Patterns of the given terms 8,9,10,11,.... is arithmetic progression, where aₙ= 8 + (n-1)d, d=1. Next three terms are 12,13,14.
As given in the question,
Given pattern is 8,9,10,11,...
First term a₁ = 8
Second term a₂ = 9
Third term a₃ = 10
Fourth term a₄ =11
d =aₙ - aₙ₋₁
=a₂ -a₁
=9 -8
=1
8,9,10,11,... represents arithmetic progression
aₙ=8 + (n-1)d
a₅ =8+ 4(1)
=2
a₆ =8 + 5(1)
=13
a₇ =8 + 6(1)
=14
Therefore, patterns of the given terms 8,9,10,11,... is arithmetic progression, where aₙ= 8 + (n-1)d, d=1. Next three terms are 12,13,14.
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6n² - 15 = 6 (5)² - 15
Answer:
6n2-15=150-15
6n2-15=135
6n2=150
divied both side by 6
n2=25
sqrt both side
n=-5 or 5 bc sqrt so 2 answer
Step-by-step explanation:
6. What's the product of 3 2/3 and 14 2/5 ?
A. 52 415
B. 42 45
C. 54
D. 52 45
Answer:
D. 52 45
Step-by-step explanation:
Determine whether the regular polygon will tessellate in the plane. Write yes or no. Explain.
triangle
Yes , Triangles are all tessellated. The triangle's three corners (A, B, and C) meet together to form a 180° angle, or a straight line, which is why the image is successful.
Is a triangle capable of tessellation?
Triangles are all tessellated. The triangle's three corners (A, B, and C) meet together to form a 180° angle, or a straight line, which is why the image is successful. We state it here since it will serve as the cornerstone of our investigation into polygon tessellations: Any triangle's total angles come to 180 degrees.To create a regular tessellation, it is necessary that the tiles may fill 360 degrees around a point (all the tiles regular polygons with same number of sides) Only 60 degree angle triangles, 90 degree squares, and 120 degree hexagons will work.
Every vertex, edge, and tile in a regular tesselation are identical.
However, there are semiregular tesselations that use more than one regular polygon, but since they must be able to fill 360 degrees around a point, it turns out that only the octagon (8 sides, 135 degrees) and dodecagon can be used as additional polygons (12sides, 150 deg).
Note that just these 5 tesselations can be utilized to fill the plane entirely with regular polygons.
Each vertex in the semiregular tessellations is the same.
Eight of them are (3,3,3,3,6), (3,3,3,4,4), (3,4,6,4), (3,6,3,6), (3,12,12), and (4,6,12). (4,8,8)
The Octagon & square tiling (4,8,8) is a very common floor tiling.
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The arithmetic mean of two terms in an arithmetic sequence is 42 . One term is 30 . Find the other term.
The arithmetic mean of two terms in an arithmetic sequence is 42 .
What is sequence?One term is 30 then other term is
42 = (x+30)/2
x=54
An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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8/3= 19/6n - 1/2n
I NEED HELP
Answer:
n = 1
Step-by-step explanation:
[tex]\frac{8}{3}[/tex] = [tex]\frac{19}{6}[/tex] n - [tex]\frac{1}{2}[/tex] n
multiply through by 6 ( the LCM of 3, 6 and 2 ) to clear the fractions
16 = 19n - 3n
16 = 16n ( divide both sides by 16 )
1 = n
The pivot or midpoint of a seesaw on a playground is 13.5 feet from the swing set. If the swing set is 8 feet from the edge of the seesaw when the seesaw is level, how long is the seesaw.
The length of seesaw will be equal to 11 feet.
It is given that midpoint of the seesaw is 13.5 feet from the swing set and swing set is 8 feet from the edge of the seesaw.
We have to find out the length of seesaw.
What do you mean by midpoint of a line segment ?
The midpoint is halfway between the two end points , whose x value is halfway between the two x values and y value is halfway between the two y values.
As per the question ;
The midpoint of the seesaw is 13.5 feet from the swing set.
and
The swing set is 8 feet from the edge of the seesaw.
So ;
The distance from the midpoint to the edge will be ;
13.5 – 8 = 5.5.
And
The length of the seesaw will be ;
= 2× (5.5)
= 11 feet
Thus , the length of seesaw will be equal to 11 feet.
