: 3.5 seconds

The maximum height achieved by the ball is 49 meters at time  t = 7/4 seconds.

What is time dependent function?

The time dependent function is the function whose values vary with change in time. For example - f(t) = 3t + 5.

Given is a ball is thrown straight up with a initial velocity of 56 ft/s. The height (h) , of the ball (t) seconds after it is thrown is given by the formula h(t) = 56t - 16t²

The given function is -

h[t] = 56t - 16t²

Now, for maximum height -

dh/dt = 0

d/dt ( 56t - 16t²) = 0

d/dt (56t) - d/dt (16t²) = 0

56 - 16 d/dt (t²) = 0

56 - 16 x 2t = 0

56 = 32t

t = 56/32

t = 7/4 seconds

Now, at t = 7/4 seconds, the height is maximum. Substituting the value

t = 7/4 seconds, we get -

h(7/4) = 56 x 7/4 - 16 x 49/16

h(7/4) = 14 x 7 - 49

h(7/4) = 98 - 49

h(7/4) = 49 meters

Therefore, the maximum height achieved by the ball is 49 meters at time  t = 7/4 seconds.

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An airplane takes off from the ground and reaches a height of 500 feet after flying 2 miles. given the formula h = d tan θ, where h is the height of the plane and d is the distance (along the ground) the plane has flown, find the angle of ascent θ at which the plane took off.

Answers

First we convert everything to the same unit taking into account the following conversion:
 1 mile = 5280 feet
 So, we have:
 h = 500 feet
 d = 2 (5280) = 10560 feet
 Substituting in the given formula we have:
 h = d tan θ
 500 = 10560tan θ
 tan θ = 500/10560
 θ = Atan (500/10560)
 θ = 2.71 degrees.
 Answer:
 the angle of ascent θ at which the plane took off is: 
 θ = 2.71 degrees.

If 5x^2 + y^4 = −9 then evaluate d^2y/dx^2 when x = 2 and y = 1. Round your answer to two decimal places.

Answers

The first derivative is found from
.. 10x +4y^3*dy/dx = 0
.. dy/dx = -5x/(2y^3)

Then
.. d^2y/dx^2 = d(dy/dx)/dx = (-5/2)(y^-3 -3xy^-4*dy/dx)

Evaluated at x=2, y=1
.. dy/dx = -5(2)/(2*1^3) = -5
.. d^2y/dx^2 = (-5/2)*(1^-3 -3*2*1^-4*(-5))
.. = (-5/2)(1 +30)
.. = -155/2 = -77.50

d^2y/dx^2 = -77.50 at the specified point.

Or an angle θ with the point (−20, −21) on its terminating side, what is the value of cosine?

Answers

cos(θ) = -20/√((-20)^2 +(-21)^2)
.. = -20/-√841 . . . . . . . . . . . . . . . . . θ is a 4th-quadrant angle, so cos(θ) > 0
.. = 20/29

The value of the cosine is 20/29.

Answer:

The value of cosine is [tex]\cos \theta=-\frac{20}{29}[/tex].

Step-by-step explanation:

It is given that an angle θ with the point (−20, −21) on its terminating side.

It means the right angle triangle is formed in third quadrant where length of the perpendicular is 21 and the base is 20.

According to the Pythagoras theorem,

[tex]hypotenuse^2=base^2+perpendicular^2[/tex]

[tex]hypotenuse^2=(20)^2+(21)^2[/tex]

[tex]hypotenuse^2=400+441[/tex]

[tex]hypotenuse^2=841[/tex]

Taking square root both the sides.

[tex]hypotenuse=\sqrt{841}[/tex]

[tex]hypotenuse=29[/tex]

In a right angled triangle,

[tex]\cos \theta=\frac{base}{hypotenuse}[/tex]

[tex]\cos \theta=\frac{20}{29}[/tex]

θ lie in the third quadrant and cosine is negative in third quadrant.

[tex]\cos \theta=-\frac{20}{29}[/tex]

Therefore the value of cosine is [tex]\cos \theta=-\frac{20}{29}[/tex].

Speed = distance divided by time taken. car 1 travels 10 miles every 5 minutes. car 2 travels 30 miles every 20 minutes. what is the difference of speed between these two cars in mph?

Answers

car 1
2 miles............................1 minute
10 miles.........................5 minutes
20 miles.........................10 minutes
40 miles..........................20 minutes
car2
1.5 miles...........................1 minute
15miles.............................10 minutes
30 miles...........................20 minutes
the difference is 0.5 miles per minute

0.5*60=30 miles/hour

Please help asap!!!!!!!!!!18 points

Answers

a hope you get a good grade
I think it is C sorry if this doesnt help :'( :)

PLEASE HELP ME WITH THIS QUESTION AND DON'T FORGET TO EXPLAIN

Answers

when n=0, d(n)=690. This is the y-intercept
All the functions given in the options are linear functions in the form y=mx+b, then we must find a function with independent term (y-intercept) b=690
The functions with b=690 are the first and third option.

