This sequence follows the rules of Arithmetic Progression
Arithmetic Progression is an example of mathematical sequences. In this sequence, the next term is generated by adding the previous term to a fixed number which is called 'Common Difference'. This is generally represented by 'd'. It is calculated by subtracting any two consecutive terms in the sequence.
We can generally find out any term of the given statement. The [tex]n^{th}[/tex] term of a sequence is calculated by adding the previous term to the common difference. The formula to calculate the [tex]n^{th}[/tex] term of an Arithmetic Progression is :
=> [tex]a_{n} = a_{n-1} + d[/tex]
Here, n = No. of term, [tex]a_{n-1}[/tex] = previous term, and d = common difference
In the given sequence, 5,22,39,56......
Each term is separated by a common difference 'd'
Calculating d = a2-a1 => d = 22-5 => d = 17
Every term has a common difference of 17 so this is an Arithmetic Sequence
To know more about Arithmetic Progression, Click here :
brainly.com/question/15412619
#SPJ4
I am doing a test and have no idea how to do this
Answer:
x squared
Step-by-step explanation:
x squared and the rest =1
a web music store offers two versions of a popular song. The size of the standard version is 2.6 megabytes (NB). The size of the high-quality version is 4.7
Yesterday, the high-quailty version was downloaded three times as often as the standard version. The total size downloaded for the two versions was 4509
How many downloads of the standard version were there?
The downloads of the standard version are 1127.25.
What are expressions?In mathematics, an expression is a sentence that contains at least two numbers or variables and at least one mathematical operation. This math operation can be addition, subtraction, multiplication, or division. An expression has the following structure: The expression is (Number/variable, Math Operator, Number/variable).So, let the download of the standard version be 'x'.
Then, automatically the download of the high-quality version becomes '3x'.
Now,
3x + x = 45094x = 4509x = 4509/4x = 1127.25 (downloads of the standard version)Then, downloads of the high-quality version: 1127.25 × 3 = 3,381.75Therefore, the downloads of the standard version are 1127.25.
Know more about expressions here:
https://brainly.com/question/723406
#SPJ9
In a class of 28 sluderds, 14 take physics and
22 take mathematics. The students in the class
take at least one of the two subjects;
Calculate how many
students take both subjects
It can be solved using a Venn diagram. Total 8 students took both subjects.
Describe the Venn diagram.A Venn diagram uses overlapping circles or other shapes to represent the relationships between two or more groups of objects. They typically serve to attractively organize objects, highlighting both the similarities and differences between the components. In the fields of mathematics, statistics, logic, education, linguistics, computer science, and business, Venn diagrams are extensively utilized.
It can be solved using a Venn diagram as
14 students take Physics, 6 students take mathematics and the rest 8 take both subjects.
where, 14(Physics) + 6(mathematics) + 8(both) = 28 (which is the total no. of students).
To know more about Venn diagrams, click on the link
https://brainly.com/question/9180480
#SPJ9
(k)(k − k + h); use h = -2, and k = 6
Answer:-12
Step-by-step explanation:
6(6-6+ -2)
6(-2)
-12
6 4 0,409, 210
onas period
ones
The number name for this number is six hundred forty million, four hundred
nine thousand, two hundred ten.
1Expanded form is a way to write a number as the sum of each
digit multiplied by its place value. Fill in the blanks to write the
number in expanded form.
The expansion of 6 4 0,409, 210 is given below with the solution.
What does "expanded form" mean?The division of numbers into groups according to place value, such as ones, tens, hundreds, thousands, ten thousand, and so on, results in the expanded form of the number. The expanded version of the number is the one that is represented by the sum of each digit times its place value.
6 4 0,409, 210 = 6 × 10,00,00,000 + 4 × 100,00,000 + 0 × 10,00,000 + 4 × 100,000 + 0 × 10,000 + 9 × 1000 + 2 × 100 + 1 ×10 + 1 × 0
A number is displayed in expanded form according to the place values of its digits.
To learn more about expanded form from given link
https://brainly.com/question/91057
#SPJ9
Rex and Samir participated in a walkathon. Rex walked for 1 2/3 hours, and Samir walked for 3 1/3 hours. complete the comparison. Samir walked _____ times ad many hours as Rex walked.
