The first term of the arithmetic sequence [tex]a_{1}[/tex] is -9
As per the question statement, we are given an arithmetic sequence whose 12th given term is 13 and common difference is 2. We are supposed to find the first term [tex]a_{1}[/tex].
We know that the [tex]n_{th}[/tex] term in an arithmetic sequence is given by:
[tex]a_{n} = a_{1}+(n-1)d[/tex]
where "n" is the number of terms and "d" is the common difference.
Now in question, [tex]a_{n} =a_{12} =13[/tex]
[tex]d=2[/tex]
[tex]n=12[/tex] and we have to find [tex]a_{1}[/tex]
Substituting values,
[tex]13=a_{1} +(12-1)*2\\13=a_{1} +11*2\\13=a_{1}+22\\a_{1} = -9[/tex]
Hence [tex]a_{1} = -9[/tex]
Arithmetic sequence: Arithmetic Progression (AP) or arithmetic sequence is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value known as common difference.To learn more about Arithmetic sequence, click on the link given below:
https://brainly.com/question/12108818
#SPJ9
Round 249798.828806 to the nearest ten
Answer:
249798.8
Hope this helps! <3
Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an (x, y) point. y ==2x² - 24r – 56
The solution of the given equation y ==2x² - 24r – 56 :
(6 , -128)
What is graphing technology?Graph technology aids in the discovery of unknown links in data that cannot be detected or examined using traditional methods. When the broad term graph is introduced as both a topic, it frequently blurs three distinct topics: graph theory, graph analytics, and graph data management.
Why is graphing useful?Graphs and charts are useful visual tools because they deliver information quickly and readily. It is hardly surprising, then, that graphs are widely utilized in print and electronic media. Data can be easier understood when displayed as a graph rather than a table since the graph can illustrate a pattern or comparison.
According to the given equation:y =2x² - 24x – 56
Solving for :
Parabola equation in polynomial form
ax² + bx + c for x = -b/(2a)
a = 2
b = -24
c = -56.
on solving we get
= -(- 24)/2* 2
= 6
The value of x = 6
putting the value of x to get y:
2x² - 24x – 56
2(6)² - 24(6) – 56
-128
the value of y = -128.
To know more about graphing technology visit:
https://brainly.com/question/1651873
#SPJ9
Write the equation of the line that is parallel to y 2/3 = x + 1 and passes through the point (–6, –1).
The linear equation with the given information is
2y+2 = 3x+18
Given :
The slope of Parallel Lines:
Slopes of parallel lines are equal. The parallel lines are equally inclined with the positive x-axis and hence the slope of parallel lines is equal. If the slopes of two parallel lines are represented as m1, m2 then we have
In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate.
The net change in the y-coordinate is represented by Δy and the net change in the x-coordinate is represented by Δx.
Hence, the change in y-coordinate with respect to the change in x-coordinate is given by,
m = change in y/change in x = Δy/Δx
Where “m” is the slope of a line.
The slope of the line can also be represented by
tan θ = Δy/Δx
So, tan θ to be the slope of a line.
Generally, the slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says (x1,y1) and (x2,y2) can be easily determined by finding the difference between the coordinates of the points. The slope is usually represented by the letter ‘m’
m1 = m2.
y 2/3 = x + 1 ...1
2y = 3x+3
y = 3/2x +3/2
m1= 3/2
x,y = -6,-1
y = mx +b
(y-y1 ) =m (x-x1) +b
m1=m2
m2= 3/2
(y +1) = 3/2 (x+6)
2(y+1 )= 3x+18
the equation of the line that is parallel to y 2/3 = x + 1 and passes through the point (–6, –1) = 2y+2 = 3x+18
More details: brainly.com/question/13911764
#SPJ9
HW 3 Linear Function Models: Problem 9
Previous Problem Problem List Next Problem
(3 points)
A new highway has just opened and tolls will be collected from vehicles using the highway. The toll will be 119 cents for cars which travel 20 miles of the
highway. The toll will be 184 cents for cars which travel 33 miles of the highway. Let T(d) be a function which gives the total toll (in cents) which will be
charged to a car which travels d miles along the highway. Assume T(d) is a linear function. Find T'(d).
T(d) =
What will be the toll to travel 96 miles?
cents
Answer:
T(d) = 5d +19T(96) = 499 . . . centsStep-by-step explanation:
Given two points on the linear toll function T(d) are (20, 119) and (33, 184), you want the equation for the function T(d), and the value of T(96).
