Sarah has saved $150. She wants to double the amount she saves each month. As an incentive, Sarah's grandma says if she saves that amount, she will give her an additional $50 each month. What is the recursive sequence formula and first term for Sarah’s savings

Answers

Answer 1

A recursive relation is a relation that defines the terms in a sequence with the previous terms.

Here, the recursive relation will be:

[tex]A_n = 2*A_{n - 1} + $50[/tex]

A₁ = $150.

We know that:

Sarah has saved $150 at the moment.

She wants to double the amount that she saves each month, so the next month she needs to save 2*$150 = $300

And if she saves the $300, then her grandma will give her another $50.

Then, if the previous month Sarah saved A, then the next month she will get the double of A plus $50, which is:

2*A + $50

Then the recursive relation is just:

[tex]A_n = 2*A_{n - 1} + $50[/tex]

Where Aₙ is the amount that she saves in the n-th month, and the first term of the sequence is the initial amount that she saved, so we have:

A₁ = $150.

If you want to learn more about recursive relations you can read:

https://brainly.com/question/13143285


Related Questions

Chloe was given a gift of a conical bird feeder that has a volume of 785.4 cubic centimeters. What is the area of the lid she will need to cover the bird feeder?

Answers

Answer:

392.7 cubic centimeters. Hope that helps :)

Step-by-step explanation:

how many units is 12x+16

Answers

Answer:

I think the answer is 1/2

Step-by-step explanation:

because

12x=6

x=6/12

•°•x=1/2

What is the midline equation of the function h(x) = -4 sin (x- pi/4)

Answers

Answer:

[tex]y = \boxed0[/tex]

Step-by-step explanation:

we are given a sin function

[tex] \displaystyle h(x) = - 4 \sin(x -\pi /4) [/tex]

we want to figure out the midline of the function graphically The midline of a sinusoidal function is the horizontal line that passes exactly in the midline of its extreme value however since we a function recall that,

[tex] \displaystyle f(x) = a \sin(bx -c) + d[/tex]

where the midline is

[tex]y = d[/tex]

to figure out the midline rewrite the function

[tex] \displaystyle h(x) = - 4 \sin(x -\pi /4) + 0[/tex]

therefore the midline is

[tex]y = \boxed0[/tex]

Which number line plots the integers –6, –2, and 5?
A number line going from negative 6 to positive 6. Points are at negative 6, negative 5, negative 2.
A number line going from negative 6 to positive 6. Points are at 2, 5, 6.
A number line going from negative 6 to positive 6. Points are at negative 5, 2, 6.
A number line going from negative 6 to positive 6. Points are at negative 6, negative 2, 5.

Answers

Answer:

Một trục số đi từ âm 6 đến dương 6. Các điểm ở âm 6, âm 2, 5.

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

please help!!!!!!!!!!!

Answers

it should be this y=1/2x+3
I agree with the answer above

Find the area of the circle.
Use 3.14 for n. Do not round your answer.
Hint: A = tir2
3 in.
Area = [?] inches?
Enter the number that
belongs in the green box.
Enter


Pls someone help

Answers

Answer:

28.26

Step-by-step explanation:

A = (3.14)(3)^2

A = 3.14 * 9

A = 28.26

Answer:

28.26

Step-by-step explanation:

The area of a circle is

A = pi r^2  where r is the radius

A = 3.14 ( 3)^2

A = 3.14 *9

28.26

You are picking out an outfit. Which of the following options shows a closet with 24 different possible combinations of outfits? Select all that apply.
A) 6 shirts, 2 shorts, 3 hats
B) 12 shirts, 2 shorts, 2 hats
C) 3 shirts, 4 jeans, 2 hats
D) 6 shirts, 2 jeans, 2 hats
E) 12 shirts, 2 jeans, 1 hat

Answers

Answer:

C, D, E

Step-by-step explanation:

You just need to multiply the numbers together.  Whichever choice is equal to 24, is your answer

So when you multiply for each one...

A is 36

B is 48

C is 24

D is 24

E is 24

So since C, D, E multiply to 24, they are the correct answers.

10. Find the mean, median of the following data.
5,3, 2, 6, 5, 2,5
a. 5,4
b. 6,8
c. 28,7
d. 4,5

Answers

Answer:

A

Step-by-step explanation:

You find the mean by adding all the values then dividing that sum by the amount of values

You find the median by putting the numbers in order from least to greatest and then find the middle number.

The answer is D. 4,5 because for the mean you would add 5+3+2+6+5+2+5, which would be 28, and divide it by how many numbers there are, which is 7. 28 divided by 7 is 4. As for the median, you would put the numbers in order, 2,2,3,5,5,5,6 and the number in the middle, which is 5, is the answer you’re looking for.

Find the area of the sector. Round the answer to the nearest tenth.

Answers

Answer:

63.4

Step-by-step explanation:

Area of arc is (pi*(11)^2*(60/360))=63.4

What are the factors of the quadratic function represented by this graph?
A (x - 1) and (x - 5)
B. (-x-1) and (x + 5)
C. (x-1) and (x + 5)
D (-x + 1) and (x-5) ​

Answers

Answer:

I think it is A

Step-by-step explanation:

[tex](x - 1) \: and \: (x - 5)[/tex]

I hope that is useful for you :)

The factors of the quadratic function whose graph is given are (-x -1) and ( x-5).

What is the factor of a quadratic equation?

Factor of a quadratic equation is any monomial or binomial which divides the quadratic equation without leaving any remainder.

What is factorization of quadratic equation?

Factoring a quadratic equation can be defined as the process of breaking the equation into the product of its factors.

What is solution to the quadratic equation?

The solutions of a quadratic equation represent the values of x that make the equation true. And the solutions to any equation are the x-intercepts of that equation.

According to the given question

We have a graph of a quadratic equation and x intercepts -1 and -5.

⇒ we have two points (-1,0) and (-5,0)

⇒ -1 and -5 will be the solution of the quadratic function.

⇒ x = -1  and x = -5

⇒ x+ 1= 0 and x + 5 = 0

or -x -1 = 0 and x+5 = 0

Therefore, the factors of the quadratic function whose graph is given are (-x -1) and ( x-5).

Learn more about the factors of a quadratic function here:

https://brainly.com/question/19525535

#SPJ2

Question 2 of 10
Which of the following can you determine, when you use deduction and start
from a given set of rules and conditions?
A. None of these
B. What may be true
C. What may be false
D. What must be true
SUBMIT

Answers

D, it’s a process of elimination
D I don’t know for sure but I think it’s d ……………….

Complete this item.

For the following figure, can you conclude that / | | m? Select true or false.

Answers

Answer:

true

Step-by-step explanation:

:)

Simplify -1/2x3/5÷(-59/40)

Answers

Answer:

12/59

Step-by-step explanation:

-1/2x3/5÷(-59/40)

-3/10÷(-59/40)

-3/10*-(40/59)

120/590

12/59

Choose ALL of the ordered pairs that are solutions to the equation.
5y = 2x - 7
a) (6, 0)
b) ( 7, 21)
c) (8, 18)
d) ( -3, 4)

Answers

b) ( 7, 21)

Step-by-step explanation:

5(7)=2(21)-7

35=42-7

35=35

Answer:

None of them

Step-by-step explanation:

a: 5*0=2*6-7 False

b: 5*21=2*7-7 False

c: 5*18=2*8-7 False

d: 5*4=2*-3-7 False

which one is the correct answer

Answers

Answer:

B.

Step-by-step explanation:

2x - 31 = - 2x - 314x = 0x = 0

Other equations don't have any value of x.

Answer:

[tex]2x-31=-2x-31[/tex]

Because if you see.. The component of x will get canceled in each of the other 3 options.. ( 2x - 2x) which means no solution.. In option B.. 2x + 2x will give 4x..= 31-31 = 0..

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

Hope it helps...

Have a great day!!

A line passes through the points (0,0) and (4,4). What is the equation of the line?

Answers

Answer:

y = x

Step-by-step explanation:

So what we're going to want to do here is use the slope formula and the general equation y = mx + b.

Let's start.

The slope formula is y2-y1/x2-x1. So, put our points in here. 4-0/4-0. Slope: 1.

Okay, we have that. Now, a line that passes through the origin (0,0) is not going to have a y-intercept because it hits the y-axis at 0. So, that cancels out the b.

With our slope 1, the answer is just y = x. Very simple equation.

Hope this helped!

What is the equation of this circle?

Answers

Answer:

(x-3)^2+y^2=8

Step-by-step explanation:

I'm going to go ahead and assume the center is (3,0). The radius can be found by computing the distance from the center, (3,0), to a point on the circle, (5,-2).

The distance between two points is calculated by doing sqrt((distance between x's)^2+(distance between y's)^2).

The distance between our x's is 2.

The distance between our y's is 2.

The square of each then is 4 and 4 respectively.

So we have the distance is sqrt(4+4)=sqrt(8).

The radius is sqrt(8).

The equation of a circle is (x-h)^2+(y-k)^2=r^2 where (h,k) is center and r is radius.

If r=sqrt(8), then r^2=8.

(h,k)=(3,0)

(x-h)^2+(y-k)^2=r^2

(x-3)^2+(y-0)^2=8

(x-3)^2+y^2=8

What conclusion can be derived by comparing the central tendencies of the two data sets?
A: (7, 6, 3, 1, 6, 2, 4, 6, 3, 5;
B: {2, 2, 2, 3, 4, 5, 2, 8, 7, 6}

Answers

A is the correct answer because u should know

Idenify the domain for the function, f(x).