Samir walked 2 times as many hours as Rex walked.
What is ratio?A ratio can be defined as the comparison of two or more numbers on the basis of their sizes in relation to each other.
It also indicates how many times one number contains another.
Given that;
Rex walked = 1 2/3 hours = 5/ 3 hoursSamir walked = 3 1/3 = 10/ 3 hoursTo determine the ratio, we have to divide Samir's walking hours by Rex's working hours
= 10/ 3 ÷ 5/ 3
Take the inverse of the divisor and multiply
= 10/ 3 × 3/ 5
= 2 hours
Thus, Samir walked 2 times as many hours as Rex walked.
Learn more about ratio here:
https://brainly.com/question/2328454
#SPJ1
decimals equivalent to 8.1
Answer:
8.10 & 8.100
Hope this helps ^^
Have a good day <3!
Find the center and the radius of each circle. x²+y²=2
The equation of the circle x^2 + y^2 = 2 has a radius of √2 and a center located at (0 , 0).
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle, x^2 + y^2 = 2, is in standard form, then
h = 0
k = 0
r = √2
Learn more about equation of a circle here: https://brainly.com/question/1559324
#SPJ4
1/16 to the power of 2
Answer: 0.00390625
Step-by-step explanation:
Answer:
The answer is 1/256 :)
Step-by-step explanation:
This one is actually quite simple! All you need to do is multiply 1/16 by 1/16! 1 x 1 is 1 of course, and 16 x 16 is 256. I've attached an image to help break it down even further. (credit to cymath.com)
Hope this helps!
[tex]If BD=3, then CD= [blank] −−−.Enter your answer as the number that correctly fills in the blank.[/tex]
The value of the triangle side segment CD is; 3
How to use triangle congruence postulate?
The HL Congruence Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.
Now, in this question, we are told that BA ≅ CA. Thus, by applying HL congruence postulate, we can say that;
BD = CD
Also, AD = AD due to reflexive property of congruence.
We are given that BD = 3. Thus, CD = 3
Read more about Congruency Postulate at; https://brainly.com/question/17239468
#SPJ1
How many times does your heart beat per second
Answer:
The average heart beats 80 - 90 timers per minute. In 1 second it beats 1.33 1.5 times
Step-by-step explanation:
Quora
Find the 17 th term of each sequence. a₁₈ = -9, d = -11
The 17 th term of each sequence. a₁₈ = -9, d = -11 is [tex]a_{17}[/tex] = -185.
What is a sequence?a₁₈ = -9, d = -11 is
[tex]a_{17}[/tex] = -9 + (16)(-11)
[tex]a_{17}[/tex] = -185.
succession: the doing of one thing after another. A list of books is presented in alphabetical order. a succession of sonnets that is continuous or connected. a later event, outcome, or repercussion; something that happens after.
A series of numbers is an ordered list. The three dots signify moving forward in the set pattern. Each digit in the sequence is referred to as a word. The first term in the list is 1, followed by the second by 3, the third by 5, and so on.
Arithmetic sequences, geometric sequences, quadratic sequences, and special sequences are the four primary categories of distinct sequences you need to be familiar with.
