The first two numbers in a sequence a are a(1) = 3 and a(2) = 12. If a is an arithmetic sequence, write a definition for the nth term of a. Explain or show your reasoning.
The formula of the nth term in the arithmetic sequence is a(n) = 3 + (n-1)9.
An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a fixed constant, called the common difference, to the preceding term.
The sequence can be represented by the general term an = a1 + (n-1)d, where a1 is the first term and d is the common difference
In an arithmetic sequence, the difference between consecutive terms is constant. Therefore, if a(1) = 3 and a(2) = 12, the common difference (d) is 12 - 3 = 9.
The nth term of an arithmetic sequence is given by the formula:
a(n) = a(1) + (n-1)d
where:
a(n) is the nth term of the sequence
a(1) is the first term of the sequence
d is the common difference
n is the position of the term in the sequence
So, for the given sequence, the nth term a(n) of the arithmetic sequence is:
a(n) = a(1) + (n-1)d = 3 + (n-1)9
This means that the nth term of the arithmetic sequence is found by adding the common difference (9) to the first term (3), and then multiplying the result by (n-1) which indicates the position of the term in the sequence.
Therefore, a(n) = 3 + (n-1)9 is the formula of the nth term in the arithmetic sequence.
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The graph of h (x) =lx-10l+6 is shown. On which interval is the graph increasing?
(-∞,6)
( -∞,10)
(6,∞)
(10,∞)
The interval in which the graph increasing is (10,∞). The correct option is D.
What is an absolute function?The absolute value or modulus of a real number x denoted |x| in mathematics, is the non-negative value of x regardless of its sign. Specifically, if x is a positive number,|x|=x.
In discrete mathematics, and more specifically in graph theory, a graph is a structure consisting of a set of objects, some of which are "related" in some way. The objects correspond to mathematical abstractions known as vertices, and each pair of related vertices is known as an edge.
The given absolute function is h (x) =lx-10l+6. When we plot the graph of the function it is observed that the graph is increasing from 10 to ∞. The graph is attached with the answer below.
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Which equation can be solved by using this system of equations? startlayout enlarged left-brace 1st row y = 3 x cubed minus 7 x squared + 5 2nd row y = 7 x superscript 4 baseline + 2 x endlayout 3 x cubed minus 7 x squared + 5 = 0 3 x cubed minus 7 x squared + 5 = 7 x superscript 4 baseline + 2 x 7 x superscript 4 baseline + 2 x = 0 7 x superscript 4 baseline + 3 x cubed minus 7 x squared + 2 x + 5 = 0.
The equation can be solved by using this system of equations is
1st Row y = 3 x cubed minus 7 x squared 5
A system of equations is a set of one or more equations involving a number of variables.
The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect.
What are the 3 types of system of equations?
There are three types of systems of linear equations in two variables, and three types of solutions.
→ An independent system has exactly one solution pair. The point where the two lines intersect is the only solution.
→ An inconsistent system has no solution.
→ A dependent system has infinitely many solutions.
Therefore, the equation can be solved by using this system of equations is
1st Row y = 3 x cubed minus 7 x squared 5
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The graphs show how many words per minute two students read.
Drag to the table the unit rate that matches each graph.
120 words per minute
186 words per minute
185 words per minute
100 words per minute
The unit rate is 120 words per minute and 185 words per minute
What is an equation?An equation consists of numbers and variables linked together by mathematical operations to form an expression.
A linear equation is in the form:
y = mx + b
Where m is the rate of change and b is the initial value
a) For the first graph, using the points (3, 360) and (2, 240)
Unit rate = Slope = (240 - 360) / (2 - 3) = 120 words per minute
a) For the second graph, using the points (0, 0) and (1, 185)
Unit rate = Slope = (185 - 0) / (1 - 0) = 185 words per minute
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What is coordinates in graph example?.
The integers of a coordinate grid are used to find points. Each point on a graph may be specified by an ordered pair of numbers called an x-coordinate and a y-coordinate, respectively.
An ordered list's pairings are indicated by parentheses (x, y) (x,y). beginning place is at (0,0). Remember that when writing coordinates, there is usually no space after the comma. The co-ordinates in graphs are the cartesian coordinate points which enables us to exactly trace the specific point on a graph. There are 4 quadrants in a graph namely first second 3rd and 4th. When we have data about X&Y coordinate of each point those points can be traced on the graph on their respective axis. For example, x,y is equal to 2, 5 lies on the first quadrant since both the values are positive.
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The complete question is as follows.
What are coordinates in the graph? give an example?
Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
The statements about his solution that are true include:
1) He should have found the average of the number of rock songs by averaging 4 and 6 to get 5.