SlopeIt is usually convenient to write the equation of a line in slope-intercept form when you want to find the value at a particular point. To use that form, we need to know the slope of the line. It is given by the formula ...
m = (y2 -y1)/(x2 -x1)
Using the given points, we have ...
m = (184 -119)/(33 -20) = 65/13 = 5
Point-slope equationThe point-slope form of the equation for a line is ...
y -k = m(x -h) . . . . . line with slope m through point (h, k)
Using the first point and the slope we found, the equation is ...
y -119 = 5(x -20)
Slope-intercept equationSolving the above equation for y, we get ...
y = 5x -100 +119 . . . . . . . simplify, add 119
y = 5x +19 . . . . . . . . . . combine terms
Using variables d and T instead of x and y, the function is ...
T(d) = 5d +19
Toll for 96 milesThe value T(96) is ...
T(96) = 5(96) +19 = 480 +19 = 499
The toll for 96 miles is 499 cents.
y=1,5 sin(x - 2п/3) + 2
Hence , the graph of the equation is y = 1.5 sin(x - 2π/3) + 3 is given below .
In math, a graph may be outlined as a representation or a diagram that represents knowledge or values in associate degree organized manner.The points on the graph usually represent the connection between 2 or additional things.The general form of a sine function is of the form:
y = a×sin(bx − c) + d,
here the amplitude is a,
the period is 2π/|b|,
the phase shift is c/b, and
the vertical shift is d.
From the given equation we have,
The amplitude, a = 1.5
The period, = 2π/|1| = 2π
The phase shift = (2π/3)/1 = 2π/3
And the vertical shift is d = 2
The given equation can be graphed using the amplitude, period, phase shift, vertical shift, and points.
Refer to the attached image(table) for the points to plot the graph.
Refer to the attached image(sine_graph) for the graph of this equation.
Learn more at:
https://brainly.com/question/10528481
#SPJ9
Disclaimer:
The question is not complete.
Assume the following to answer this question.
Graph of the equation: y = 1.5 sin(x - 2π/3) + 3
Which is the equation of a hyperbola centered at the origin with focus (-3,0) and vertex (-2,0)
Main answer:[tex]x^{2}[/tex]/4 - [tex]y^{2}[/tex]/5=1
Definition of Hyperbola=a symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone.
Formula=[tex](x-x1)^{2}[/tex]/[tex]a^{2}[/tex] - [tex](y-y1)^{2}[/tex]/[tex]b^{2}[/tex]=1
Given,
origin o(0,0) , focus s(-3,0) , vertex v(-2,0)
and , x1=0, y1=0
then, equation of hyperbola becomes= [tex]x^{2}[/tex]/[tex]a^{2}[/tex]-[tex]y^{2}[/tex]/[tex]b^{2}[/tex]=1
a is the distance between center and the vertex,
distance between o and v = 2
c is the distance between center and the focus,
distance between o and s =3
[tex]a^{2}[/tex]+[tex]b^{2}[/tex]=[tex]c^{2}[/tex]
4+[tex]b^{2}[/tex]=9
[tex]b^{2}[/tex]=5
Then the equation of hyperbola becomes=[tex]x^{2}[/tex]/4 -[tex]y{2}[/tex]/5=1
to learn more about Hyperbola visit:
brainly.in/question/41061731
#SPJ9
how do you find the perimeter on a coordinate plane
Answer: You draw the shape on the coordinate plan and then you can count the number of unit squares
Step-by-step explanation:
Find the difference between 8.72 and 0.872
Answer:
Step-by-step explanation:
Find the difference between 8.72 and 0.872. This just means to subtract 0.872 from 8.72. [tex]8.72-0.872=7.848[/tex]
What can you multiply 4 by to get 120?
Answer:30
Step-by-step explanation:
30+30+30+30 just do 120/4
Find the value of X NEED HELP YRGENTLY
Answer:
x = 11°
Step-by-step explanation:
You want to know the value of x given a triangle with exterior angles 147°, 4x, and an interior angle of x at the third vertex.
SetupThe exterior angle of the triangle at B is the supplement of x: 180°-x. The sum of the exterior angles of a polygon is 360°, so we have ...
147° +4x +180° -x = 360°
SolutionCollecting terms, we have ...
327° +3x = 360°
3x = 33° . . . . . . . . . subtract 327°
x = 11° . . . . . . . . . . divide by x
Select the expression that are equivalent to -3(g+2)
Answer:
Step-by-step explanation:
-3g-6
15. Isabel made the following graph to show
the daily share price for Company XYZ.
What was the change in the price from
Monday to Friday?
The change in the price from Monday to Friday is $0.75
How to determine what was the change in the price from Monday to Friday?The graph that completes the question is added as an attachment
From the attachment, we have:
Monday = $0.75
Friday = $1.50
There are 5 days between Monday and Friday
So, we have the change in the price from Monday to Friday to be
Change = Friday - Monday
This gives
Change = $1.50 - $0.75
Evaluate
Change = $0.75
Hence, the change in the price from Monday to Friday is $0.75
Read more about rate of change at
https://brainly.com/question/664324
#SPJ1
A test consists of 100 multiple choice questions, each with five possible
answers, only one of which is correct. A student randomly guesses at all
100 questions.
Use the Mean And Standard deviation to determine how many questions correct we could usually expect from a student who randomly guesses at all 100 questions.
Mean = 20; standard deviation = 4;
Let x be the success of receiving the right response.
The total number of trials in this case is 100.
The likelihood of receiving the right response is p = 1/5.
In light of the average number of correct answer;
μₓ = np
μₓ = 100 * (1/5);
μₓ = 20;
The standard deviation is now; σ = √(n)(p)(1 - p)
σ = √(100)(1/5)(4/5)
σ = 4
To learn more about standard deviation, visit: https://brainly.com/question/11738379
#SPJ9
Suppose the geographic area of Los Angeles County is 4,751 square miles. If the state of California has an
area of 1.637 x 105 square miles, that means that it would take approximately 35 Los Angeles Counties
to make up the state of California. As of 2013, the population of Los Angeles County was 1 x 107 people.
If the population were proportional to area, what would be the population of the state of California?
Answer:
go get smart and stop cheating on online websites
Step-by-step explanation:
5/6 divided by 3/5 =
A. 18/25
B. -25/18
C. 25/18
D. -18/25
Answer:
5/6*5/3
25/18
so the answer is 25/18
Solve: -7+5 > 2. Write your solution in interval notation.
(If there is no solution, enter your answer as Ø.)
Answer:
-7+5 >2
-7+5=2
collect like terms
-7 =2-5
-7 = -3
therefore: -7>-3Hope this helpsGood luck ✅Find the inverse of the linear function
Answer:
D [tex]y = - \frac{1}{4} x - \frac{1}{4} [/tex]
Step-by-step explanation:
See attached image for explanationThe longer side of a golden rectangle has length of 13. In order to find the length of the shorter side, divide 13 by what
in order to find the shorter side of a golden rectangle we need to divide 13
by 1.6180.
A golden rectangle is a rectangle in geometry whose side lengths are in the golden ratio, or display style 1:tfrac 1+sqrt 5 2 which is display style 1:varphi 1:varphi (the Greek letter phi), where display style var phi var phi is roughly 1.618.
All rectangles made by including or excluding a square from one end are also golden rectangle, which is a unique example of self-similarity.
Length of longer side a = 13
let the length of shorter side is b.
them by the property of golden rectangle,
a : b = 1: (1+sqrt 5)/2
by substitution method
13 : b = 1 : (1+sqrt 5)/2
b = 8.034
so to get the length of shorter side we need to divide by 1.6180
Read more about golden rectangle here:
https://brainly.com/question/27915841
#SPJ4
e table shows ordered pairs of the function . What is the value of y when ? A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 1, 1, 4, 8, 10. The second column is labeled y with entries 14, 10, 6, 0, question mark, negative 12. –20 –8 8 48
y = -8.
An ordered pair is a composition of the x coordinate and the y coordinate, having two values written in a fixed order within parentheses. It helps to locate a point on the Cartesian plane for better visual comprehension.
Ordered pairs are often used to represent two variables. When we write (x, y) = (7, - 2), we mean x = 7 and y = - 2. The number which corresponds to the value of x is called the x-coordinate and the number which corresponds to the value of y is called the y-coordinate.
see attachment for the table
we observe from the given table that
As x increases by 2, y decreases by 4
As x decreases by 2, y increases by 4
for example x = 10, y = -12
when x decreases by 2 (to 8), the value of y will increase by 4 (to -8).