To learn more about sequence from the given link:
brainly.com/question/21961097
#SPJ4
Find the sum of each finite series. Σ¹° n = 1 (3 n-4)
The sum of the given finite series is 125
The given finite series is:
[tex]\sum\limits^{10}_{n=1} {(3n-4)}[/tex]
Use the properties of sum operator:
[tex]\sum\limits^{10}_{n=1} {(3n-4)}=\sum\limits^{10}_{n=1} {3n}-\sum\limits^{10}_{n=1} {4}[/tex]
Calculate each term on the right side:
[tex]\sum\limits^{10}_{n=1} {4}=4+4+...+4=10\times4=40[/tex]
[tex]\sum\limits^{10}_{n=1} {3n}=3\sum\limits^{10}_{n=1} {n}[/tex]
= 3.(1 + 2 + 3 + ... + 10)
The series in the brackets is an arithmetic series with :
the first term: a(1) = 1
the last term: a(10) = 10
the common difference: d = 2 - 1 = 1
Use the sum formula for arithmetic series:
S(n) = n/2 [a(1) + a(n)]
S(10) = 10/2 [1 + 10]
=5 . 11 = 55
Therefore,
[tex]\sum\limits^{10}_{n=1} {3n}=3\times{55}=165[/tex]
Combine the sum:
[tex]\sum\limits^{10}_{n=1} {3n}-\sum\limits^{10}_{n=1} {4}=165-40[/tex]
= 125
Learn more about sum of a series here:
https://brainly.com/question/28062936
#SPJ4
Write an equation of a parabola with vertex at the origin and the given focus. (0,6)
Answer:
27273763hebvrhejwj27222
I'm more sophisticated than my little sister. I save my money in a bank account that pays
me 3% interest on the money in the account at the end of each month. (If I take my money
out before the end of the month, I don't earn any interest for the month.) I started the
account with $50 that I got for my birthday. How much money will I have in the account at
the end of 10 months? How many months will it take to have at least $100? Justify your
answer with a mathematical model of the problem situation.
The amount of money after 10 months will be $67.2. The number of months (n) that it takes to have at least $100 will be 2 years or 24 months.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
[tex]\rm A = P \left (1 + r \right ) ^{t}[/tex]
Where A is the amount, P is the initial amount, r is the rate of interest, and t is the number of months.
I keep my savings in a bank account that, at the end of each month, gives me 3% interest on the balance. (If I withdraw my funds before the end of the month, I forfeit the interest I would have accrued.) I opened the account using the $50 I received as a birthday gift.
The amount of money after 10 months will be
A = 50 (1 + 0.03)¹⁰
A = 50(1.03)¹⁰
A = 50 x 1.344
A = $67.2
The number of months (n) that it takes to have at least $100 will be
100 = 50 (1.03)ⁿ
2 = (1.03)ⁿ
n ln 1.03 = ln 2
n = ln 2 / ln 1.03
n = 23.5 ≈ 24 months or 2 years
More about the compound interest link is given below.
https://brainly.com/question/25857212
#SPJ1
Need help asap please
Answer:
1) the center is (3,4), radius is 3. 3) ( x − 2 )^2 + ( y − 14 )^2 = 9, 5) the center is (12,5), the radius is 4
Step-by-step explanation:
For the graphs just look for the middle point, and thats essentially your center, and the radius is how many units the edge of the circle is to the center. So for 1 the center would be (3,4) and the radius 3. For problem 3 use the equation ( x − a )^2 + ( y − b )^2 = r^2, where you substitute the radius for r, your x center coordinate as a, and your y coordinate as b. In problem 5, use 12 as your x value for the center coordinate, and 5 as your y value. Then just take the root of 16 to get your radius, and apply that to the other problem. Hope this helps :)
In the regular polyhedron described below, all faces are congruent polygons. Use a system of three linear equations to find the numbers of vertices, edges, and faces.
Every face has five edges and every edge is shared by two faces. Every face has five vertices and every vertex is shared by three faces. The sum of the number of vertices and faces is two more than the number of edges.
A normal polyhedron shape is defined as a polyhedron having a symmetry group that acts transitively on the flags. Regular polyhedral are highly symmetrical because they are all edge-transitive, corner-transitive, and face-transitive. Many different equivalent definitions are used in classical contexts. There are many definitions in mathematics defining a regular polyhedron, and is that the faces of a polyhedron are nothing but congruent regular polygons that are constructed in the same way around each vertex of the polyhedron. So the polyhedron having faces/sides that are congruent with regular polygons and the exact number of faces that meet at each vertex is called a regular polyhedron.
Euler's polyhedron formula describes the relationship between the number of vertices, edges, and faces of a three-dimensional polyhedral shape.
V-E+F=2 gives Euler's polyhedron formula.
Where V-corner, E-edge, F-face.
