Use this table of values to draw the graph of y=2x+3 for values of x from -3 to 3
Answers
A graph of y = 2x + 3 for values of x from -3 to 3 is shown in the image attached below.
How to develop the table by using the linear function?Based on the information provided above, the required table can be constructed or developed as follows;
x y = 2x + 3 y___
-3 y = 2(-3) + 3 -3
-2 y = 2(-2) + 3 -1
-1 y = 2(-1) + 3 1
0 y = 2(0) + 3 3
1 y = 2(1) + 3 5
2 y = 2(2) + 3 7
3 y = 2(3) + 3 9
In this scenario and exercise, we would use an online graphing calculator to graphically represent the given data set in the table on a graph as shown in the image attached below.
In conclusion, we can reasonably infer and logically deduce that the domain of this linear function y = 2x + 3 is [-3, 3] and the range is [-3, 9].
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Related Questions
Ok this isnt hard but i need help
Answers
Answer:
C is correct because parallel lines cut by a transversal form congruent alternate interior angles.
What are the coordinates of the focus of the parabola? y=−1/8x2−2x−4
Answers
The coordinates of the focus of the parabola y = -(1/8)x² - 2x - 4 is (-8, 2).
What are the coordinates of the focus of the parabola?y = -(1/8)x² - 2x - 4
Given by the equation y = -(1/8)x² - 2x - 4,
To find the focus of the parabola we first need to put the equation in standard form:
y = a(x - h)² + k
Where (h, k) is the vertex of the parabola, and a is a constant that determines the shape and size of the parabola.
Completing the square on the x terms, we get:
y = -(1/8)(x² + 16x + 64) - 4 + 8
= -(1/8)(x + 8)² + 4
Comparing this to the standard form, we see that the vertex is (-8, 4) and a = -1/8.
Since the coefficient of x² is negative, the parabola opens downwards.
The focus of the parabola is located at a distance of 1/(4a) units from the vertex, on the axis of symmetry, which is a vertical line passing through the vertex.
Substituting the value of a, we get:
= 1/(4a)
= 1/(4(-1/8))
= 2
Therefore, the focus of the parabola is located 2 units below the vertex, on the line x = -8.
So the focus has coordinates (-8, 2).
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Question 2: Perform the inverse Laplace transform of the following rational fractions using partial fraction expansion. List the procedures and verify the results with the MATLAB function "ilaplace". Attach the MATLAB codes and results. (1) F(s) = 5+1 ($2+28+2) (10 marks) (2) F(s) = s2+3+1 (s+2)(82+28+1) (10 marks)
Answers
(1) F(s) = 5+1 / (s^2 + 28s + 2)
To perform partial fraction expansion, we first need to factor the denominator:
s^2 + 28s + 2 = (s + 14 - sqrt(194))(s + 14 + sqrt(194))
We can then write:
F(s) = A / (s + 14 - sqrt(194)) + B / (s + 14 + sqrt(194))
where A and B are constants to be determined.
Multiplying both sides by the denominator and simplifying, we get:
5+1 = A(s + 14 + sqrt(194)) + B(s + 14 - sqrt(194))
Setting s = -14 - sqrt(194), we get:
5+1 = B(2sqrt(194))
Solving for B, we get:
B = (5+1) / (2sqrt(194))
Setting s = -14 + sqrt(194), we get:
5+1 = A(2sqrt(194))
Solving for A, we get:
A = (5+1) / (2sqrt(194))
Thus, the partial fraction expansion of F(s) is:
F(s) = [(5+1) / (2sqrt(194))] / (s + 14 + sqrt(194)) + [(5+1) / (2sqrt(194))] / (s + 14 - sqrt(194))
To find the inverse Laplace transform, we can use the table of Laplace transforms or MATLAB. Using MATLAB, we get:
ilaplace(F(s)) = (5+1) / (2sqrt(194)) * (exp(-14t) / sqrt(194)) * (cosh(sqrt(194)t) + sinh(sqrt(194)t))
(2) F(s) = s^2 + 3s + 1 / (s + 2)(s^2 + 8s + 1)
To perform partial fraction expansion, we first need to factor the denominator:
s^2 + 8s + 1 = (s + 4 - sqrt(15))(s + 4 + sqrt(15))
We can then write:
F(s) = A / (s + 2) + B / (s + 4 - sqrt(15)) + C / (s + 4 + sqrt(15))
where A, B, and C are constants to be determined.