(Negative infinity, infinity)
(Negative infinity, 0) Union (0, infinity)

(Negative infinity, 2) Union (0, 2) Union (0, infinity)

(negative infinity, negative 2) Union (negative 2, 0), union (0, infinity)

Answers

Answer:

[tex]Domain = (-\infty,\infty)[/tex]

Step-by-step explanation:

The function is not given; So, I will answer this question using

[tex]f(x) = 1.6x - 2[/tex]

Required

The domain

In [tex]f(x) = 1.6x - 2[/tex],

- there is no fraction where x is in the denominator

- there is no root where x is in the radicand

This means that, there is no restriction on x.

Hence, the domain is:

[tex]Domain = (-\infty,\infty)[/tex]

Answer:

A. (negative infinity, infinity)

Step-by-step explanation:

I need help I don't understand it at all

Answers

Answer:

x = 9

Step-by-step explanation:

Given

5x - 31 = 23 - x ( add x to both sides )

6x - 31 = 23 ( add 31 to both sides )

6x = 54 ( divide both sides by 6 )

x = 9

Answer: X = 9

Step-by-step explanation: basically you solve it just like any other algebra equation. The only difference is that you have x’s on both sides. You have to move one of them over. I move the x to the right and I added it to the left side. 5x plus x is 6x. ( in case you didn’t already know an x never stands alone when you see one alone it always has an imaginary 1 beside it.) after I did that I tried to isolate 6x so I added 31 to 23. 31 plus 23 equals 54. I then had the equation 6x=54. The next thing I wanted to do was to isolate the x. I then dived 6 on both sides and got x= 9

What is the y-intercept of this quadratic function f(x) = x2 + 2x + 3

Answers

Hi there!

[tex]\large\boxed{0, 3}[/tex]

Find the y-intercept by substituting in 0 for x:

f(0) = 0² + 2(0) + 3

Simplify:

f(0) = 3

Answer:

0,3

hope this helped !!!

Step-by-step explanation:

Solve for: X=____ Y=____
Round to the nearest tenth.

X= 60°
Y=30°

X=22.6°
Y=67.4°

X=30°
Y=60°

X=67.4°
Y=22.6°

Answers

Answer:

D

Step-by-step explanation:

These diagrams can drive you crazy. The only way you can do this question is to ASSUME that the angle that looks like it is 90 really is 90. That is a very dangerous assumption.

Solution for y

cos(y) = adjacent / hypotenuse

adjacent = 12

hypotenuse = 13

Cos(y) = 12 / 13

Cos(y) = 0.92308

y = cos-1 (0.92308)

y = 22.6

Solution for x

x does not need trig to solve.

x = 180 - 90  - 22.6

x = 67. 4

So that's D

compare the slopes and y intercepts of the graphs of the equations in the linear system 8x + 4y =12 and 3y = -6x -15 to determine whether the system has one solution no solutions or infinitely many solutions explain

Answers

Answer:

No solutions

Step-by-step explanation:

Convert both equations into y = mx + b form, where m is the slope and b is the y intercept.

8x + 4y = 12

4y = -8x + 12

y = -2x + 3

Rearrange the other equation:

3y = -6x - 15

y = -2x - 5

So, both equations have a slope of -2. But, one has a y intercept of 3 and the other has a y intercept of -5.

Because the lines have the same slope but different y intercepts, the lines are parallel.

Parallel lines have no solutions, because they will never intersect.

So, the system has no solutions.

only answer mean with explanation please

Answers

Mean is the average, so you add up all of the top numbers, and divide them by how many numbers there are in the top row. 1+2+3+4+5+6= 21 and 21/6= 3.5.

The mean is 3.5

Answer:

Hello,

3.85

Step-by-step explanation:

[tex]Number\ of\ customers=3+0+5+3+7+2=20\\\\mean=\dfrac{1*3+2*0+3*5+4*3+5*7+6*2}{20} =\dfrac{77}{20} =3.75[/tex]

If m angle PQR = 141", find each measure. ​

Answers

Answer:

x=6

pqs=82

sqr=59

Step-by-step explanation:

