Circle O shown below has a radius of 9 inches. To the nearest tenth of an inch,
determine the length of the arc, x, subtended by an angle of 81°.
9 inches
10=81°
Answer:
[tex]\boxed{12.7\;inches}[/tex]
Step-by-step explanation:
For a circle of radius r, the circumference is given by the expression
C = 2πr
So for this circle of radius 9", the circumference is 2 x π x9 = 18π
The entire circle covers a total angle of 360°
If there is a sector of the circle that is subtended by an angle Ф, then the length of that arc will be Ф/ 360 x C
Here Ф = 81°
So length of arc is
[tex]\dfrac{81}{360} \times 18 \pi\\\\\\\textrm {Using a calculator this works out to }\\\\[/tex]
[tex]\dfrac{81}{360} \times 18 \pi = 12.72345\\\\[/tex]
Rounded to the nearest tenth of an inch this would be
[tex]\boxed{12.7\;inches}[/tex] ANSWER
what is the value of L? 5L-6-7L=8
Answer:
L = -7
Step-by-step explanation:
5L - 6 - 7L = 8
combine like terms
5L - 7L - 6 = 8
-2L - 6 = 8
add 6 to both sides
-2L = 14
divide by -2
L = -7
Artaud noticed that if he takes the opposite of his age and adds 43 he gets the number 27. How old is Artaud?
Step-by-step explanation:
Suppose that his age is x.
then the opposite of his age is -x.
from the question above, the equation can be written as
[tex] - x + 43 = 27[/tex]
[tex]then \: \\ x = 16[/tex]
in figure ab||CD angle AFC=75° and angle BCD=45° find angle FCB, angle EFB and angle CFB
Answer:
30, 75, 105
Step-by-step explanation:
A survey of 481 of your customers shows that 79% of them like the recent changes to the product. Is this percentage a parameter or a statistic and why?Statistic as it represents the populationParameter as it represents the populationParameter as it represents the sampleStatistic as it represents the sample
In this case, the proportion (79%) only applies to the sample of 481 consumers and thus it is a statistic because it represents the sample.
The distinction between a parameter and a statistic is that a parameter refers to a sample property, but a statistic is referred to as a population distribution characteristic.
For instance, a population mean is a parameter, but a sample mean is a statistic.
Although we can use it to draw conclusions about the population, in this case, the proportion (79%) only applies to the sample of 481 consumers and is thus only a statistic.
Therefore, This percentage is a statistic because it represents the sample.
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Suppose $a$ and $b$ are positive integers such that $\gcd(a,b)$ is divisible by exactly $7$ distinct primes and $\mathop{\text{lcm}}[a,b]$ is divisible by exactly $28$ distinct primes. If $a$ has fewer distinct prime factors than $b$, then $a$ has at most how many distinct prime factors
The number of distinct prime factors are 17
The term prime factors in math is defined as a method to find the prime factors of a given number and it can be said a composite number.
As per the definition of prime factor here we have know that a and b have 7 prime factors in common.
Then it can be written as a*b has 28 prime factors
And here we also know that the number of prime factors of a or b that are not common to both is 21
Here we have also know that a has less prime factors than b so at most 10 of these 21 extra prime factors belong to a
Then the the most prime factors that a can have is calculated as
=> 7 + 10 = 17
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An Isosceles triangle and a square have the same perimeter. Find the side lengths of the triangle.
triangle base: 3x
triangle height: 2x+1
square length: 4
Answer: 5, 5, 6
How you get this answer?
Answer:
In isosceles triangle two sides are equal,
So,
3x-1=2x+2
x=3
Perimeter=sum of all sides
=3x-1+2x+2+2x
=7x+1
Substituting value of x
Perimeter=7(3)+1
=21+1
=22
Thus x=3
:. Perimeter of a triangle=22 square units
1. Describe the end-behavior of the polynomial: f(x) = -2x4 - 3x³ +3x-5
A) f(x) → -∞, as x → -∞
f(x) →∞, as x → ∞
B) f(x) → ∞, as x → -∞
f(x) →∞, as x → ∞
C) f(x) →-∞, as x →-∞
f(x) →∞, as x → ∞
D) f(x) →∞, as x →-∞
f(x) →-∞, as x → ∞
5) Use the graph of f shown to find the x-values (if any) at which f is not continuous.
