Given:
The arithmetic sequence is:
10, 12, 14, 16, ...
To find:
The function that generates the given sequence if n is an integer.
Solution:
We have,
10, 12, 14, 16, ...
Here, the first term is 10 and the common difference is:
[tex]d=a_2-a_1[/tex]
[tex]d=12-10[/tex]
[tex]d=2[/tex]
The nth term of an arithmetic sequence is:
[tex]a_n=a+(n-1)d[/tex]
Where, a is the first term, d is the common difference and [tex]n\geq 1[/tex].
Putting [tex]a=10,d=2[/tex] in the above formula, we get
[tex]a_n=10+(n-1)2[/tex]
[tex]a_n=10+2n-2[/tex]
[tex]a_n=8+2n[/tex]
Therefore, the function [tex]a_n=8+2n, n\geq 1[/tex] generates the sequence.
What is the circumference of the table top? Write your answer using
Show your work.
Answer
the diameter is 44
Step-by-step explanation:
the radius is just half of the diameter so to get the diameter from the radius just multiply it by two.
Hi guys can some one help me with this question pls this is kinda hard pls upload in a paper i need all answer i will give them 100 points pls
note: anyone give answer wrong answer for points reporte to moderator
Answer:
Step-by-step explanation:
Amelia made a line plot of her scores on 25-point math quizzes.
What is the difference between the total of her most frequent number of points per quiz and
the total of her greatest number of points scored per quiz?
A. 0 points
B. 6 points
C. 18 points
D. 22 points
Answer:
How do I ask a question on here?
Step-by-step explanation:
Answer:
B.6 points
Step-by-step explanation:
First you can see that one is bigger and taller and if you count on the number line it will be 18, and 18 has 6 dots so it is B which says 6 dots.
A mattress store is having a sale all mattresses are 30% of. Nate wants to know the sale price of a mattress that is regularly $1,000
Answer: $700
Step-by-step explanation:
The store is selling at 30% off.
If a mattress is $1,000, first find out what 30% of $1,000 is:
= 1,000 * 30%
= $300
The store is selling 30% off, this means that they are reducing the price by 30%:
= 1,000 - 300
= $700
HELP PLEASE. !!!!!!
Answer:
12
Step-by-step explanation:
Find the circumference.
Use 3.14 for tı.
-
r = 6 ft
C = [?] ft
C=rd
Answer:
37.69911184
Step-by-step explanation:
because circumference is equal to pi multiplied by diameter, you will not get the circumference with the radius times pi. in order to get the diameter, you multiply the radius by 2, because the diameter is the length across the circle. So the diameter of this circle is equal to 12. so simply multiply that number by pi (3.14) and there is your answer. Hope i helped.
Circle A has center of (6, 7), and a radius of 4 and circle B has a center of (2, 4), and a radius of 16. What steps will help show that circle A is similar to circle B?
Answer:
1) Use translation to coincide the center of a circle with the center of the other circle.
2) We construct the respective loci for the circles.
3) Compare each loci by direct inspection ([tex]f(x,y)[/tex] must be the same and radii must be different but constant) to conclude the similarity of the two circles.
Step-by-step explanation:
Geometrically speaking, a circle is formed after knowing its center and radius.
1) Use translation to coincide the center of a circle with the center of the other circle. In this case, we translate the center ([tex]C_{A} (x,y) = (6,7)[/tex]) of the circle A to the location of the center of the circle B ([tex]C_{B}(x,y) = (2,4)[/tex]):
[tex]C_{A'} (x,y) = (6,7) + [(2,4) - (6,7)][/tex]
[tex]C_{A'} (x,y) = (2,4)[/tex]
2) We construct the respective loci for the circles.
By Analytical Geometric, a circle is represented by the following locus:
[tex](x-h)^{2}+(y-k)^{2} = r^{2}[/tex]
Where:
[tex]x, y[/tex] - Coordinates of a point of the circunference.
[tex]h, k[/tex] - Coordinates of the center of the circle.
[tex]r[/tex] - Radius of the circle.
3) Compare each loci by direct inspection ([tex]f(x,y)[/tex] must be the same and radii must be different but constant) to conclude the similarity of the two circles.
Then, the circles A' and B are represented by the following loci:
Circle A'
[tex](x-2)^{2} + (y-4)^{2} = 16[/tex]
Circle B
[tex](x-2)^{2} + (y-4)^{2} = 256[/tex]
Since both the [tex]f(x,y)[/tex] component of each circle is the same and radii are different but constant, then we conclude that circle A is similar to circle B.