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Please help me with this math problem! Will give brainliest!! :)
Answer:
f (x^2-4) = 2x^2 - 5
Step-by-step explanation:
PLEASE HELP
PLEASE SHOW HOW U CHECKED UR WORK
The equation and the solution are 2 = -8 * -x and x = 1/4, respectively
How to determine the equation and the solution?On the model, we have the following representations
[1][1] [-1][-1][-1][-1][-1][-1][-1][-1][-x]
When represented as an equation, we have the following equation
So, we have
2 = -8 * -x
Evaluate the product in the above equation
So, we have
2 = 8x
Divide both sides of the above equation by 8
So, we have
1/4 = x
Rewrite the above expression as
x = 1/4
Hence, the equation and the solution are 2 = -8 * -x and x = 1/4, respectively
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Write a function g whose graph represents the indicated transformation of the graph of f(x)=-2|x-4|+2
Using translation concepts, the function g is given as follows:
g(x) = -|x - 4| + 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, we have that function g(x) is the function f(x) vertically compressed by a factor of 2, hence:
g(x) = 0.5f(x)
g(x) = 0.5(-2|x - 4| + 2)
g(x) = -|x - 4| + 1
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Silas pays 8% interest on his $22,000 college loan and 11% interest on his $10,000 car loan. What average interest rate does he pay on the total $32,000 he owes? Round your answer to the nearest tenth of a percent.
The average interest rate does he pay on the total $32,000 he owes is 9. 5%
How to determine the average
From the information given, we have that;
8% interest on his $22,00011% interest on his $10,000Given the total pay he owes as;
= $22, 000 +$ 10, 000
= $32, 000
The average interest rate is expressed as;
= sum of interest rate for college loan and car/ number of interest rate
Substitute the values
= 8 + 11/ 2
= 19/ 2
Find the quotient
= 9. 5%
Thus, the average interest rate does he pay on the total $32,000 he owes is 9. 5%
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Plot two numbers that are 5 units from zero on the number line.
The two numbers which are 5 units away from zero on the number line as required in the task content are; -5 and 5.
Which two numbers are 5 units away from 0 on the number line?It follows from the task content that the numbers which are 5 units away from zero on the number line be identified and plotted.
Hence, given that the numbers in discuss are represented by; x; we have;
| x - 0 | = 5
| x | = 5
Ultimately, x = ±5. where +5 is to the right and -5 is to the left of zero respectively.
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In the Mars Cars video game, players gain and lose points by avoiding or hitting obstacles on a martian race track. First, Gary gained 20 points by jumping over a crater. Then, he lost 45 points for getting stuck in a dust storm.
What was Gary's score after getting stuck in the dust storm?
The Gary's score after getting stuck in the dust storm will be -35 points.
It is given in the problem that,
The points gained by Gary by jumping over a crater = 20 points
And then,
The points lost by Gary for getting stuck in a dust storm = 45 points
We need to find,
The Gary's score after getting stuck in the dust storm
As in the beginning of the game, Gary's account had 20 points but as he then stuck in the dust storm he lost 45 points, which means he has lost points more than he had. So, now Gary would have negative points left in his account in the game
= 10 - 45
= - 35
Hence, the Gary's score after getting stuck in the dust storm will be -35 points.
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The heights of a sample of 15 students are recorded in
the stemplot below.
Heights of Students
What is the mean height, in inches, of this sample?
65
65.2
66
67
The mean height of the given sample of values is approximately 65.20.
The heights of the 15 students are as follows:
{59, 61, 62, 63, 63, 64, 65, 65, 66, 67, 67, 67, 67, 69, 73}
To find the mean (average) height of the given values, we need to add up all the heights and then divide the sum by the total number of heights:
59 + 61 + 62 + 63 + 63 + 64 + 65 + 65 + 66 + 67 + 67 + 67 + 67 + 69 + 73
= 978
So, the mean height can be calculated as:
Mean height = Total height / Number of heights = 923 / 15 = 65.2
Therefore, the mean height is approximately 65.20.
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Given f (x) = 3x – 5 and g(x) = 2x + 1, find g(f(x)).
Answer:
g(f(x)) = 6x -9
Step-by-step explanation:
Given f(x) = 3x –5 and g(x) = 2x +1, you want to find g(f(x)).
Function evaluationA function is evaluated by simplifying the result of substituting the argument for the function's variable.
g(f(x)) = 2·f(x) +1 = 2(3x -5) +1 = 6x -10 +1
g(f(x)) = 6x -9
A bee flies at 12 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 18 minutes, and then flies directly back to the hive at 8 feet per second. It is away from the hive for a total of 22 minutes.
write this as an equation
Answer:
Step-by-step explanation:
Givens
Flight speed there = 12 feet / second
Flight speed back = 8 feet / second
Total time = 22 minutes
Time at rest = 18 minutes
Time in flight = 22 - 18 = 4 minutes
Equation
Let the time going to the flowerbed = t
12*t + 8*t + 18 = Distance travelled + time at rest.