A) 3
B) 2
C) 2,-3
D) 0
E) None of these
The end-behavior of the polynomial is:
A) f(x) → -∞, as x → -∞
f(x) →∞, as x → ∞
What in mathematics is a polynomial?
The only operations used in a polynomial are addition, subtraction, multiplication, and non-negative integer exponentiation. In mathematics, variables are occasionally referred to as indeterminates. An example of a polynomial with a single variable x is x2 4x + 7.
The leading term of the polynomial is -2x⁴, which is negative for negative x and positive for positive x. As x approaches negative infinity, -2x⁴ approaches negative infinity, so the entire polynomial approaches negative infinity. Similarly, as x approaches positive infinity, -2x⁴ approaches positive infinity, so the entire polynomial approaches positive infinity.
Therefore, the end-behavior of the polynomial is:
f(x) → -∞, as x → -∞
f(x) →∞, as x → ∞
E) None of these
The polynomial is continuous for all real values of x. The only way for a polynomial to not be continuous is if there is a hole or a vertical asymptote in its graph. Since the graph of a polynomial is a smooth curve, there are no holes or vertical asymptotes, so the polynomial is continuous for all real values of x.
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Pls help very urgent Write the rule for the linear function. Remember a function rule is written using f(z). 4 2- -2 2 X
Boris runs 7 miles in 50 minutes. At the same rate, how many miles would he run in 75 minutes
Answer: 10.5 miles
Step-by-step explanation:
Find the area enclosed by the curve x=t^2-2t , y = √t and the y axis.
The area enclosed by the curve x = t² - 2t, y = √(t), and the y-axis is 0.754 square units.
First, find the value of t at x = 0
x = t² - 2t
⇒ t² - 2t = 0
⇒ t(t - 2) = 0
Therefore, t = 0, t = 2.
Derivative of area, dA/dy
dA/dy = (0 - x)
dA = (0 - x) × dy
Since the curve has a negative x in this region.
y = √t (given)
dy/dt = (1/2)/√t
dA = [0 - (t² - 2t)] [(1/2)/√t]dt
dA = [2t - t²]/[(1/2)/√t]dt
dA = [[tex]t^{1/2}[/tex] - (1/2)[tex]t^{3/2}[/tex]]dt
Integrating to obtain A,
A = (2/3)[tex]t^{3/2}[/tex] - (1/5)[tex]t^{5/2}[/tex]
Now apply the limits t = 0 to t = 2
Area = [(2/3)[tex]2^{3/2}[/tex] - (1/5)[tex]2^{3/2}[/tex]] - [0]
Area = √[2(4/3 - 4/5)]
Area = √[2(8/15)]
Area = √(16/15)
Area = 0.754
Thus, the area enclosed by the given curves is 0.754 square units.
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(03.06 LC)
Which is the standard equation of the hyperbola centered at the origin, with a vertical transverse axis and values of a = 7 and b = 10?
On solving the the provided question we can say that - in the equation we have 12a - 3b = 84 - 30 = 54
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
here, we have
a = 7 and b = 10
so, 12a - 3b
84 - 30 = 54
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Andre is going to buy a new couch. His current couch is 90 inches long. The new couch he is looking at is 25% less than that. How long is the new couch?
Answer:
Step-by-step explanation:
90 inches
10%=9 inches
5%=4.5 inches
5x5=25
4.5 inches x5=22.5 inches
90-22.5=67.5
the new couch is 67.5 inches long
lim x-> ∞ (sinh(x)/e^x)
Answer: [tex]\lim_{x \to \infty} (\frac{sinh(x)}{e^x})[/tex][tex]= 0[/tex]
Step-by-step explanation:
[tex]\lim_{x \to \infty} (\frac{sinh(x)}{e^x})[/tex]
[tex]\lim_{n \to \infty} \frac{sinh(\infty)}{e^(\infty)}[/tex]
As x approaches infinity, the exponential term e^x becomes much larger than the hyperbolic sine function sinh(x), so the entire expression sinh(x)/e^x becomes very close to zero.