Convert to an improper fraction: 4 3/5
Answer:
23/5
Step-by-step explanation:
multiply denominator by whole number. add the numberator. sum will now be your new numberator (denominator always stays the same).
hope this helps! (❁´◡`❁)
A triangle has two sides with lengths 7 and 12 which of the folowing lengths could represent the third side
Answer:
If s₃ is the length of the 3rd side, the possible values are in the interval.
5 < s₃ < 19
Step-by-step explanation:
For a triangle, we know that the sum of any two sides is always larger than the other side.
So if a triangle has 3 sides:
s₁, s₂, and s₃, we have:
s₁ + s₂ > s₃
s₁ + s₃ > s₂
s₂ + s₃ > s₁
In this case, we know that two sides are:
s₁ = 7
s₂ = 12
And we want to find the possible values of s₃.
Then if we use the above inequalities, we get:
7 + 12 > s₃
7 + s₃ > 12
12 + s₃ > 7
With the first one we get:
19 > s₃
Now we can rewrite the other two as:
s₃ > 12 - 7 = 5
s₃ > 7 - 12 = -5
The first one is more restrictive than the second:
s₃ > 5 > -5
So we can use only the first one.
Then the two inequalities are
s₃ > 5
s₃ < 19
Then the range is:
5 < s₃ < 19
This means that any value between 5 and 19 can be a possible length of the third side (5 and 19 are not possible lengths)
The volume of a cone shaped object is approximately 27 pie ft^3 If the height of this cone is 9 ft, what is the radius of the base of the cone?
a. 2 ft
b. 9 ft
c. 3 ft,
d. 6 ft
Answer:
is b
Step-by-step explanation:
Oceanside Bike Rental Shop charges 18 dollars plus 8 dollars an hour for renting a bike. Alyssa paid 50 dollars to rent a bike. How many hours did she pay to have the bike checked out ?
Answer:
4 hours
Step-by-step explanation:
Cost of renting a bike at Oceanside Bike Rental Shop = 18 + 8x
Where,
x = number of hours for renting the bike
Alyssa paid 50 dollars to rent a bike.
How many hours did she pay to have the bike checked out ?
C = 18 + 8x
50 = 18 + 8x
Subtract 18 from both sides
50 - 18 = 18 + 8x - 18
32 = 8x
Divide both sides by 8
32 / 8 = 8x / 8
4 = x
x = 4 hours
PLEASE HELP ASAP!! will mark brainlest!
Answer:
1. Axis of Symmetry: x=-4, Vertex: (-4, -6)
2. Axis of Symmetry: x=2, Vertex: (2, 8)
Step-by-step explanation:
What is -61=8-1/3(12w+42)-w
If you don't know do not answer
MUST SHOW WORK!!!!!
Answer:
w = 11
Step-by-step explanation:
In photo
Complete the equation so it will have no solution. 5x - 8 = _ +2
Answer:
5x
Step-by-step explanation:
If the blank were to be occupied with 5x there would be no solutions
Observe...
5x - 8 = 5x + 2
* subtract 5x from each side *
5x - 5x cancels out
5x - 5x cancels out
we're left with -8 = 2
which is not true
Hence if the blank = 5x the equation will have no solution
The souvenir stand sells the hats for $11.75 each , the postcards for $0.25 each , and the magnets for $3.50 each . Write an expression for the total amount of money they would take in if they sold all the items
Answer:
9.2h+50
Step-by-step explanation:
im not sure if this is correct and im only in middle school but i had this same quetsion and got that snwer
6) Evaluate 2xy - 5 , for x= -3 and y=4
Your answer
Answer:
answer = -29
Step-by-step explanation:
2*-3*4-5
Answer:
-29
Step-by-step explanation:
=2(-3)(4)-5
=-6(4)-5
=-24-5
=-29
Hope this helps.
What is the volume of a rectangular prism with the length of 4.5 ft, the width of 3.5 ft, and the height of 5.5 ft?
Answer:
The volume would be 86.63 feet squared
Hope this helps!
Mark me brainliest if I'm right :)
describe the relationship between the zeros of the quadratic function and linear factors of the expression
Answer:
F(x) represents the zeros of the given quadratic function. i.e. the linear factors represents zero when we resolve the expression
Step-by-step explanation:
Describing the relationship between the zeros of the quadratic function and the linear factors of the expression using an example as shown below
lets describe this using the example below :
quadratic expression : F(x) = ax^2 + bx + c
let the linear factors of F( x ) = 0
F(x) represents the zeros of the given quadratic function above i.e. the linear factors represents zero when we resolve the expression
Convert 100° to radians. Will mark brainlist if correct
Examine the expression. 17x - 34 Which is an equivalent expression? O 17*(1 + ) O 17x (1-2) O 17+(1-1) O 17*(1 + 2)
Answer:
17(x-2)
Step-by-step explanation:
Given the expression
17x - 34
We are to factorize it
Get their factors
17x = 17 * x
34 = 17 * 2
Since 17 is common to both factors, hence 17 is the GCF
17x - 34 = 17(x - 2)
Hence the equivalent expression is 17(x-2)
Here is a list of numbers:
-5, -15, -10, 5, 14, 5, -18, 11, -4
State the median.