Answer
12*t + 8*t + 18 = Distance travelled + time at rest
Use the given information to write an equation of the circle.
center (2,1) , through (6,4)
Using the given information, the equation of the circle with center located at point (2 , 1) and passes through the point (6 , 4) is (x - 2)^2 + (y - 1)^2 = 25
Using the distance formula, get the radius of the circle by solving for the distance between the center (2 , 1) and the point (6 , 4).
radius = distance = √(x2 - x1)^2 + (y2 - y1)^2
radius = √(6 - 2)^2 + (4 - 1)^2
radius= √16 + 9
radius = √25
radius = 5
The standard form of the equation of the 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.
Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (2 , 1)
r = 5
(x - 2)^2 + (y - 1)^2 = 5^2
(x - 2)^2 + (y - 1)^2 = 25
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For each system, choose the method of solving that seems easier to use. Explain why you made each choice. Solve each system.
6x - 3y = 3 , 5x - 5y = 10
By elimination, the solution of the system of equations, 6x - 3y = 3 and 5x - 5y = 10, is (-1 , -3).
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
First, simplify both equations by dividing the first equation by 3 and the second equation by 5.
6x - 3y = 3 ⇒ 2x - y = 1 (equation 1)
5x - 5y = 10 ⇒ x - y = 2 (equation 2)
Use the elimination method since subtracting the two equations will eliminate the variable y.
2x - y = 1 (equation 1)
x - y = 2 (equation 2)
x = -1
x = -1
Substitute the value of x to any of the two equation and solve for y.
6x - 3y = 3 (equation 1)
6(-1) - 3y = 3
-3y = 3 + 6
-3y = 9
y = -3
Hence, the solution of the system of equations is (-1 , -3).
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Evaluate the expression and enter your answer in the box below.
[(5+11) 4]+9. (6-4)
÷
Answer here
Answer:
22 :)
Step-by-step explanation:
I've attached an image to help break down the answer. (credit to cymath.com)
Hope this helps!
Prove or disprove that the product of a nonzero rational number and an irrational number is irrational.
Answer: The claim is true
The proof is below
=====================================================
A = some nonzero rational number
B = some irrational number
Because value A is rational, this means A = p/q where p,q are nonzero integers.
Let's do a proof by contradiction. The claim is that A*B is irrational, but let's do the opposite and assume A*B is rational. We should get to a contradiction somewhere based on this assumption.
If A*B is rational, then A*B = r/s for some integers r and s
Then we can have the following steps
A*B = r/s
(p/q)*B = r/s
B = (r/s)*(q/p)
B = (rq)/(sp)
B = (some integer)/(some other nonzero integer)
B = some rational number
Recall we made B irrational. There's no way to have B rational and irrational at the same time. This is where the contradiction happens. This causes the original assumption of "A*B is rational" to be false. Therefore, the opposite must be the case and A*B has been proven to be irrational.
Therefore, the product of a rational number and an irrational number is irrational.
------------------------
Example:
5 is rational
sqrt(3) is irrational
5*sqrt(3) is irrational
Gio sells gelato and collected sales data for the past few days. gio wants to use the naive method to forecast. calculate the naive forecast for day 6. day 1 2 3 4 5 sales 90 97 92 95 93
The naive forecast for day 6 is 94.
What is a naive forecast?A method of estimation that uses the last period's actuals as the forecast for a current period without making any adjustments or attempting to identify the causes. It is solely used to compare forecasts using more advanced (better) approaches.The calculation of an angle histogram using the naive assumption that the accumulation of points corresponding to the directions of interest will produce peaks that may be seen.There are three fundamental categories: causal models, time series analysis and projection, and qualitative approaches.The main four quantitative budget forecasting techniques—straight line, moving average, simple linear regression, and multiple linear regression—are covered in this article despite the fact that there are many other regularly used quantitative budget forecasting tools.
The naive forecast for the nth period is calculated as follows.
Forecast period Yn=Yn−1
Period Sales Naive Forecasts
1 90 -
2 97 90
3 92 97
4 90 92
5 94 90
6 94
Hence, the naive forecast for day 6 is 94.
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If Y=3x+5 and x=0 what is y
. If AD=26, BF=8, and DF=8, then what is the value of AB?
By using collinearity assumptions and addition and subtraction of line segments, the length of the line segment AB is 26 units.
What is the length of missing line segment?
Let A, B, D, F be points lying on the same line such that A(x) ≤ B(x) ≤ D(x) ≤ F(x), where x is the position of each point on a number line. Then, the value of the length of the line segment AB is:
AB = AD + DF - BF
AB = 26 + 8 - 8
AB = 26
Please notice that B(x) = D(x) as AB = AD.
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What is the solution to the linear equation?
-12+36-1--5-b
O b=-2
O b=-1.5
O b= 1.5
O b=2
Answer:
where is the equal to sign????
A zoo has two elephants, Sally and Joe. Sally weighs 7,645 pounds, and Joe weighs 12,479 pounds. How much do Sally and Joe weigh in all?
As per given data of two elephants, Sally weighs 7,645pounds and Joe weighs 12,479 pounds then total weight of Sally and Joe is equal to 20,124pounds.
As given in the question,
Number of elephants in zoo = 2
Sally weighs = 7,645 pounds
Joe weighs = 12, 479 pounds
Total weight of Sally and Joe is equal to
= ( 7,645 + 12,479 ) pounds
= ( 20,124 ) pounds
Therefore, as per given data of two elephants, Sally weighs 7,645pounds and Joe weighs 12,479 pounds then total weight of Sally and Joe is equal to 20,124pounds.
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Kayla buys candy that costs $7 per pound. She will buy less than 8 pounds of candy. What are the possible amounts she will spend on candy? 
Use c for the amount (in dollars) Kala will spend on candy. Write your answer as in inequality solved for c.
Answer:
[tex]0 \leqslant c \leqslant 56[/tex]
Step-by-step explanation:
Since candy costs $7 per pound, and Kayla will buy less than 8 pounds, she will spend no more than $7 × 8, or $56.
5n+ 1 = 5n -1
Solve for n
Answer:
no solution
Step-by-step explanation:
5n + 1 = 5n - 1 ( subtract 1 from both sides )
5n = 5n - 2 ( subtract 5n from both sides )
0 = - 2 ← not possible
this indicates that the equation has no solution
Determine the slope of the line that contains the given points.
G(-4,3), H(-4,7)
The slope of the line that contains the points G(-4,3), H(-4,7) is not defined.
Slope of a line containing two points (a,b) and (c,d) is denoted by
[tex]slope=\frac{d-b}{c-a}[/tex]
In the given question
The points given are G(-4,3), H(-4,7)
a=-4, b= 3 and c= -4 and d=7
Substituting the values in formula of slope we get
[tex]slope=\frac{d-b}{c-a}[/tex]
[tex]slope=\frac{7-3}{-4-(-4)}\\ \\ =\frac{4}{-4+4} \\ \\ =\frac{4}{0}[/tex]
Since the division of any number by zero is not defined .
Therefore , the slope of the line that contains the points G(-4,3), H(-4,7) is not defined.
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Write 18x²-2/ 3x²-5x - 2} in simplest terms.
F. 18/ 3x+1
G. 2(3 x+1)/x-2
H. 2(3 x-1)/x-2
J. 2(3 x-1)
18/ 3x+1 is 18x²-2/ 3x²-5x - 2} in simplest terms.
What are examples of linear equations?
Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). When attempting to solve systems involving two linear equations, this form is also quite helpful.18 x² - 2 / 3x² - 5x - 2
3x² - 5x - 2 = 3x² - ( 6- 1 ) x - 2 = 0
⇒ 3x² - 6x + x - 2 = 0
⇒ 3x( x - 2 ) + 1 ( x - 2) = 0
⇒ ( 3x + 1 ) ( x - 2 ) = 0
put in equation -
= 18 x² - 2 / ( 3x + 1 ) ( x - 2 )
= 18/ 3x+1
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Write an explicit and a recursive formula for each sequence. 1,1 1/3, 1 2/3, 2, . . . . . .
an=a1+d(n−1) is the explicit and a recursive formula for each sequence .
What is sequence?An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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HELP ASP SHOW UR WORK YOULL GET BRAINLEST
Answer:
X=2
Step-by-step explanation:
Add four to both sides
2x-4=0
2x-4+4=0+4
Add the numbers 2x = 4
2x =4
2x/2 = 4/2
cancel the terms
divide the numbers
= x=2
