The formula of the given geometric sequence is: a(n) = 1024 . (0.5)ⁿ⁻¹ and the first five terms are: 1024, 512, 256, 128, and 64.
The formula of the n-th term of a geometric sequence is:
a(n) = a₁ . r^(n-1)
Where:
a₁ is the first term
r is the ratio = a(n)/a(n-1)
Parameters given in the problem:
a₁ =1024, r=0.5
Plug these parameters into the formula, then we get the explicit formula of the n-th term:
a(n) = 1024 . (0.5)ⁿ⁻¹
The first 5 terms:
a₁ = 1024
a(2) = 1024 . (0.5)²⁻¹
= 1024 . (0.5)¹ = 512
a(3) = 1024 . (0.5)³⁻¹
= 1024 . (0.5)² = 256
a(4) = 1024 . (0.5)⁴⁻¹
= 11024 . (0.5)³ = 128
a(5) = 1024 . (0.5)⁵⁻¹
= 1024 . (0.5)⁴ = 64
Learn more about geometric sequence here:
https://brainly.com/question/16833212
#SPJ4
40 times 40 equals what
Answer:
1600
Step-by-step explanation:
1600
Answer:
1600
Step-by-step explanation:
I need help with 1 and 2
How many groups of 1/9 are there In 2
Answer:
18
Step-by-step explanation:
Is an elevation of -10 feet closer or farther from the surface of the ocean than an elevation of -8 feet?
The elevation of -10 feet is farther from the surface level of the ocean than an elevation of -8 feet.
Here, we are given two elevation levels from the surface of the ocean.
One elevation is of -10 feet and another one is of -8 feet.
An elevation of -10 feet implies that the distance from the surface level is 10 feet.
On the other hand an elevation of of -8 feet implies that the distance from surface level is 8 feet.
Thus, by comparing the distances, we can see that elevation of -10 feet is farther from the surface level of the ocean than an elevation of -8 feet. To be more precise, it is 2(10-2) feet farther than an elevation of -8 feet.
Learn more about surface level elevation here-https://brainly.com/question/27894219
#SPJ9
The Equation a = 1/2(8)h Represents the area a of a triangle with base of 8cm and a height of h cm. Make a table to find the areas of triangles with heights of 6 cm, 7cm, 8 cm, and 9 cm.
The table derive from the area formula of a triangle is summarized below:
h (cm) A (cm²)
6 24
7 28
8 32
9 36
What are the areas of the triangle for a given set of areas?
The area formula of a triangle (A), in square centimeters, is equal to the half of a product of the base (b), in centimeters, and the height (h), in centimeters. In this question we have the following triangle formula:
A = (1 / 2) · (8) · h
A = 4 · h
Where h is the height of the triangle.
Now we proceed to make a table with the given heights:
h (cm) A (cm²)
6 24
7 28
8 32
9 36
To learn more on area formulas: https://brainly.com/question/3134284
#SPJ1
I need help with number 42 please
Answer:
yes, it’s proportional
Step-by-step explanation:
Determine whether each series is arithmetic or geometric. Then evaluate the finite series for the specified term number. 2+7+12+ . . . . . . ; n=8
The given series is an arithmetic series. The sum of its first 8 terms is 156.
To determine whether the series is an arithmetic or geometric one, we need to check how the consecutive terms relate to each other.
If it is an arithmetic series, then:
a(n) = a(n-1) + d
where d is the common difference.
If it is a geometric series, then:
a(n) = a(n-1) . r
where d is the common ratio.
The given series is:
2+7+12+ . . . .
and the number of terms is 8.
In the given series:
a(1) = 2
a(2) = 7
a(3) = 12
Notice that the difference is constant,
d = a(3) - a(2) = a(2) - a(1)
= 7 - 2 = 5
Sum formula for the first n term of an arithmetic series is:
S(n) = n/2 . [2a(1) + (n - 1) . d]
Substitute n = 8, a(1) = 2, and d = 5
S(8) = 8/2 ( 2.(2) + (8 -1) .5)
S(8) = 4. 39 = 156
Learn more about series here:
https://brainly.com/question/8919590
#SPJ4
Two similar hexagonal prisms have volumes of 250 cubic feet and 2 cubic feet. What is the ratio of the height of the large cylinder to the height of the small cylinder?
The ratio of the height of the larger prism to the smaller prism is a/b = 5.
To solve this problem we must know what a scale factor is.
What is the scalar factor?The scale factor is a dimensionless number that allows us to relate dimensions in figures, it is also known as numerical ratio or proportion.