Therefore, the limit of the expression as x approaches infinity is 0:
Forgotten completely how to do this
Would love an explanation too
Answer:
Step-by-step explanation:
I WILL GIVE BRAINLEY TO PERSON WHO ANSWERS!! (Correctly) HELP
Answer:
it's the second
Step-by-step explanation:
i did this before and it was the second one
What are the solutions of 3x² 6x 2 0?
There are two solutions for equation [tex]3x^2-6x+2=0[/tex] are [tex]1+\frac{1}{\sqrt{3}} , 1-\frac{1}{\sqrt{3}}[/tex].
and solutions are irrational solutions.
Every nth degree equation has a total of 'n' real or hypothetical roots. The polynomial [tex]f (x)[/tex] is exactly divisible by ([tex]x -a[/tex] ), which means that ([tex]x -b[/tex] ) is the factor of the provided polynomial [tex]f(x)[/tex].
The theory of equations in algebra refers to the study of algebraic equations, which are equations defined by polynomials. Any expression with one or more terms is considered to be a polynomial. Knowing when an algebraic problem has an algebraic solution was a major challenge in the theory of equations.
Here solution of equation:
[tex]3x^2-6x+2=0\\3x^2-6x+2+1-1=0\\3x^2-6x+3=1\\3(x^2-2x+1)=1\\3(x-1)^2=1\\x=1+\frac{1}{\sqrt{3}} , 1-\frac{1}{\sqrt{3}}[/tex]
So here two solutions are presented for given equation.
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At a market, a pear cost bc and an apple cost 5 ¢ less than a pear. Mrs Ravi bought 5 pears and an apple. (a) (b) Find the total amount in cents Mrs Ravi paid in terms of b. If each pear cost 60 c, how much did Mrs Ravi pay? Leave your answer in cents.
Answer:
$355
Step-by-step explanation:
if each pear is 60c and apples are 5c less...
60×5=300
300+55=355
because 60-5=55
Based on the information below, what are the values of x and y of the solution to the system of equations used to create the information?
?
my guess would be to pick the THIRD ONE
3
x=9.5 y= -2.0
GDP Gross Domestic Product (GDP) is a measure of a country’s wealth. Indonesia had an estimated GDP in 2017 of 1,020,515,000,000. Madagascar had an estimated GDP of 10,372,000,000 in 2017. About how many orders of magnitude as great is Indonesia’s GDP?
The number of Empire State building‑height stacks of dimes required is 589,008.
What is the height of the Empire State building?The height of the Empire States Building including the antenna is 1,454 feet.
here, we have,
The height of a stack of 100 dimes is 5.3 inches.
The value of a stack of 100 dimes is 10 dollars.
The 2017 U.S. gross domestic product (GDP) = 19,390,604,000 dollars.
Number of stacks of dimes needed = $19,390,604,000 / $10 = 1,939,060,400 stacks of 100 dimes
Height of 1,939,060,400 stacks of 100 dimes in feet = 1,939,060,400 x 5.3/12
Height of 1,939,060,400 stacks of 100 dimes in feet = 856,418,343.3 feet
Number of Empire State building‑height stacks of dimes = 856,418,343.3 / 1,454
Number of Empire State building‑height stacks of dimes = 589,008
In conclusion, the number of Empire State building‑height stacks of dimes required is obtained from the height of the Empire State building and the height of a stacks of 100 dimes.
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10.
(15x - 7)
х
37°
11.
Check the picture below.
What is the DIFFERENCE in rates between the 2 people below:
The difference in rates between the 2 peoples is 2.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
John y=5x
For sally we have to find the equation
m=28-14/4-2
m=14/2=7
14=7(2)+b
b=0
So for Sally y=7x
Hence, the difference in rates between the 2 peoples is 2.