2) He did not multiply the numerator and denominator by the correct number to equal 1,500.
5) He should have multiplied the numerator and denominator by 75, not 30, because 20 x 75 = 1,500
How to illustrate the word problem?From the information, Josiah kept track of how many songs of each genre were played in an hour from his MP3 player and the counts are displayed in the table below.
In this case, it should be noted that he should have found the average of the number of rock songs by averaging 4 and 6 to get 5.
In this case, the correct options are 1, 2 and 5.
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Answer for this and an simple explanation thank you very much
The percentage of 100 square quadrilateral grid shaded is 96%.
What is a Square?Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. The equal sides and 90° internal angles of each square form serve as indicators of its identity.A square is a closed, four-sided, two-dimensional (2D) shape. In a square, all four sides are equal and parallel to one another.A square is a closed form with four equal sides and interior angles that are both 90 degrees. Three fundamental square formulas are frequently employed in geometry. The first one involves computing its area, the second one involves computing its perimeter, and the third one involves computing the diagonal of a square formula.since there are 4 unshaded grids and rest 96 are shaded then the percentage will be
shaded percentage = 96 × 100/100 = 96%
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Steve bought $2,000 worth of tock in 2019. The value of the tock ha been decreaing by 10 percent each year. What will the value of the tock be in 2024? Round your anwer to the nearet dollar
The value of the stock will be $1,179.98 in 2024 (After rounding the answer off to the nearest dollar).
It is given that steve bought $2,000 worth of stocks in 2019 and its values have been decreasing by 10% each year,
So in 2020 the value will become
$(2,000-(10% of 2,000))
=$(2,000-(200))
=$1,800
in 2021,
$(1,800-(10% of 1,800))
=$(1,800-(180))
=$1,620
in 2022,
$(1,620-(10% of 1,620))
=$(1,620-(162))
=$1,458
in 2023,
$(1,458-(10% of 1,458))
=$(1,458-(145.8))
=$1,312.2
and finally in 2024,
$(1,312.2-(10% of 1,312.2))
=$(1,312.2-(131.22))
=$1,179.98
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Bigger cylinder has 16 litres and smaller cylinder has 2 litres and height of 10 cm.
if smaller cylinder has 10 cm ,calculate height of big cylinder.
Answer:
10cm
Step-by-step explanation:
same gghshbsbbsnsnnsbsbxbbxbdbbxbxbbdbdbdbbdbdndndnndndndnnfnfbbdhdn
If Diane can select from a list of 40 CDs, how many groups of 6 different CDs are possible
Why is it called logarithm?.
The word "logarithm" is derived from the Greek meanings for "ratio" (logos) and "number" (arithmos).
In the 17th century, Scottish mathematician John Napier (1550-1617) developed logarithms as a tool for computing. He derived the phrase from the Greek words for ratio (logos) and number (arithmos).
Before mechanical (and later electronic) computers were developed, logarithms were essential for simplifying calculations in astronomy, navigation, surveying, and afterwards engineering. A logarithm is a mathematical formula that calculates how many times the base, or initial number, must be multiplied by itself to produce the target number. As a result of the relationship between logarithms and geometric progressions.
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P=0.25q constant of proportionality
The constant of proportionality in the given equation as represented in the task content is; 0.25.
What is the constant of proportionality in the given equation?It follows from the task content that the constant of proportionality of the given equation as required in the task content be identified.
Since the given equation in the task content is;
p = 0.25q
As evident in the equation above, there exists a directly proportional relationship between the quantities p and q.
Hence, the constant of proportionality in the give. equation is; 0.25.
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What is the y-intercept of 2x y =- 2?.
The y - intercept of 2x + y = -2 is -2.
Given straight line is 2x + y = -2.
We know that standard slope form of straight line is y = mx + c
Now we transform given equation to standard form of straight line :
2x + y = -2y = -2 - 2xThe point at which a straight line cut the y-axis is called the y-intercept. Any point on the y-axis has a x-coordinate of zero.
Therefore, x-coordinate of y-intercept is 0.
For finding y-intercept, we can substitute x by 0 and solve for y:
y = -2 - 2x0y = -2Therefore, the y - intercept of 2x + y = -2 is -2.
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The equation y = 13,000x + 65,000 can be used to determine the total number of miles driven, y, on Franklin's used car based on the number of months, x, after he purchased it. What is the meaning of the y-intercept of the function?
A.Franklin drove about 13,000 miles each month.
B.The car had been driven 65,000 miles when Franklin purchased it.
C.The car had been driven 13,000 miles when Franklin purchased it.
D.Franklin drove about 65,000 miles each month.