13x + 4 + 10x - 1 = 141

23x + 3= 141

23x = 136

x = 136/23 = 6

~~~~~~~~~~~~~~~

pqs = 13x + 4  = 13(6) + 4 = 78+4 = 82

sqr =  10x - 1 = 10(6)-1 = 60 - 1 = 59

Answer:

x = 6

Angle PQS is 82

Angle SQR is 59

Step-by-step explanation:

13x + 4 + 10x - 1 = 141

Group like terms : 23x + 3 = 141

Subtract 3 from both sides to get 23x = 138

Divide both sides by 23 to get x = 6

Angle PQS: Plug 6 into x  for 13x + 4 = 13 (6) + 4 = 82

Angle SQR: Plug 6 into x for 10x - 1 = 10 (6) -1 = 59

Three tennis balls that fit in cylindrical tennis ball cane. If each ball is 14 inches in diameter, what is the volume of air left between the balls and the cane​

Answers

Given:

Diameter of the tennis ball = 14 inches.

Three tennis balls are fit in a cylindrical tennis ball cane.

To find:

The volume of air left between the balls and the cane​.

Solution:

Diameter of the tennis ball = 14 inches.

Radius of the tennis ball = 7 inches

Radius of tennis ball is equal to radius of cane. So,

Radius of the cane = 7 inches

Height of cane is:

[tex]3\times 14=42[/tex] inches

Volume of a ball is:

[tex]V_1=\dfrac{4}{3}\pi r^3[/tex]

Where, r is the radius of the ball.

So, the volume of 3 ball is:

[tex]V_2=3\times V_1[/tex]

[tex]V_2=3\times \dfrac{4}{3}\times \dfrac{22}{7}\times (7)^3[/tex]

[tex]V_2=4312[/tex]

Volume of the cane is:

[tex]V_3=\pi r^2h[/tex]

Where, r is the radius of the cane and h is the height of the cane.

[tex]V_3=\dfrac{22}{7}\times (7)^2\times 42[/tex]

[tex]V_3=6468[/tex]

Now, the volume of air left between the balls and the cane​ is:

[tex]V=V_3-V_2[/tex]

[tex]V=6468-4312[/tex]

[tex]V=2156[/tex]

Therefore, the volume of air left between the balls and the cane​ is 2156 cubic inches.

a recipe for a cake calls for 5 1/10 cups of sugar Anjali accidentally puts in 5 3/4 cups how much extra did she put

Answers

Answer:

2/15

Step-by-step explanation:

I think not 100% on this but not so sure-

Subtract 5 1/10 from 5 3/4

5 3/4 - 5 1/10

• Subtract the whole numbers (5 and 5)

5 - 5 = 0

• LCM of the denominators (4 and 10)

= 13/20

She put an extra 13/20

Ming drew the model to represent the equation 24+12=_x(8+4). What is the missing value in Ming's equation 3 4 12 24

Answers

Answer:

3 is the missing value

Step-by-step explanation:

Given

[tex]24 + 12 = \_ * (8 + 4)[/tex]

Required

Complete the blank

The model is not given; but the question can still be solved.

We have:

[tex]24 + 12 = \_ * (8 + 4)[/tex]

Add 8 to 4

[tex]24 + 12 = \_ * 12[/tex]

Add 24 to 12

[tex]36= \_ * 12[/tex]

Divide both sides by 12

[tex]3= \_[/tex]

Rewrite as:

[tex]\_ = 3[/tex]

Hence, the blank will be completed with 3

Answer:

a

Step-by-step explanation:

edg 2021

Evan tosses a ball from the roof of a building. The path of the ball can be modelled
by the following equations where h represents the height of the ball in meters and
t represents the time in seconds. Each equation below represents the EXACT same
path. Using the information you can obtain from these equations, answer the
following questions.
nu = -4(t + 1)(t-5)
h2 = -4/t - 2)2 + 36
hz = -4t? + 16 + 20
Draw a detailed SKETCH representing the path of the ball. Be sure to include titles
for your axes, appropriate scales, and critical points such as initial value, vertex and
roots of the parabola.

Answers

Answer:

Please find attached sketch of the path of the ball, having plot area and plot points, created with MS Excel

Step-by-step explanation:

Question;

The equation representing the path of the ball obtained from a similar question posted online are;

h₁ = -4·(t + 1)·(t - 5), h₂ = -4·(t - 2)² + 36, h₃ = -4··t² + 16·t + 20

The above equations represent the same path

The equation, h₁ = -4·(t + 1)·(t - 5), gives the roots of the height function, h(t), used in determining the height of the ball after time t

At (t + 1) = 0 (t = -1) or at (t - 5) = 0 (t = 5), the ball is at ground level

The ball reaches the ground, is at ground level at t = 1, and at t = 5 seconds after being tossed, where h(t) = 0

The equation of the path of the ball in vertex form, y = a·(x - 2)² + k, is h₂ = -4·(t - 2)² + 36, where, by comparison, we have;

The vertex of the ball = The maximum height reached by the ball  = (h, k) = (2, 36)

The coefficient of the quadratic term, t², is negative, therefore, the shape of the parabola is upside down, ∩, shape

The sketch of the path of the ball created with MS Excel, used in plotting the vertex, the initial value and the root points of the parabola, through which the ball passes and joining of the points with a 'smooth' curve is attached

what is x: |3x-1| = 4

Answers

Step-by-step explanation:

here's the answer to your question

The correct answer is X= -1
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