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Find the Taylor polynomial T3(x) for the function f centered at the number a.
f(x) = x + e−x, a = 0
T3(x)=?
T3(x) = x - x^2/2 + x^3/6.
The Taylor polynomial of degree 3 for the function f(x) = x + e^-x centered at a = 0 is given by:
T3(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3
= 1 + (-1 + 1)x + (e^-0 - (-1)(-1)e^-0)x^2/2! + (0 + (-1)(-1)(-1)e^-0)x^3/3!
= x - x^2/2 + x^3/6
So T3(x) = x - x^2/2 + x^3/6.
An infinite sum of words that are expressed in terms of a function's derivatives at a single point is known as the Taylor series or Taylor expansion of a function in mathematics.
The nth Taylor polynomial of the function is a polynomial of degree n that is created by the partial sum of the first n + 1 terms of a Taylor series. Approximations of a function made by Taylor polynomials get generally better as n rises. Quantitative estimates of the mistake brought about by the use of such approximations are provided by Taylor's theorem. If a function's Taylor series is converging, its total is the upper bound of the Taylor polynomials' infinite sequence. A function's Taylor series sum may not match.
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A mathematics class is given the following trinomial to factor using the grouping method. 6x2 + 11x - 10 Which of the following students has correctly identified the first step towards factoring this trinomial correctly
The factorise form of the trinomial 6x² + 11x - 10 is (3x - 2)(2x + 5).
How to factorise polynomial?Trinomials is a polynomial that has three terms. Let's factorise the trinomial by grouping as follows:
6x² + 11x - 10
The grouping method can be used to factor polynomials whenever a common factor exists between the groupings.
Hence, let's find the factor of 6x² + 11x - 10
6x² + 11x - 10
let's find two numbers we can multiply to get -60 and add to get 11.
6x² + 15x - 4x - 10
3x(2x + 5) - 2(2x + 5)
Hence,
(3x - 2)(2x + 5)
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What is the measure of angle x?
Answer:
[tex]67^{\circ}[/tex]
Step-by-step explanation:
Angles that form a linear pair add to [tex]180^{\circ}[/tex].
Answer:
Step-by-step explanation:
Since angles x and 113° all lie on a straight line,
x + 113° = 180° (angles on a straight line add up to 180°)
therefore, x = 180°-113°
x = 67°
Subtract 9x+2 from 2x−7
Answer:
(2x-7)(9x+2)
Step-by-step explanation:
Find The Least Common Multiplier of 9x+2, 2x-7
An arcade sells game cards that customers can use to play the arcade games. A game card
comes stocked with credits, and each game costs 5 credits to play. Shivani was able to play
16 games before her card ran out of credits.
Graph the function that models the relationship between the number of games Shivani
played, n, and the number of credits remaining on her card, C(n).
Select points on the graph to plot them.
Answer: The function that models the relationship between the number of games played (n) and the number of credits remaining on the card (C(n)) is C(n) = 5n.
Step-by-step explanation: This function can be derived by realizing that each game costs 5 credits to play, so as the number of games played (n) increases, the number of credits remaining on the card (C(n)) decreases by 5 for each game played.
For example, if Shivani played 16 games before her card ran out of credits, we can substitute n = 16 into the function to find that C(16) = 5(16) = 80 credits. This means that her card had 80 credits on it before she started playing games.
To plot points on the graph, we can select a few different values of n and substitute them into the function to find the corresponding values of C(n). Here are a few examples:
When n = 0, C(n) = 5(0) = 0. This represents the case when Shivani has not played any games yet and has no remaining credits on her card.
When n = 8, C(n) = 5(8) = 40. This represents the case when Shivani has played 8 games and has 40 credits remaining on her card.
When n = 16, C(n) = 5(16) = 80. This represents the case when Shivani has played 16 games and her card has no remaining credits.
We can plot these points on the graph and label them (0,0), (8,40), (16,0) respectively.
Note that the y-intercept is (0,0) and the x-intercept is (16,0)
Graph:
n C(n)
0 0
8 40
16 0
The graph is a straight line starting from (0,0) and going down till (16,0) with a slope of -5.
______ is a set of tools which helps in organizing, presenting information, and extracting meaning fromraw data.
Answer:
Data analytics. Data analytics is a set of tools which helps in organizing, presenting information, and extracting meaning from raw data.
Pls mark me as brainliest :)
(complete solution)
can someone help me here please thank you everyone! lovelots
Answer:
The expression a2+a4+a6+a8+......a20 can be written in sigma notation as:
∑ a(2n) where n = 1 to 10
To expand this summation, we can substitute in the values of n and evaluate the series:
a(21) + a(22) + a(23) + ... + a(210) = a2 + a4 + a6 + ... + a20
The expression (-1) + 2 +(-3) + 4 + (-5) ....+(-25) can be written in sigma notation as:
∑ (-1)^n*n where n = 1 to 25
To expand this summation, we can substitute in the values of n and evaluate the series:
(-1)^11 + (-1)^22 + (-1)^33 + ... + (-1)^2525 = -1 + 2 - 3 + 4 - 5 +... - 25
Note that the series (-1)^n*n is an alternating series, where the signs of the terms alternate between positive and negative. This series has no closed form solution, but we can evaluate them by adding and subtracting each term.
Answer:
[tex]\displaystyle \sum_{n=1}^{10} a_{(2n)}[/tex]
[tex]\displaystyle \sum_{n=1}^{25} n (-1)^{n}[/tex]
Step-by-step explanation:
Part ISigma notation means the sum of the series.
Given series:
a₂ + a₄ + a₆ + a₈ + ... + a₂₀Therefore:
First term is a₂Second term is a₄Third term is a₆So each term is a₂ₙ
Therefore, the expression in sigma notation is:
[tex]\displaystyle \sum_{n=1}^{10}a_{(2n)}[/tex]
Given series:
(-1) + 2 + (-3) + 4 + (-5) + ... + (-25)The absolute value of each term of the series is n.
The signs of each term alternate between negative and positive.
Therefore, the expression in sigma notation is:
[tex]\displaystyle \sum_{n=1}^{25} n (-1)^{n}[/tex]
Part IIThe expansion of each summation has been given in Part I.
However, the full expansions are:
[tex]\displaystyle \sum_{n=1}^{10} a_{(2n)}=a_2+a_4+a_6+a_8+a_{10}+a_{12}+a_{14}+a_{16}+a_{18}+a_{20}[/tex]
[tex]\displaystyle \sum_{n=1}^{25} n (-1)^{n}=(-1)+2+(-3)+4+(-5)+6+(-7)+8+(-9)+10+(-11)+12+\\\phantom{wwwwwwww}(-13)+14+(-15)+16+(-17)+18+(-19)+20+(-21)+22+\\\\\phantom{wwwwwwww}(-23)+24+(-25)[/tex]
Part IIIThe evaluation of each series is:
[tex]\displaystyle \sum_{n=1}^{10} a_{(2n)}=a_2+a_4+a_6+a_8+a_{10}+a_{12}+a_{14}+a_{16}+a_{18}+a_{20}[/tex]
[tex]\displaystyle \sum_{n=1}^{25} n (-1)^{n}=-13[/tex]
can y’all help me pleaseee
Answer:
5. False.
Look at the graph.
Every one day, the cost jumps $30 instead of $60.
Therefore, it is false.
6. True.
Like I said, Every one day, the cost jumps $30.
So when x increases by 1, y increases by 30.
So, y = 30x is correct.
7. False.
Use the equation in the 6th question.
y = 30x.
Put x = 7.
You get y = 210, not 200.
So. it is false.
8. True
Again, same thing.
Use the equation in the 6th question.
y = 30x.
Put x = 9.
You get y = 270.
So the statement is correct.
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