For the slope (m), we can calculate it with 2 points of the table:
n1=0, d(n1)=690
n2=2, d(n2)=560

m=[d(n2)-d(n1)] / (n2-n1)
m=(560-690) / (2-0)
m= (-130) / 2
m=-65

Then the function must be:
d(n)=mn+b, m=-65, b=690
d(n)=-65n+690

Answer: Third option d(n)=-65n+690 
 

Two angle measures in a scaled Triangle are 77 and 62 what is the measure of the third angle

Answers

Hey there :)

We know that the sum of all 3 angles in a triangle is 180°

Two angles are given to be 77° and 62°

We can find the 3rd angle by:
77 + 62 + x = 180           ( x is the angle to be found, you can use any variable, if not given)
180 - ( 77 + 62 ) = x
180 - 138 = x
41°

The area of a triangle is 40sq inches. If the base of the triangle is 10 inches what is it’s height?

Answers

area of a triangle= 1/2 base times height
substitute

40=1/2*10*x
40=5x
x=8

the height is 8 inches

Answer:

Step-by-step explanation: 8 inches

1/3 math questions. pls help! 20 pts!

Answers

Since one cm on the map represents 2 km on the trail, we can use unit rates and proportions to solve this.

8 × 1 = 8
8 × 2 = 16

The actual length of the trail is 16km.

Hope this helps!

One angle of atriangle measures 12 degrees. the second angle's measurements is five times the third. what is the measure of the third angle

Answers

28 degrees. This is because the first angle is 12 degrees, the third is x degrees and the second is 5x. You know that in a triangle the angles add up to 180 degrees so 12 + 5x + x = 180. Then you get 6x =168 and x =28 degrees. (**x being the thrid angle**)

The measure of the third angle is; 28 degrees.

How does an angle form?

An angle requires two straight line/ line segments/rays, such that they're connected on one of their endpoints.

The point of their joint is called vertex of that angle.

Those two line segments forming it are called arms of that angle.

The angle is the degree of rotation that it will take for the moving side to go from initial side to the position it is currently on.

Let the third angle be x

Given that One angle of a triangle measures 12 degrees. the second angle's measurements is five times the third.

We know that in a triangle the angles add up to 180 degrees.

so, 12 + 5x + x = 180.

Then we get

6x =168

x =28 degrees.

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Using complete sentences, explain the key features of the graph of the sine function.

Answers

check the picture below.

please help asap! match equation to the graph

Answers

The answer is a)7x+7y=0

Answer:

B) -7x + 7y= -49

Step-by-step explanation:

Using the general equation for a line

y=mx+b

where m is the slope (positive if the line goes up from left to right and negative is it goes down from left to right)

and b is the point where the line crosses the y-axis

By th graph we can see that the line goes up from left to right, so the slope is positive, and that it crosses the y axis in -7, b= -7 and x is positive.

Solving for y in all the options

A) y = -x

B) y = x - 7

C) y = -x +7

D) y= x+7

the option that describes the line in the graph is B) -7x + 7y= -49 since when clearing for y we get y = x - 7 wich has a positive slope, and has an interception b = -7.

I️ need to find the answer

Answers

(a) m∠RQS = (1/2)m∠QPR = 37°

(b) m∠QPR = m(arc QR) = 74° . . . . . an arc has the same measure as its central angle

Someone help me ASAP!!!!!!

Answers

C looks the most similar to what I have.
The points are (7.5, 0) and (0, -5)

John let out 50 foot of kite string when he observes that his kite is directly above a point on the ground 30 feet away from him, how high is the kite ?

Answers

70 feet i believe confuseing to me

Answer:

the answer is 40 i had it on USATestPrep

Step-by-step explanation:

ion need one lml

The quotient of a number and 2 is the same as the difference of the number doubled and 3

Answers

x/2=2x+3 is the expression you would use!

Amys class is selling books to raise money for a field trip. If each book sells for $7, how many books will they need to sell to raise $125?

Answers

You would start by setting up the equation:

7x=125 where x is equal to the number of books sold

x=17.9

Since you cannot sell .9 of a book, this must be rounded up to 18.
Therefore, Amy must sell 18 books.

A ball is thrown into the air from the edge of a 48 foot cliff so that it eventually lands on the ground. The graph below shows the height, y, of the ball from the ground after x seconds.

For which interval is the ball’s height always decreasing?

A. 48 B.0 C.2.5 D.146

Answers

the answer should be C, 2.5<x<5.5

2.5 < x < 5.5 seconds is the time interval when ball's height always decreasing.

What is time interval?

" Time interval is the division of time into small equal intervals to have a proper observation of any data."

According to the given graph,

x represents time in seconds along x-axis

y represents height in foot of the ball along y-axis

As per observation,

Height of the ball increasing from 48 to 146 in the time interval

0< x < 2.5.

Height of the ball decreasing from 146 to 0 in the time interval           2.5< x < 5.5.

Hence, we conclude that 2.5 < x < 5.5 seconds is the time interval when ball's height always decreasing.

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Roasting meats at high temperatures makes them moist and tender.

True False

Answers

The answer is false

Answer:

False

Step-by-step explanation:

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