Answer:
4
Step-by-step explanation:
-18, -15, -10, -5, 4, 5, 5, 11, 14
There are 9 terms. So the one in the middle is the median.
-18, -15, -10, -5, 4, 5, 5, 11, 14
1 2 3 4 5 6 7 8 9
So 4 is the median.
---
hope it helps
In a academic contest, correct answers earn 12 points and incorrect answers lose 5 points. In the final round, school A starts with 165 points and gives the same number of correct and incorrect answers. School b starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the 2 schools as a tie
Answer:
20
Step-by-step explanation:
In an academic contest correct answers earn 12 points and incorrect answers lose 5 points. In the final round school A starts with 165 points and gives the same number of correct and incorrect answered. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. How many answers did each school get in the final round?
Let x = number correct answers
because school a , gives the same correct and wrong answers, their equation can be represented as :
165 - 5x + 12x =
165 + 7x
School b gives no wrong answer. their equation can be represented as
65 + 12x
to fing the number of correct answers given, equate the two equations
165 + 7x = 65 + 12x
collect like terms
165 - 65 = 12x - 7x
100 = 5x
x = 20
If a line falls on the points (1, 2) and (8,7), what is its slope? Enter your answer as a fraction in lowest terms. Use a slash mark (/) as the fraction bar.
Answer:
m= 5/7
Step-by-step explanation:
y2-y1 / x2-x1
7-2/8-1
5/7
If a cylinder has a height of 7 m and its base has a radius of 6 m, what is its volume? Use 3.14 for 5 and
round the answer to the nearest whole number.
O 490 m3
791 m3
923 m3
1,583 m3
Answer:
Step-by-step explanation:
I know this may seem annoying, but how did you get 13/3 and 4/4 from 3 1/4 and 3/4?
"A processing machine crushes 3 1/4 kilograms of dried fruits in 3/4 minutes.
What is the rate, in kilograms per minute, at which the machine crushes dried fruits?"
All you're doing here is finding the unit rate at which the machines crushes the fruit. This boils down to dividing the amount it can crush (3 + 1/4 kg) by the time it takes to do the crushing (3/4 min):
(3 + 1/4 kg) / (3/4 min)
We can omit the units, just remember everything is measured in kilograms per minute. So we want to simplify the expression,
(3 + 1/4) / (3/4)
Write the numerator as an improper fraction:
3 + 1/4 = 12/4 + 1/4 = 13/4
(since 12 = 3*4)
Then
(3 + 1/4) / (3/4) = (13/4) / (3/4)
Multiply this by 1 = 4/4. In other words, multiply both the numerator and denominator by 4. This eliminates the fractions in either part, and you get the answer:
(13/4) / (3/4) * 4/4 = (13/4 * 4) / (3/4 * 4) = 13/3
So in one minute, the machine can crush 13/3 kg ≈ 4.333 kg of dried fruit.
calculate the lateral area and volume of a truncated cone of radii 10cm and 12cm and a slant height of 15cm
Answer:
The lateral surface is 212
Step-by-step explanation:
Lateeal surface area is = Ph
12+12+10+10(15)=212
A guitar string has a lenght of 0.5 m. If the string is vibrating with a wavelength of 0.25 m, what harmonic is it vibrating at?
1st
4th
Зrd
2nd
Answer:
4th
Step-by-step explanation:
string length is 0.5m and the wavelengths are 0.25meters. This tells us there are two complete waves in the guitar string. This gives us a total of four antinodes; thus we are in the fourth harmonic.
Then find the values of x and y.
Answer:
y = 4
x = 104°
Step-by-step explanation:
3y = y + 8
-y -y
2y÷2 = 8÷2
2y÷2 cancels out so
8 ÷ 2 = 4
y = 4
all sides are congruent so all angles are congruent so that means that all the angles are 104°
What is the percent increase or decrease between $7.80 and $6.63?
Sebastian bought 4 basketballs for $37.60 what is the rate price for per basketball?
Answer:
9.40$
Step-by-step explanation: