The 14th term of the arithmetic sequence x-1x−1, 7x-77x−7, 13x-13, ...13x−13,... is -79.
The nth term of a particular arithmetic sequence can be found by, an = a + (n – 1)d. So in order to find the nth term, substitute the given values [tex]a_{1}[/tex] and d into the formula. So to find the 14th term, substitute n = 14 into the equation which is the nth term.
Given,
[tex]a_{1}[/tex]= x-1x-1
[tex]a_{2}[/tex]= 7x-77x−7
[tex]a_{3}[/tex]= 13x-13
n= 14
We have to find the common difference d from differences in adjacent terms [tex]a_{1}[/tex],[tex]a_{2}[/tex],[tex]a_{3}[/tex] . That is,
[tex]a_{2}-a_{1} =a_{3} -a_{2}[/tex]
[tex]7x-77x-7-(x-1x-1)=13x-13-(7x-77x-7)[/tex]
[tex]7x-77x-7-x+x+1=13x-13-7x+77x+7\\-70x-8x=-6+6\\-78x=0\\ x=0[/tex]
Put x=0 in x-1x-1, 7x-77x-7, 13x-13
Therefore,
[tex]a_{1}[/tex] = -1
[tex]a_{2}[/tex] = -7
[tex]a_{3}[/tex] = -13
Then, d will be [tex]-7-(-1)[/tex] or [tex]-13-(-7)[/tex]
So, d= -6
Put [tex]a_{1}[/tex], d, and n in the equation [tex]a_{n} =a+(n-1)d[/tex] to find the 14th term.
Therefore,
[tex]a_{14}=-1+(14-1)-6\\ =-1-78\\=-79[/tex]
The 14th term of the given arithmetic sequence is -79
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Samuya is multiplying 0.7 by 0.003. how many zeros will be to the right of the decimal point in the product?
After multiplying 0.7 by 0.003 there are two zero to right of the decimal point in the product.
Here,
Samuya is multiplying 0.7 by 0.003.
We have to find, zeros will be to the right of the decimal point in the product.
What is Product?
The product of two numbers is the result you get when you multiply them together.
Now,
Product of 0.7 and 0.003 we get;
0.7 x 0.003 = 0.0021
Clearly, there are two zero to the right of the decimal point in the product.
So, After multiplying 0.7 by 0.003 there are two zero to right of the decimal point in the product.
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Michael is planning a trip to Hooperville. On the map, it is 3.5 inches from his home town. The map’s scale is 1.5 inches : 50 miles. How far away is Hooperville from his home town?
The real distance between Hooperville and Michael's home town is 116.667 miles.
How to use scales to estimate distancesScales are ratios commonly used to contain great extensions of land in images and maps and offer a quick though efficient manner to estimate distances. The real distance between Hoopersville and Michael's home town can be found thorugh this formula:
d' = d / r
Where:
r - Scale, in inches per miled - Reduced distance, in inchesd' - Real distance, in milesIf we know that d = 3.5 in and r = 1.5 in / 50 mi, then the real distance between Hooperville and Michael's hown town is:
d' = 3.5 in / (1.5 in / 50 mi)
d' = 116.667 mi
The real distance between Hooperville and Michael's home town is 116.667 miles.
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Why is the standard deviation of the distribution of means generally smaller than the standard deviation of the population of individuals?
The standard deviation of the distribution of means is generally smaller than the standard deviation of the population of individuals.
What is the standard deviation?The standard deviation mathematical and statistical analysis tool used to explain the diversity of treatments or values around the Mean is the standard deviation, which is also known as the square root of variance.
The population of individuals is always smaller than the entire population, therefore the possibilities for variances will be lower with the sample than with the population. The higher the population, the greater the chances for deviation from the mean.
Therefore, the standard deviation of the distribution of means is generally smaller than the standard deviation of the population of individuals.
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What is the f(n) for -5?
A.4
B.1
C.-1
D.-6
Use the Segment Addition Postulate to solve the problem below.
Point E is the midpoint of line segment YT.
line segment YT = 14
line segment YE = 3x + 1
What is the value of x?
Given that Point E is the midpoint of line segment YT, the numerical value of x is 2.
What is the numerical value of x?A midpoint is simply a point that divides a segment into two equal halves.
Given the data in the question;
Point E is the midpoint of line segment YTLine segment YT = 14Line segment YE = 3x + 1Numerical value of x = ?Point E is the midpoint of line segment YT, YT is divided into two equal halves. Hence, Two times Line segment YE equals to YT.
2( Line segment YE ) = Line segment YT
Plug in the given values and solve for x.
2( Line segment YE ) = Line segment YT
2( 3x + 1 ) = 14
Expand using distributive property
2 × 3x + 2 × 1 = 14
6x + 2 = 14
Collect like terms
6x = 14 - 2
6x = 12
6x/6 = 12/6
x = 12/6
x = 2
Given that Point E is the midpoint of line segment YT, the numerical value of x is 2.
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Directions: Determine whether each relation is a function. Explain your answer.
Just need 16-18
From the rule for when a relation represents a function, we have that:
16) Is not a function.
17) Is a function.
18) Is not a function.
When does a relation represents a function?A relation represents a function when each value of the input is mapped to only one value of the output.
For this problem, we have that:
In item 16, input 5 is mapped to outputs 2 and 4, hence it is not a function.In item 17, each input is mapped to only one output, hence it is a function.In item 18, input -2 is mapped to outputs 13 and 15, hence it is not a function.More can be learned about relations and functions at https://brainly.com/question/12463448
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factor the expressions:
1234567890123456789012345678901234567890
The musical note E can be modeled by the function, y = asin(1320πx), where a = 1 and x is the time in seconds. Playing note E on your computer, you notice that it is not loud enough to be heard across the room.
What change can you make to the function to make note E louder than the original?
Using translation concepts, the note E would be louder with a higher amplitude of y, hence constant a has to be multiplied by a positive constant greater than 1.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, the function is given by:
y = asin(1320πx)
The intensity of a sound is given by it's amplitude a, hence, to make the sound stronger, we need to vertically stretch the graph of y, which is done when constant a is multiplied by a positive constant greater than 1.
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Help its for a test grade
X-5y=8
4х+5y=7
Answer:
x = 3 y = -1
Step-by-step explanation:
x - 5y = 8
x = 5y + 8
replace x with 5y + 8 in the other equation
4(5y + 8) + 5y = 7
20y + 32 + 5y = 7
25y = 7 - 32
25y = -25
y = -25/25
y = -1
x = 5(-1) + 8
x = -5 + 8
x = 3
Mrs. Martina wants to put a wire fence around her garden which is 12 feet long and 6 feet wide. How much fencing does she need?
If fencing costs $3 per foot, how much will it cost her to purchase the fence?
The cost for her to purchase the fence is $108.
How to calculate the cost?Since she wants to put a wire fence around her garden which is 12 feet long and 6 feet wide, the total perimeter will be:
= 2(length + width)
= 2(12 + 6)
= 36 feet
Therefore, the cost will be:
= Total feet × Amount
= 36 × $3
= $108
Therefore, the cost for her to purchase the fence is $108.
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helppppppppppppppppppp
Answer:
19
Step-by-step explanation:
5w+3°=98°
5w=98°-3°
5w=95°
therefore w=95/5=19
Make a Prediction Predict the sum of -2 + 2. Explain
your prediction and check it using the number line.
Answer:
My prediction of the sum is 0.
Hope this helps :)
Step-by-step explanation:
It is 0 because if you owe 2 dollars and you pay it back with 2 dollars then you have 0 dollars owed.
--------------------> 2nd: 2 (positive two - move right)
<-------------------- 1st: - 2 (negative two - move left)
<----------l----------l-----------l----------l----------l--------->
-2 -1 0 1 2
What is the value of c?
Enter your answer in the box.
Answer:
26 units
Step-by-step explanation:
By using the Pythagoras Theorem,
C^2 = A^2 + B^2
Substitute in given values for A and B.
C^2 = 10^2 + 24^2
= 100 + 576
= 676
[tex]c = \sqrt{676} \\ = 26[/tex]
Hope this helped! ^^
Sidenote: Pythagoras Theorem can only be used on right-angled triangles.
An isotope with z > 83, which lies close to the band of stability, will generally decay through_______
An isotope with z > 83, which lies close to the band of stability, will generally decay through decay.
What do we mean by decay?The process by which an unstable atomic nucleus loses energy through radiation is known as radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, as well as nuclear disintegration). Radioactive material is one that contains unstable nuclei. Radioactive decay is the spontaneous transformation of one element into another. This can only happen by changing the number of protons in the nucleus (an element is defined by its number of protons). A radioactive procedure in which a nucleus spontaneously transforms into one or more different nuclei while emitting radiation, losing electrons, or fissioning. An isotope with z > 83, for example, which is close to the band of stability, will generally decay through decay.Therefore, an isotope with z > 83, which lies close to the band of stability, will generally decay through decay.
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8.) What is the circumference of a circle?
It is the perimeter of the circle?
It is the area of the circle?
Answer:
[tex]\large\boxed{\textsf{The Circumference is the Perimeter of the circle.}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to identfy what the Circumference is.}}[/tex]
[tex]\Large\underline{\textsf{What is the Circumference?}}[/tex]
[tex]\textsf{The Circumference is a fancy word to describe the sum of the arcs of a circle.}[/tex]
[tex]\textsf{The total of the area 'on' the circle is commonly referred to as the Perimeter.}[/tex]
[tex]\mathtt{Circumference = (diameter)\pi }[/tex]
CAN SOMEONE HELP ME PLEASE I don't know what -2 1/3+(-1 3/4)=? in factions
The solution to the fraction expression -2 1/3 + (-1 3/4) is -4 1/12
How to evaluate the fraction?The fraction expression is given as
-2 1/3 + (-1 3/4) =
Express the terms of the expression as an improper fraction
So, we have
-2 1/3 + (-1 3/4) = -7/3 + (-7/4)
Remove the bracket in the above expression.
So, we have
-2 1/3 + (-1 3/4) = -7/3 - 7/4
Take the LCM in the above expression.
So, we have
-2 1/3 + (-1 3/4) = (-7 * 4 - 7 * 3)/12
Evaluate the difference
-2 1/3 + (-1 3/4) = -49/12
Express the fraction as a mixed fraction
-2 1/3 + (-1 3/4) = -4 1/12
Hence, the solution to the fraction expression -2 1/3 + (-1 3/4) is -4 1/12
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The heights of young women are approximately normal with mean 64.5 inches and standard deviation 2.5 inches. what are the deciles of this distribution?
Deciles are 61.3 and 67.7
What are deciles?
Deciles are measures of position calculated on a set of data. The deciles are the values that separate a distribution into ten equal parts, where each part contains the same number of observations). The decile is a member of the wider family of quantiles.
Given:
Normal distribution =64.5 inches
Standard deviation=σ =2.5 inches
So, here the z- score for left decile= -1.28
and for right decile= +1.28
we know,
z= x-[tex]\mu[/tex]/σ
x= zσ + [tex]\mu[/tex]
x=-1.28*2.5 + 64.5
x= 61.3 and,
x= 1.28*2.5 + 64.5
x=67.7
hence, the deciles are 61.3 and 67.7
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Calculate the density of a solid substance if a cube measuring 2.57 cm on one side has a mass of 120. g
The required density of the given solid substance is 7.07 g/cm³.
What is the density of a substance?
The density of a substance is the property which is obtained by dividing the mass of the given substance by its volume. Its SI unit is kg/m³.
Calculation for the density of a solid substance
Mass of the given substance = 120 g
Side of cube, a = 2.57 cm
The volume of the given substance = a³
= 2.57³
= 16.97 cm³
The density of the given substance is given by the mass of the substance/volume of the substance
= 120 / 16.97
= 7.07 g/cm³
Hence, the density of the given solid substance is 7.07 g/cm³.
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Simplify: 3/4y - 2/4y + 7 = 2/4y - 1. Show your work.
help please
I'm assuming the equation is
[tex]\frac{3}{4}y - \frac{2}{4}y+7 = \frac{2}{4}y-1[/tex]
Let me know if the equation is different so I can update the solution.
-----------------
Fractions are a pain to deal with, so it's best to eliminate them whenever we can. In equations like this, we can multiply both sides by 4 since this is the LCD (which stands for "lowest common denominator").
If we multiply both sides by 4, then all the denominators of 4 will cancel.
We'll have these steps:
[tex]\frac{3}{4}y - \frac{2}{4}y+7 = \frac{2}{4}y-1\\\\4\left(\frac{3}{4}y - \frac{2}{4}y+7\right) = 4\left(\frac{2}{4}y-1\right)\\\\3y - 2y + 28 = 2y - 4 \ \ \text{ ... denominators cancel after distributing}\\\\y + 28 = 2y - 4\\\\y- 2y =- 4-28\\\\-y = -32\\\\y = \frac{-32}{-1}\\\\y = 32\\\\[/tex]
Final Answer: y = 32Answer:
[tex]y=32[/tex]
Step-by-step explanation:
Given the following question:
[tex]\frac{3}{4}y-\frac{2}{4}y+7=\frac{2}{4}y-1[/tex]
[tex]\frac{3}{4}y-\frac{2}{4}y+7-7=\frac{2}{4}y-1-7[/tex]
[tex]\frac{3}{4}y-\frac{2}{4}y=\frac{y}{2}-8[/tex]
[tex]\frac{3}{4}y-\frac{2}{4}y-\frac{y}{2}=\frac{y}{2}-8-\frac{y}{2}[/tex]
[tex]-\frac{y}{4}=-8[/tex]
[tex]4\left(-\frac{y}{4}\right)=4\left(-8\right)[/tex]
[tex]\frac{-y}{-1}=\frac{-32}{-1}[/tex]
[tex]y=32[/tex]
Therefore "y = 32."
Hope this helps.
what are the dimensions of a rectangle with an area equal to the parallelogram with the vertices (6,21) (14,15) (6,0) (-2,6)
The dimensions of the rectangle are:
width = 10 units
length = 17 units
What are the Dimensions of the Triangle?
We are given to find the dimensions of a rectangle with an area equal to the parallelogram with vertices (6, 21), (14, 15), (6, 0), and (-2, 6).
If we have two points with coordinates as (a, b) and (c, d) The distance is given by the formula: √[(c - a )² + (d - b)²]
Now, of the coordinates are labelled as;
A(6, 21), B(14, 15), C(-2,6), (6,0)
Thus;
AB = √(14 - 6)² + (15 - 21)² = √100 = 10 = CD
AC = √(-2 - 6)² + (6 - 21)² = 64 + 225 = √289 = 17 = BD
Thus the dimensions of the rectangle are:
AB = 10 = width
AC = 17 = length
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Which of the following is a trinomial with a constant term?
O A. yo +8y³ +GAY
OB. X
OC. x³ + y
OD. x+ 2y + 10
Option D x+2y+10 .
A trinomial with a constant term will have three terms, and one of those terms will be a constant, which is a number.
we also know about the Constant
A fixed value. In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number.
Some relatable terms are :
Monomial: Polynomial having a single term.
Binomial: Polynomial having two terms.
Trinomial: Polynomial having three terms.
In given option we'll define
in option A there is no constant .
option B there i sonly given x which is also not constant.
further in option c it is simply binomial in which only two terms are given without constant .
so at last conclusion is in option D there are three terms are given with one constant which is number 10 .
x+2y+10 is trinomial with a constant.
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what’s the growth factor of 24,12,6,3,1.5
Answer:
0.5
Step-by-step explanation:
12/24 = 0.5
6/12 = 0.5
3/6 = 0.5
1.5/3 = 0.5
Answer: 0.5
help with
absolute value functions
The method of altering a graph to produce a different version of the one that came before is known as graph transformation. The graphs are movable in the x-y plane and can be translated. Along with these modifications, they can also be stretched.
Horizontal stretching
Vertical stretching
Vertical translation
Horizontal translation
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The sum of Melanie's and her brother's ages is 35. Four years from now, Melanie will be 5 years older than her brother. How old is Melanie? How old is her brother?
Answer:
Sum of ages is 35
Since there are two persons and it says four years from now, each year 2 more years will be added on to the 35 so year 1: 2years Year 2:4years Year 3:6years Year 4 : 8years
35+8= 43
Remember that Melanie will be 5 years older ( which she should have already been)
so 43+5= 48 ( Melanie's age)
and 48-5 = 43 ( Her brother's age)
Show the correct steps and solution
After simplifying the expression, - ( 7 x - 3 y ) + 2 ( 3/4 x + 1/2 y), we get the result as - 11 / 2 x + 4 y.
- ( 7 x - 3 y ) + 2 ( 3/4 x + 1/2 y)
First we will multiply 2 and open the brackets.
So, we get that:
- 7 x + 3 y + 3/2 x + y
Combining the like terms, we get that:
= ( - 14 + 3 ) x / 2 + 3 y + y
Simplifying and solving the expression to obtain the result, we get that:
= - 11 / 2 x + 4 y.
Therefore, after simplifying the expression, - ( 7 x - 3 y ) + 2 ( 3/4 x + 1/2 y), we get the result as - 11 / 2 x + 4 y.
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14. Determine whether the relation shown in the
table is a function. Explain. (Lesson 2-1)
Domain
Range
-4
8
2
11
-4
13
5
13
Now, it is not a function, same domain has different ranges
What are the zeros of the expression (x-5)(2x+7)
Answer:
The zeros are x =5, -7/2
Step-by-step explanation:
To find the zeros, set the expression equal to zero
(x-5)(2x+7) =0
Using the zero product property
(x-5)=0 (2x+7)=0
Solve each equation
x=5 2x = -7
x=5 x = -7/2
The zeros are x =5, -7/2
Answer:
5, -7/2
Step-by-step explanation:
[tex]x - 5 = 0 = 5\\\\2x + 7 = 0\\2x + -7 = 0\\\frac{2x}{2} = \frac{-7}{2}\\ x = \frac{-7}{2}\\x = -\frac{7}{2}[/tex]
Thus,
x = 5
x = -7/2
Question 3 (1 point)
What is the correct solution for the following addition, reported to the correct
number of significant digits? Assume all numbers are measurements.
3001+ 20.3 +0.009
a) 3021
b) 3021.3
c) 3021.309
d) 3021.30
Answer:
I think it's C but I'm not 100% sure
(solve the literal equation for y.)
6 - 3y = -6
Answer:
4
Step-by-step explanation:
use this to find the equation of the tangent line to the curve at the point and write your answer in the form: , where is the slope and is the y-intercept.
The equation can be simplified and written in a slope-intercept form as: [tex]y=18 \sqrt{3} x-6(\sqrt{3} \pi-1)[/tex]
What do we mean by equations?An equation is a mathematical declaration composed of two expressions joined by an equal sign. An equation is 3x - 5 = 16. By solving this equation, we obtain the value of the variable x as x = 7.To find the equation:
When we differentiate the function [tex]y=6 \sec (x)-12 \cos (x)[/tex], we get:
[tex]\begin{aligned}y^{\prime} &=\frac{d}{d x}(6 \sec (x)-12 \cos (x)) \\&=6 \frac{d}{d x}(\sec (x))-12 \frac{d}{d x}(\cos (x)) \\&=6 \sec (x) \tan (x)+12 \sin (x)\end{aligned}[/tex]
The slope of the tangent line is given by this derivative at the point [tex]x=\frac{\pi}{3}[/tex]:
[tex]y^{\prime}\left(\frac{\pi}{3}\right)=6 \sec \left(\frac{\pi}{3}\right) \tan \left(\frac{\pi}{3}\right)+12 \sin \left(\frac{\pi}{3}\right)=18 \sqrt{3}[/tex]The general equation y applies to the tangent line passing through the point [tex](a, y(a))[/tex] on the curve [tex]y(x)-y(a)=y^{\prime}(a)(x-a)[/tex].The tangent line in this case passes through the point [tex]\left(\frac{\pi}{3}, y\left(\frac{\pi}{3}\right)\right)=\left(\frac{\pi}{3}, 6\right)[/tex] and has the slope [tex]y^{\prime}\left(\frac{\pi}{3}\right)=18 \sqrt{3}[/tex].As a result, this tangent line has the equation: [tex]y-6=18 \sqrt{3}\left(x-\frac{\pi}{3}\right)[/tex]
Therefore, the equation can be simplified and written in a slope-intercept form as: [tex]y=18 \sqrt{3} x-6(\sqrt{3} \pi-1)[/tex]
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The correct question is given below:
Find the equation of the tangent line to the curve y = 6 sec (x) at the point ([tex]\pi[/tex]/3, 6). Give your answer in the form y = mx + b where m is the slope and b is the y--intercept.