Answer:
B.The car had been driven 65,000 miles when Franklin purchased it.
What is 9x2 factored?.
The components of the polynomial given as 122 9z - 4 + 3 are (4 - 3). (3- 1) 122 - 92 - 4a + 3 polynomial the provided polynomial has been factored 922 think about the polynomial 12z 4a + 3.
Taking 34 common terms from the first two terms and 1 common term from the last two terms, we get 3a2(4z - 3) - 1(4* - 3) when we factorise using grouping of terms. Taking (4x-3) common once more, we have (4z - 3)(322- 1). Therefore, (4z - 3) is the factor of the provided polynomial 12a - 9z'- 42 + 3. (3r - 1).
The given polynomial, 12x3-9x2-4x+3, has the components (4x-3) (3x2) - 12x3-9x2-4x+3 polynomial the provided polynomial has been factored. The term "factor" refers to a number that, when multiplied or divided, yields a specific number. Think about the polynomial 12x3-9x2-4x+3. We'll factorise based on a collection of terms, Using the first two terms' 3x2 common value and the last two terms' -1 common value, we arrive to.
Complete question:
What is 9x2 factored?.What distinguishes the two polynomials and its conclusion?
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The expression 9x² can be factored as 3x². The expression 9x² can be factored by dividing both 9 and x² by their greatest common factor of 3.
In other words, 9x² can be written as 3 * (x²) which is equivalent to 3x². Factoring is a useful technique for simplifying expressions and solving equations, as well as for understanding the relationship between different terms in a polynomial.
By factoring an expression, we can see how it can be written as a product of simpler expressions, which can sometimes make it easier to manipulate or solve for a particular variable.
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Complete Question:
What is 9x² factored?.
What are angles 3 4 5 Triangle angles?.
The 3 4 5 triangles angles are applicable for the right angle triangle.
The sum of all angles of triangle is 180 degree.
A 3 4 5 triangle is right angle triangle in which 3 and 4 is the base and perpendicular, where 5 is the hypotenuse of that triangle.
Properties of 3 4 5 triangle.
It generally used in the trigonometry to makes the trigonometric equations easy.The right angle in the 3-4-5 triangle is, of course, 90 degrees. The other two angles are always 53.13 degrees (opposite the 4 side) and 36.87 degrees (opposite the 5 side) (opposite the 3 side)Maintaining the ratios of this triangle also maintains the angles' measurements. Any triangle proportional to the 3-4-5 triangle has the same angle measurements.To Learn more about triangles visit: https://brainly.com/question/2456591
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So far Mr. Sahid ha read 177 page of her 392 page book about how many page doe he have left to read
Mr. Sahid has 215 pages left to read.
To determine how many pages Mr. Sahid has left to read, you simply need to subtract the number of pages he has already read (177) from the total number of pages in the book (392).
392 pages (total number of pages in the book)
177 pages (number of pages already read)
= 215 pages (number of pages left to read)
So, Mr. Sahid has 215 pages left to read.
It's important to note that this calculation assumes that Mr. Sahid has not skipped any pages and has read every page from start to finish.
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What's the square of 144?.
The square of 144 is 20736. We can get the square of a number when the number is multiplied by itself.
A square of a number can determined when a number or integers multiplied by itself. For example,
when 4 is multiplied by 4 itself we get the number 16. 16 is the square of 4. similarly, when 144 is multiplied by itself we get the value of 20736. here, 20736 is the square of 144.
Multiplying the number with itself is called the square of that number. For the square of a number the exponent used is 2. square of number can be taken as positive. It is because when the negative number is multiplied by itself it becomes positive. so the square of a number is always a positive number.
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solve for x x/5+5=8
Answer:
x<13
Step-by-step explanation:
Answer:
x=15
Step-by-step explanation:
x+25/5=8
x+25=40
x=40-25
x=15
The surface area to volume ratio for a cube is written as 6x²: x³, where x > 0. What value of x would make the ratio 1: 1?
Answer:
x = 6
Step-by-step explanation:
6x²/x³ = 1/1
6/x = 1
x = 6
What is the domain and range of the function all integer numbers?.
The greatest integer function has the domain of a set of all real numbers (R), and its range is the set of all integers (Z).
The greatest integer function gives the greatest integer, which is less than or equal to a given number. The greatest integer less than or equal to a given number x can be represented as ⌊x⌋. Mathematically, the greatest integer function ⌊x⌋ is defined as follows:
⌊x⌋ = a, where a ≤ x < a + 1 and 'a' is an integer.
The greatest integer function has the domain of the set of all real numbers (R), and its range is the set of all integers (Z).