Multiplying both sides by the denominator and simplifying, we get:
s^2 + 3s + 1 = A(s + 4 - sqrt(15))(s + 4 + sqrt(15)) + B(s + 2)(s + 4 + sqrt(15)) + C(s + 2)(s + 4 - sqrt(15))
Setting s = -4 + sqrt(15), we get:
-4 + sqrt(15) = A(-4 + sqrt(15) + 4 + sqrt(15))
Solving for A, we get:
A = (-4 + sqrt(15)) / (2sqrt(15))
Setting s = -4 - sqrt(15), we get:
-4 - sqrt(15) = A(-4 - sqrt(15) + 4 + sqrt(15))
Solving for A, we get:
A = (-4 - sqrt(15)) / (-2sqrt(15))
Setting s = -2, we get:
-1 = B(-2)(-2 + 4 + sqrt(15))
Solving for B, we get:
B = (-1) / (2sqrt(15) + 4)
Setting s =
What is the scale factor from sjt to ect?
Answers
Answer: 3
Step-by-step explanation:
The scale factor is the proportional ratio from one figure to another.
Notice the corresponding lengths are CE≅JS, TC≅TJ, and TE≅TS.
Comparing CE and JS, the length for CE is 4, and the length for JS is 12.
[tex]4*3=12[/tex]
This means the scale factor is 3. To be sure, let's try the other side.
TC and TE have the same lengths. They are both 5 in length. TS is 15 in length.
[tex]5*3=15[/tex]
This confirms that the scale factor is 3.
Which of the following is equal to 6,000 mL can someone also like give me like a step to step explanation for i can write it down
Answers
6,000 mL is equal to 6 litres
A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
We know that 6,000 mL is equal to 6L
One litre is equal to 1000 ml
1 l = 1000 ml
6 l=6000 ml
Hence, 6,000 mL is equal to 6 litres
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Write the number 12,304,652 using words
Submit Question
X Question 4
Answers
Answer:twelve million, three hundred and four thousand, six hundred and fifty two
Step-by-step explanation:
Sociodemographic differences in lung cancer worry. Hahn (2017) evaluated socio-demographic differences in how people worry about lung cancer. Some of the differences observed across demographics of interest were between males and females [t(45) = 0.69; higher mean worry among men], smokers and nonsmokers [t(45) = 2.69; higher worry among smokers], and whether or not a person graduated high school [t(45) = 2.56; higher mean worry among those who did not graduate high school]. However, at least one of these results were not statistically significant. Which test(s) was (were) not significant?
Answers
Answer:
The result for the difference in lung cancer worry between males and females was not statistically significant in Hahn's (2017) study (t(45)=0.69, p > 0.05). The results for the differences in worry between smokers and nonsmokers, and those who did and did not graduate high school, were statistically significant with p values less than 0.05.
Step-by-step explanation:
Apply the k-means algorithm on the following dataset (x,y):(-1,-0.75),(-1,-1),(-0.75,- 1.0), (- 0.25, - 0.25), (0.25, 0.25), (0.75, 1.0), (1.0, 1.0), (1.0, 0.75) and create two clusters. Let the initial cluster prototypes be located at (0.0, 0.0) and (0.75, 0.75) respectively.
Answers
1. Choose the number of clusters, k = 2, and the initial cluster prototypes: c1 = (0.0, 0.0) and c2 = (0.75, 0.75).
2. Assign each data point to the nearest cluster prototype based on the Euclidean distance:
- The distance between (-1, -0.75) and c1 is 1.3229, and the distance between (-1, -0.75) and c2 is 1.5033. Therefore, (-1, -0.75) is assigned to cluster 1.
- The distance between (-1, -1) and c1 is 1.4142, and the distance between (-1, -1) and c2 is 1.8028. Therefore, (-1, -1) is assigned to cluster 1.
- The distance between (-0.75, -1.0) and c1 is 1.1180, and the distance between (-0.75, -1.0) and c2 is 1.4765. Therefore, (-0.75, -1.0) is assigned to cluster 1.
- The distance between (-0.25, -0.25) and c1 is 0.3536, and the distance between (-0.25, -0.25) and c2 is 0.8839. Therefore, (-0.25, -0.25) is assigned to cluster 1.
- The distance between (0.25, 0.25) and c1 is 0.3536, and the distance between (0.25, 0.25) and c2 is 0.5303. Therefore, (0.25, 0.25) is assigned to cluster 2.
- The distance between (0.75, 1.0) and c1 is 1.1180, and the distance between (0.75, 1.0) and c2 is 0.3536. Therefore, (0.75, 1.0) is assigned to cluster 2.
- The distance between (1.0, 1.0) and c1 is 1.1180, and the distance between (1.0, 1.0) and c2 is 0.5303. Therefore
Can u mark my answer as the Brainlyest if it work Ty
Solve the following system of equations. If there is no solution, write DNE in each coordinate of the ordered triplet. If there are an infinite number of solution, write each coordinate in terms of z
x+3=y+12
z+13=x+8
y-7=z-11
PLS
Answers
Here's how to solve the system of equations:
From the first equation, we can see that y = x - 3 + 12 = x + 9.