More similar problems are solved in the given link below.
https://brainly.com/question/2321456?referrer=searchResults
#SPJ4
In this problem, you will explore changing dimensions in circles.
f. If the scale factor from ®A to ®B is 1/3 , and the circumference of ®A is 12 inches, what is the circumference of ®B ?
The circumference of ®B is 36 units.
What is scale factor?A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object.
Now it is given that,
The scale factor from ®A to ®B = 1/3
⇒Ks = 1/3
∵ Ks = A/B
By comparison we get,
A = 1
and B = 3
Thus, circumference (CA) of ®A = 12
⇒ Since scale factor for A = 1
⇒ 2πr = 12
⇒ r = 6/π
Now, circumference (CB) of ®B = 2πr = 2π* 6/π
⇒ circumference (CB) of ®B = 12
Since scale factor for B = 3
⇒ circumference (CB) of ®B = 3 * 12
⇒ circumference (CB) of ®B = 36 units.
Thus, the circumference of ®B is 36 units.
To learn more about scale factor:
brainly.com/question/24771289
#SPJ4
What do you notice about the measures of anges the are side by side?
they add up to 180 degrees
Which of the following expressions shows how to rewrite 4 − 5 using the additive inverse and displays the expression correctly on a number line?
The expression that shows how to rewrite 4 − 5 using the additive inverse is (a)
How to determine the expression that shows how to rewrite 4 − 5 using the additive inverse?The expression is given as
4 - 5
The law of additive inverse states that
x + (-x) = 0
This means that x and -x are additive inverses
Using the above as an illustration,
4 - 5 can be rewritten as 4 + (-5)
And the above implies that the number line moves 4 points to the right and 5 points to the left
Hence, the expression that shows how to rewrite 4 − 5 using the additive inverse is (a)
Read more about number line at
https://brainly.com/question/24644930
#SPJ1
& Check
# 18 1
The function b(x)= |x-45] represents the absolute deviation (in inches) of a boy's height x (in inches) from the average height of boys in a kindergarten class. The
function g(x)= |x-44| represents the absolute deviation (in inches) of a girl's height x (in inches) from the average height of girls in a kindergarten class. Compare
the absolute deviations for a boy and a girl who are both 43 inches tall.
I don't know lol ididjdjdj
pls answer this question als0oo
what do i do when my algebra has something like this 9x+45=15x+3/7x im used to having constants and variables on both sides
Answer:
x = 2 11/12
Step-by-step explanation:
First of all, on the right you have to combine 15x+3/7x which equals 15 3/7x.
9x + 45 = 15 3/7x
-9x -9x Next step is to subtract 9x from both sides.
45 = 15 3/7x
/ /
15 3/7 15 3/7 Third step is to divide 15 3/7 on both sides to leave x
by itself.
35/12 = 2 11/12 = x
x = 2 11/12
The circle below is centred at O.
a) Work out the size of angle x.
b) Which of the circle theorems below allows
you to calculate this angle?
O
X
Not drawn accurately
31°
The perpendicular line from the centre of a circle to a chord
bisects the chord
Two tangents that meet at a point are the same length
The angle at the circumference in a semicircle is a right angle
Opposite angles in a cyclic quadrilateral add up to 180°
The angle between the tangent and the radius at a point
on a circle is 90°
Answer:
[tex]\textsf{a)} \quad x = 59^{\circ}[/tex]
[tex]\textsf{b)} \quad \boxed{\begin{minipage}{8.5 cm}\sf The angle between the tangent and the radius at a point \\on a circle is $90^{\circ}$.\end{minipage}}[/tex]
Step-by-step explanation:
Part (a)As two sides of the triangle inside the circle are the radius of the circle, the triangle is an isosceles triangle.
Therefore, its two base angles are 31°.
The tangent of a circle is:
A straight line that touches the circle at only one point.Always perpendicular to the radius.Therefore:
[tex]\implies x + 31^{\circ} = 90^{\circ}[/tex]
[tex]\implies x +31^{\circ}-31^{\circ}= 90^{\circ} - 31^{\circ}[/tex]
[tex]\implies x = 59^{\circ}[/tex]
Part (b)The circle theorem that allows you to calculate angle x is:
[tex]\boxed{\begin{minipage}{8.5 cm}\sf The angle between the tangent and the radius at a point \\on a circle is $90^{\circ}$.\end{minipage}}[/tex]
Solve each equation for y .