--The given question is incorrect; the correct question is
" What is the domain and range of the greatest integer function?"--
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What function models the height of the periscope lens at time (variable it t)? If the periscope reaches its maximum height after ascending for 22 seconds, what is the maximum height?
The answer is:
The height function modeled by the periscope is h(t) = 24 + 6 × t.The maximum height is 156 inches.The given parameters are:
Start = 24 inches
Rate = 6 inches/second
The function model of the height is determined using a linear function:
h(t) = Start + Rate × t
Where: t represents the time in seconds
So, we have:
h(t) = 24 + 6 × t
This gives
h(t) = 24 + 6t
After 22 seconds, the height of the periscope will be
h(22) = 24 + 6 × 22
Multiply
h(22) = 24 + 132
Add
h(22) = 156
Hence, the maximum height is 156 inches.
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The complete question is:
what function models the height of the periscope lens at time t? If the periscope reaches its maximum height after ascending for 22 seconds, what is the maximum height in feet? ( 24 inches above the surface and ascends at 6 inches per sec.)
Does sides 5 12 13 make a right triangle?.
The sum of two sides is always greater than the third side. So the side lengths 5, 12 and 13 can form a right triangle.
In the given question, we have to define the side lengths 5, 12 and 13 form a right triangle.
If the sum of two sides is greater than the sum of the third side, the side can form a right triangle.
We add the provided sides to see if a right triangle can be formed from them.
5 + 12 > 13
17 > 13 (True)
5 + 13 > 12
18 > 12 (True)
12 + 13 > 5
25 > 5 (True)
Hence, we can see that the sum of two sides is always greater than the third side. So the side lengths 5, 12 and 13 can form a right triangle.
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121 divided by 12.75
Answer: 9.49 or (484/51)
Step-by-step explanation:
121/12.75 = 9.49 as a decimal or 484/51 as a fraction
complementary angles. If mA = (8x + 5) and
ZA and ZB are
m/B = (3x + 8)°, then find the measure of ZB.
Answer:
44 degrees
Step-by-step explanation:
if it's worded the way I think. You definitely have the wording mixed up but you add both angles together and set equal to 90.
Hope it helps! :)
How do you plot and label points on a coordinate plane?.
Two parallel lines called the x axis and the y axis are employed for graph or plot points. The x axis is on the horizontal number line, while the y axis is on the vertical line. The positive and negative axes of the x axis are arranged to the right and left of the origin, respectively.
The following format is employed to plot a point's coordinates: (x, y). As is evident, the x-coordinate is frequently placed first. For example, we have determined the x and y coordinates for the respective points B and D in the diagram we have been using. Point B's x-coordinate is 100.
Any position on the plane may have its x- and y-coordinates established using its horizontal and vertical distances from the origin. In essence, what we do when we sketch a point is the complete antithesis of what we do here.
Labelling:
Our x-coordinate is as follows:
Positive if it's in the appropriate area of our plane.
If it is on the left side of our plot, it is not ideal.
If it is on the x-axis, then it is 0.
Our y-coordinate is as follows:
If it is in the top part of our plot, it is a good indicator.
If it is in the bottom part of our plot, it is not good.
If it is on the y-axis, it will be 0.
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All the angles in the figure are right angles and lengths are measured in centimeters. What is the area, in square centimeters, of the figure?
Answer:
So, the area of the rectangle is
13
×
3
=
39
square centimeters.
The figure was divided such that none of the shapes overlapped.
However, the shapes combinedly form the entire figure.
So, the area of the entire figure is
36
+
39
=
7
In need if helpp ..................
Answer: A:171
Step-by-step explanation:
What is the slope of =- 6?.
Since the line is constantly at 6, it crosses the y-axis at that point. The slope is 0 because the line is horizontal.
What is Y = - 6's slope?The slope is 0 0 when expressed in the slope-intercept form. All parallel lines to y=6 have a slope of 0, which is the same.
How should the slope intercept form be written?When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). The y value of the y intercept point is represented by b in the equation.
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Write the polynomial expression is which the GCF of is factored from the polynomial 2x^(6 - )12x^(4)
The polynomial expression 2x⁶ - 12x⁴ in GCF factored form is 2x⁴(x² - 6).
What is the greatest common factor?The greatest number that can divide the numbers in equal parts.
It is called as greatest common factor.
Given:
A polynomial expression,
2x⁶ - 12x⁴.
To factor the polynomial using GCF:
The GCF of 2x⁶ and 12x⁴,
= 2x⁴.
So, the polynomial is,
2x⁶ - 12x⁴ = 2x⁴(x² - 6)
Therefore, the GCF form of the polynomial is 2x⁴(x² - 6).
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