If we have as reference the volumes of two hexagonal prisms, with the values of:
250 cubic feet2 cubic feetIf the reason or scale for the volume is given by
a³/b³ = 250/2a³/b³ = 125Let's go for the reason of the length, for this we apply the cubic root.
a³/b³ ⇒ ∛(a³/b³)
∛250/2
a/b = 5
Learn more about scale factor in:
https://brainly.com/question/28562468
#SPJ4
Translate the sentence into an equation.
Five less than the product of 3 and a number 6 equals .
Use the variable b for the unknown number.
Answer: b = 11/3 (or) 3.67
Step-by-step explanation:
Five less than the product of 3 and a number 6 equals .
five less = - 5
product of 3 and a number = (multiply) 3 x b
equals 6 = = 6
3b - 5 = 6
3b = 6 + 5
3b = 11
b = 11/3
b = 3.67 ( rounded )
Determine whether each sequence is arithmetic. If so, identify the common difference and find the 32 nd term of the sequence. 7,10,13,16, . . . . .
Common difference = 3 , 32nd term = 100
The arithmetic sequence is the sequence where the common difference remains constant between any two successive terms.
The given series is
7, 10, 13, 16....
common difference = 10-7 = 13- 10= 16-13 = 3
Therefore there is a common difference between the two consecutive number.
In this series the common difference is 3.
Hence we get to know that the given series is an arithmetic series.
To identify the 32nd term we have a formula:
[tex]t_{n}[/tex] = a +(n-1)d
Here a = first number of the series
n = number of series
d = common difference
[tex]t_{32}[/tex] = 7 + (32-1)3
= 7 + 31×3
= 7 + 93
= 100
Hence the 32nd term is 100.
To know more about the arithmetic series refer to the link given below:
https://brainly.com/question/22972770
#SPJ4
Bert is 11 kilometers away from brenda. both begin to walk toward each other at the same time. bert walks at 3 kilometers per hour. they meet in 2 hours. how fast is brenda walking?
2.5x4=10(Bert's walking distance)
22-10=12(Brenda's walking distance)
12/4=3
3km/h is Brenda's walking distance.
What is a Kilometer?The International System of Units (SI) defines the kilometer, sometimes known as the kilometer in American English, as one thousand meters (kilo- being the SI prefix for 1000). The United States and the United Kingdom are significant outliers, where the statute mile is the unit of measurement used to express distances between geographical locations on land.
1 mile is equivalent to 1.609 kilometers. Both the mile and the kilometer are units of measurement. A mile is longer than a kilometer, nevertheless. A larger unit is a "mile."
1000 meters make up one kilometer. We use kilometers to calculate distance when traveling between two points.
To learn more about Kilometer from the given link:
brainly.com/question/13987481
#SPJ4
Solve each equation. 4+x=-52
The soluton of the given linear equation in one variable 4 + x = -52 is x = -56.
According to the given question.
We have a linear equation in one variable 4 + x = -52.
Since, we have to solve the above equation for x.
As we know tha, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Thereofore, the solution of the above equation 4 + x = -52 is given by
4 + x = -52
⇒ x = -52 - 4 ( subtract 4 both the sides)
⇒ x = -56
Hence, the soluton of the given linear equation in one variable 4 + x = -52 is x = -56.
Find out more information about equation here:
https://brainly.com/question/15265517
#SPJ4
-0.4-x=
−0.4−x=
\,\,-6(x-3.1)+6x
−6(x−3.1)+6x
Answer:
Step-by-step explanation:
I think you meant
-0.4 - x = -6(x - 3.1) + 6x
-0.4 - x = -6x + 6x + 18.6
-0.4 - x = 18.6
-x = 18.6 + 0.4
-x/-1 = 19/-1
x = -19
check
-0.4 - (-19) = -6(-19 - 3.1) + 6(-19)
18.6 = -6(-22.1) + (-114)
18.6 = 132.6 - 114
18.6 = 18.6
3. Plot 2 ordered pairs on the initial climb (first part of the rollercoaster going up) and determine the slope.
Points: Work to find Slope: Slope: ________
4. What is the equation of the line in slope-intercept form that represents your initial climb (first part of the rollercoaster going up)?
Equation: ___________
5. What is the domain and range of your entire roller coaster? (HINT: use compound inequalities)
Domain: Range:
6. a) Plot 2 ordered pairs at the top and the bottom of each hill (not the loop).
Hill 1 points: _________ Hill 2 points: _________
b) Find the rate of change going down each hill.
Work for Hill 1: Work for Hill 2:
Rate of change down Hill 1: _______ Rate of change down Hill 2: _______
c) Which hill is steeper? How do you know that hill is steeper?
Hill 1 or Hill 2 (circle/underline/pick one)
Explanation:
7. Is the roller coaster a function? Why or why not?
Function: YES or NO (circle/underline/pick one)
Explanation:
Using function concepts, it is found that:
3. Two ordered pairs are: (0, 0) and (130,260). The slope is of 2.
4. The equation of the line is of y = 2x.
5. The domain is 0 ≤ length ≤ 400, and the range is 0 ≤ height ≤ 260.
6. a)
For Hill 1, we have that:
The bottom point is (130,260).The top point is (170,60).For Hill 2, we have that:
The bottom point is (400,0).The top point is (360,80).6. b) The rate of change down Hill 1 is of -5, while it is of -2 for Hill 2.
6. c) Due to the higher rate of change, Hill 1 is steeper.
7) The roller coaster is not a function, as for lengths between 190 ft and 240 ft, there are vertically aligned points on the graph.
What are the two ordered pairs on the initial climb, what is the slope, and what is the equation of the line?Two ordered pairs are: (0, 0) and (130,260).
The slope is given by change in y divided by change in x, hence:
m = (260 - 0)/(130 - 0) = 2.
Considering the slope and the intercept(which is of 0, as when x = 0, y = 0), we have that:
The equation of the line is of y = 2x.
What are the domain and the range of the graph?The domain of a function is the set that contains all possible values of the input. In the graph, it is all the values assumed by the horizontal axis.The range of a function is the set that contains all possible values of the output. In the graph, it is all the values assumed by the vertical axis.Hence:
The domain is 0 ≤ length ≤ 400, and the range is 0 ≤ height ≤ 260.
Bottom and top of the hills:For Hill 1, we have that:
The bottom point is (130,260).The top point is (170,60).For Hill 2, we have that:
The bottom point is (400,0).The top point is (360,80).The rates of change(change in height divided by change in length) are given as follows:
Hill 1: (-200)/40 = -5.Hill 2: -80/40 = -2.Due to the higher rate of change, Hill 1 is steeper.
Is the graph a function?A graph is a function if it has no vertically aligned points, that is, each value of the input is mapped to only one value of the output.
Hence:
The roller coaster is not a function, as for lengths between 190 ft and 240 ft, there are vertically aligned points on the graph.
More can be learned about function concepts at https://brainly.com/question/10891721
#SPJ1
Mark grew 9 flowers with 3 seed packets. With 5 seed packets, how many total flowers can Mark have in his garden? Assume the relationship is directly proportional.
Answer:
15
Step-by-step explanation:
9 seeds in 3 packets is a 3:1 ratio which means that there are 3 seeds per packet. With 5 packets you simply multiply 5 by 3
Find the measure of the missing angles.
b
80°
Answer:
b=100 c=80
Step-by-step explanation:
The cost to rent a car is $19.50 plus $0.25 per mile. If you have $44
to rent a car, what is the greatest number of miles that you can
drive?
...............................................
Answer:
3
Step-by-step explanation:
1.5/1*2
Make a conjecture about the distances from the center of rotation P to each corresponding vertex of ABCD and A' B' C' D' .
Software to rotate △ABC 75°, I can see that this image coincides with △A″B″C″.
What is a math conjecture?
A mathematical assertion that hasn't been thoroughly proven is referred to as a conjecture. When one observes a pattern that holds true in numerous instances, hypotheses start to form. A pattern may be true in many instances, but that does not guarantee that it will be true in all instances.A rotation of 75° (because 30 + 45 = 75) should map △ABC to △A″B″C″. By using the
software to rotate △ABC 75°, I can see that this image coincides with △A″B″C″.
Learn more about conjecture
brainly.com/question/24881803
#SPJ4
a. The 9 th and 11 th terms of an arithmetic sequence are 132 and 98 . What is the 10th term?
The 10th term of an arithmetic sequence is found to be a₁₀ = 115.
What is the sequence of AP arithmetic progression?In Arithmetic Progression, the difference between two mathematical orders is a constant quantity (AP). Arithmetic Sequence is another name for it.
We'd come across a few specific terms in AP that had been labeled as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)As shown below, the AP can also be viewed in analysed in terms of common differences.
The following is the procedure for evaluating an AP's n-th term: an = a + (n − 1) × dThe arithmetic progression sum is as follows: Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, as per the given question;
Let the 9th term be 'a₉' = 132.
The 11th term be 'a₁₁' = 98.
The 10th term be 'a₁₀'.
The AP must have contain equal common difference. So,
d = a₁₀ - a₉
d = a₁₀ - 132
And, also
d = a₁₁ - a₁₀
d = 98 - a₁₀
Since, a₁₀ - a₉ = a₁₁ - a₁₀ for forming an AP.
Equate the common difference.
a₁₀ - 132 = 98 - a₁₀
Bring the variable part on single side.