-10 y=5 x
y = -x/2 is the value of y in the equation -10 y=5 x
⇒ -10 y=5 x
⇒ y = -5x/10
⇒ y = -x/2
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
Learn more about linear equations
brainly.com/question/14323743
#SPJ4
Find the sum of each finite series. Σ⁴ n=1 2ⁿ
A sequence is a geometric sequence if all the numbers of a list are found by multiplying the preceding term by the common ratio r of that sequence. Sigma notation can represent the sum of a finite number of terms (although higher mathematics will tell you how it works for infinite numbers as well).
Now the given problem is,
calculate ∑ n=1, 4, 2n
∑n=1 , 4 , 2n
Since the bounds are finite, the number of terms is finite as well, and we just calculate the sum by summing up the terms.
(∑n=1 4 ,2n) = (2+4+8+16) (∑n=1 4, 2n) = (2+4+8+16)
(∑n=1 4 ,2n) = (30) (∑n=1 4, 2n) = (30)
Hence,
∑n=1 4, 2n=30 ∑n=1 4, 2n=30
Answer:
∑n=1 4, 2n=30
More similar problems are solved in the link below.
https://brainly.com/question/12685015?referrer=searchResults
#SPJ4
what is the value of 7 -(-4)
PLEASE HELP ANSWER I CANT FIND ANSWERS ANYWHERE THIS IS MY LAST HOPE PLS
which expression is equivalent to 1/3 + (3/4+3/4)
1/3 + (3/4 +3/4)
1/3 (3/4+2/3
3/4 - 2/3 + 1/3
(1/3+3/4) +2/3
question 2
Which property explains why these two expressions are equal?
(w+ 2/3) + 5 = w + (2/3 + 5)
A)
associative
B)
commutative
C)
distributive
D)
transverse
Which property is BEST to use when combining
3/5 +1/4 +2/5?
additive inverse property
distributive property
commutative property of addition
identity property of addition
Answer For Question 2: Associative property. The associative property says that even if you rearrange the parenthesis () the result will still be the same. And that is what is happening in question 2
Answer For Question 3: Commutative property of addition. This is the BEST choice because you will first want to add 3/5 + 2/5. And since the Commutative property says that no matter the order of the addends, you can add what ever you think is the best choice.
Here are some answers. I couldn't really understand Question 1 so i didn't want to give you an incorrect answer. Also are the pictures questions too? Im not too sure but here you go hope this helps you in some way
the question is hard
The correct completion of the given two column proof is as below.
How to carry out a Two column proof?
From the given two column proof, the correct way to complete it is;
Statement 1; m║n
Reason 1; Given
Statement 2; ∠3 and ∠6 are same side interior angles
Reason 2; Definition of Same side interior angle theorem
Statement 3; ∠3 and ∠6 are supplementary
Reason 3; Definition of Supplementary
Statement 4; m∠3 + m∠6 = 180°
Reason 4; Same side interior angle theorem
Read more about Two column proof at; https://brainly.com/question/1788884
#SPJ1
b. Explain how your answer to part (a) relates to the explicit formula a n = a+(n-1) d
My answer to part (a) relates to the explicit formula in an n = n+6 n a= n+6 n.
a= n+6 n
Step-by-step explanation:
n=an−1−5
Step 1: Flip the equation.
an−6=n
Step 2: Add 6 to both sides.
an−6+6=n+6
an=n+6
Step 3: Divide both sides by n.
an n = n+6 n a= n+6 n
What is explicit formula?An arithmetic sequence has the explicit formula a = a + (n - 1)d, and each term of the sequence may be computed without knowing the values of the previous terms. The nth term of an arithmetic, geometric, or harmonic series is usually the explicit formula.
The formal equations for L-functions in mathematics are Riemann's zeta function and links between sums over an L-complex function's number zeroes and sums over prime powers.
To learn more about explicit formula from the given link:
brainly.com/question/18069156
#SPJ4