Hence, the value of y when x = 8 is -8
To learn more about ordered pairs
visit - brainly.com/question/17215264
#SPJ9
Not sure how to solve this problem
Answer:
98
Step-by-step explanation:
For every 1 true or false question, there are 2 answers
so that means, it would mean you could do
7 x 7 = 49
then do 49 x 2 =
98
the reason you would do this is that you want to find all the possible answers chances.
does anyone know how to solve this pre cal question Im super confused
Answer:
f(-3) = 3*-3 + 4 = -9 + 4 = -5
f(3) = 2*3 - 2 = 6 - 2 = 4
f(0) = 2*0 - 2 = 0 - 2 = -2
What is the standard form of 10 to 5 power
Answer:
100,000
Step-by-step explanation:
Multiply 10 by 10 by 10 by 10 by 10 to get 100000
How many times larger is 7.785 x 10^10 than 1.5 x 10^8?
05.19
19.3
193
519
Answer:
(d) 519
Step-by-step explanation:
You want the ratio of (7.785×10^10) to (1.5×10^8) expressed in standard form.
DivisionSince you want the result in standard form, it can work well to make the numerator and denominator powers of ten be the same.
[tex]\dfrac{7.785\times10^{10}}{1.5\times10^8}=\dfrac{7785\times10^7}{15\times10^7}=\dfrac{7785}{15}=\boxed{519}[/tex]
In a survey of 400 households regarding ownership of HDTVs and DVD players, the following data were obtained. 315 households own one or more HDTVs. 150 households own one or more HDTVs and one or more DVD players. 16 households do not own an HDTV or a DVD player. How many households only own one or more DVD players?
Number of households only own one or more DVD players = 219
Total number of households considered for the survey = 400
Let n(A) represent the number of households only own one or more HDTVs.
Then n(A) = 315
Let n(B) denotes the number of households only own one or more DVD players. We need to find n(B).
Number of households own one or more HDTVs and one or more DVD players, n(A∩B) = 150
Number of households do not own an HDTV or a DVD player = 16
So the number of households which own an HDTV or a DVD player, n(A∪B) = 400 - 16 = 384
Then we have the formula relating n(A∪B), n(A), n(B) and n(A∩B).
n(A∪B) = n(A) + n(B) - n(A∩B)
⇒ n(B) = n(A∪B) - n(A) + n(A∩B)
= 384 - 315 + 150
= 219
The number of households only own one or more DVD players = 219
Learn more about union and intersection of sets at https://brainly.com/question/2166579
#SPJ1
How to set up equation
Answer:
To set up an equation, you must first see what the question is looking for.
Hope this helps :)
Answer:
Basic Steps to Setting Up EquationsDetermine what the question is asking. Write down the relevant information in simple statements. Assign symbols to unknown values that need to be found. Determine how the statements relate to each other mathematically.
Step-by-step explanation:
if right mark as brainliestWhich of the following describe 0?
What is 639 ÷ 0.3 I neeed I help pls this is due Tomorrow help pls
Answer:
Step-by-step explanation:
639÷0.3=
2130
the answer is
639÷0.3=
2130
The Washington Football Team won 6 of their 13 games. What percentage of their games did they win?
Answer:
46.2%
Step-by-step explanation:
6 divided by 13 multiplied by 100. rounded up
will mark u brainliest
A state park has an area of 112 acres. The table shows the estimated park populations for several animals. Find the population density in animals per acre for each animal?
Animal-Population
otter-35
raccoon-186
fox-9
bobcat-3
The population density of otter, raccoon, fox and bobcat is 0.3125, 1.66, 0.0803 and 0.0267 per acre
Total park area of the state park = 112 acres
Number of Otter = 35
Number of Raccoon = 186
Number of Fox = 9
Number of Bobcat = 3
The formula of population density is given by:
Population Density = Number of animals/Area of land
Population density of Otter in the park = 35/112 = 0.3125 Otter per acre
Population density of raccoon in the park = 186/112 = 1.66 Raccoon per acre
Population density of fox in the park = 9/112 = 0.0803 Fox per acre
Population density of bobcat in the park= 3/112 = 0.0267 bobcat per acre
Learn more about population density:
https://brainly.com/question/1581160
#SPJ1