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:
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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
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.
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
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.
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)
Answer:
I think it is AStep-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:
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Find the area of the sector. Round the answer to the nearest tenth.
Answer:
63.4
Step-by-step explanation:
Area of arc is (pi*(11)^2*(60/360))=63.4
What is the midline equation of the function h(x) = -4 sin (x- pi/4)
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]
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)
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:
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.
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
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
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.
please help!!!!!!!!!!!
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
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
how many units is 12x+16
Answer:
I think the answer is 1/2
Step-by-step explanation:
because
12x=6
x=6/12
•°•x=1/2
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
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
Simplify -1/2x3/5÷(-59/40)
Answer:
12/59
Step-by-step explanation:
-1/2x3/5÷(-59/40)
-3/10÷(-59/40)
-3/10*-(40/59)
120/590
12/59
which one is the correct answer
Answer:
B.
Step-by-step explanation:
2x - 31 = - 2x - 314x = 0x = 0Other 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!!
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°
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
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?
Answer:
392.7 cubic centimeters. Hope that helps :)
Step-by-step explanation:
Complete this item.
For the following figure, can you conclude that / | | m? Select true or false.
Answer:
true
Step-by-step explanation:
:)
what is x: |3x-1| = 4
Step-by-step explanation:
here's the answer to your question
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
What is the equation of this circle?
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
A line passes through the points (0,0) and (4,4). What is the equation of the line?
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 y-intercept of this quadratic function f(x) = x2 + 2x + 3
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:
If m angle PQR = 141", find each measure.
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
I need help I don't understand it at all
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
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
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
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}
only answer mean with explanation please
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]
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
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.
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.
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:
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)
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