2a₁₀ = 98 + 132
2a₁₀ = 230
a₁₀ = 115.
Therefore, the value of the 10 th term is estimated as a₁₀ = 115.
To know more about the arithmetic progression, here
brainly.com/question/16954227
#SPJ4
Need help with this please
The range of the function is represented by y ∈ [- 0.5, 3].
How to find the range of a function
Functions are relations between an input set named domain and an output set named range such that each element of the domain is related only to one element of the range. Graphically speaking, the range of the function is represented by the vertical axis of the Cartesian plane.
The picture shows that the range of the function is between - 0.5 and 3. Then, the range of the function is represented by y ∈ [- 0.5, 3].
To learn more on functions: https://brainly.com/question/12431044
#SPJ1
Split 84 into two parts so that one part is five times the other part
5/18 + 7/18
9/17+ 2 8/17
3 9/10 + 1 3/10
11/16 + 3/16
5 13/16 + 6 1/16
7/19 + 14/19
7/25 + 16/25
13/15 + 8/15
9/11 + 5/11
12 11/25
11 9/25
1.) 0.66666666666
2.) 3
3.) 5.2
4.) 0.875
5.) 11.875
6.) 1.10526315789
7.) 0.92
8.) 1.4
9.) 1.27272727273
10.) 12.44
11.) 11.36
Here ya go!
HELP ASAP!!! WILL MARK BRAINLIEST!!!
Find the equation of the line that is perpendicular to y=2x+8 and passes through the point (8, -8).
A. y = 2x + 12
B. y = 1/2x - 4
C. y = -1/2x - 4
D. y = -2x + 12
Answer:
c. y = -1/2x - 4
Answer:
C
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c (m is the slope and c the y- intercept )
y = 2x + 8 ← is in slope- intercept form
with slope m = 2
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex] , then
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation of the perpendicular line
to find c substitute (8, - 8 ) into the partial equation
- 8 = - 4 + c ⇒ c = - 8 + 4 = - 4
y = - [tex]\frac{1}{2}[/tex] x - 4 ← equation of perpendicular line
Can someone please help me out? I don’t really understand the problem.
Answer:
-3x+y=14
Step-by-step explanation:
add the x and -4x which gives you -3x
add the -y and 2y which is y
then -14 and 28 add up to 14
What is the solution of the system of equations? r - 2x + 8y = -8 5x - 8y = 20
The solution of the given system of equations is (4,0)
We can use 3 methods to solve a system of equations:
- graphical method
- elimination method
- substitution method.
The given system of equation is:
-2x + 8y = -8 ....... (1)
5x - 8y = 20 ........(2)
Notice that in the both equations the coefficients of y are -8 and 8, hence if we add those coefficients, they will be cancelled out.
Therefore, we will choose elimination method.
Add equation (1) and equation (2)
-2x + 8y = -8
5x - 8y = 20 +
3x = 12
x = 12/3 = 4
Substitute x = 4 into equation (1):
-2x + 8y = -8
-2.(4) + 8y = -8
-8 + 8y = -8
Add 8 to both sides:
-8 + 8y +8 = -8 + 8
8y = 0
y = 0
Thus, the solution is (4,0)
Learn more on how to solve system of equations here:
https://brainly.com/question/25976025
#SPJ4
17xy +4-3x
Term(s):
Coefficient(s):
Variable(s):
Constant(s):
Answer:
Terms: 17xy, 4, 3x
Coefficients: 17, 3
Variables: x, y
Constants 4, 3
Find measure.
m ∠ 6
The Measurement of ∠6 i.e. m∠6 is 120°
What is measurement of an angle ?The measurement of angle if the degree of that angle or we can also say that the angles are always measured in degrees. In geometry, the complete one revolution of four quadrants is of 360 degrees (360°) and divided into total of 360 parts where each part of this represents a degree.
How to find angle measurement ?As stated above there are total 360 parts in one revolution thus thus we can find value of particular angle by subtracting the angle from 360.
In the question
as ∠7 is an alternate angle to 60 degree,
thus ∠7 = 60°
According to sum of angle property :
∠7 + ∠6 = 180
60 + ∠6 = 180
∠6 = 180-60 = 120
Thus m∠6 = 120°
To know more about measurement of angle, visit :
https://brainly.com/question/27243531
#SPJ4
The complete question is :
Find measure m∠6
I need this answered please
help plepqsqasseee im exhausted ONLY A,B AND C
Step-by-step explanation:
A) x(2x-4)
=2x^2-4x
B) 2y^2(3x+4y)
=6xy^2+8y^3
C) (x-3)(x+8)
=x^2+8x-24