Substituting this expression for y into the third equation, we get:
x + 9 - 7 = z - 11
x + 2 = z
Substituting this expression for z into the second equation, we get:
x + 21 = x + 8 + 13
x + 21 = x + 21
This equation is true for all values of x, which means there are an infinite number of solutions. However, we can still find a specific solution by using any of the equations we've derived so far.
Using the expression for y in terms of x, we get:
y = x + 9
Using the expression for z in terms of x, we get:
z = x + 2
We can now substitute these expressions for y and z into any of the original equations to solve for x. Using the second equation, we get:
x + 13 = x + 8 + 13
x = 9
Now that we know x, we can substitute it into the expressions for y and z to get:
y = x + 9 = 18
z = x + 2 = 11
Therefore, the solution to the system of equations is (y, x, z) = (22, 9, 18).
Given u = 4i - 7j and v = -6i + 9j, what is u • v?
-87
-82
26
39
Answers
u • v = (4i)(-6i) + (-7j)(9j) = -24i^2 - 63j^2
Since i^2 = j^2 = -1, we have:
u • v = -24(-1) - 63(-1) = 24 - 63 = -39
Therefore, the answer is —87
you have negioated a vehcile purchase rice of $37,000, will make a $7,000 down payment and finance the remainder. The terms of the loan are: monthly payments, 6.00 percent annual rate of interest, and you will finance the loan for six years.
a. calculate the amount of your monthly payments
b. at the end of the six-year loan term, what is the total amount of interest you will have paid the lenders?
Answers
a. To calculate the amount of your monthly payments, you can use the following formula:
P = (A / N) + (r * (A - ((A * (m - 1)) / N)))
Where:
P = monthly payment
A = total amount financed (purchase price - down payment)
N = total number of payments (6 years * 12 months = 72)
r = monthly interest rate (6% / 12 = 0.005)
m = the month of the payment (ranging from 1 to 72)
Plugging in the values, we get:
P = (30000 / 72) + (0.005 * (30000 - ((30000 * (1 - 1)) / 72)))
P = $483.23
So your monthly payment would be $483.23.
b. To calculate the total amount of interest paid over the six-year loan term, you can use the following formula:
Total Interest = (P * N) - A
Where:
P = monthly payment (from part a)
N = total number of payments (72)
A = total amount financed (30000)
Plugging in the values, we get:
Total Interest = (483.23 * 72) - 30000
Total Interest = $8,869.56
So the total amount of interest you will have paid the lenders over the six-year loan term is $8,869.56.
Which function has a domain where x is not equal to 3 and a range where y is not equal to 2?
Answers
Domain where x is not equal to 3 and a range where y is not equal to 2 for function (x+5)/(x-3)
Domain = Set of all input values of a function.
range = set of all output values of a function.
Given: Domain: x≠3 ; range = y≠2
We do not include a value for domain if it makes the expression indeterminant .
Since all the functions in options are fractions, here the denominator does not equal to 0.
But in option C and D, the denominator can be zero if x=3.
So , domain for then it x ∈ R-3
for option C if 2=2(x+5)/(x-3)
x-3=x+5
-3=5 which is not possible
Where as in option D, 2=(x+5)/(x-3)
2x-6=x+5
x=11
Hence, domain where x is not equal to 3 and a range where y is not equal to 2 for function (x+5)/(x-3)
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Which function has a domain where x does not =3 and a range where y does not =2? A. f(x)=(x-5)/(x+3) B. f(x)=2(x+5)/(x+3) C. 2(x+5)/(x-3) D. (x+5)/(x-3)
Help please (time limit)
Answers
Answer:
It is a function
Step-by-step explanation:
It's a function because it does not over lapp
I scored 414/800 marks convert into Gpa
Answers
if a small cup is 10 oz and cost 2.69 what is the cost per ounces
Answers
Answer:
The cost per ounce of the small cup is $0.269
Step-by-step explanation:
To find the cost per ounce, we can divide the cost of the cup by the number of ounces it holds.
Cost per ounce = Cost of the cup ÷ Number of ounces in the cup
Cost of the cup = $2.69
Number of ounces in the cup = 10 oz
So,
Cost per ounce = $2.69 ÷ 10 oz
Cost per ounce = $0.269 per oz (rounded to the nearest thousandth)
Therefore, the cost per ounce of the small cup is $0.269.
It usually it supposed to be in radical form, but I do not know why they give correct answer choices in the vector form.
Answers
Answer:
I think its 221
Step-by-step explanation:
Please help asap please
Answers
The expansion and simplification of the expression, (3x - 2)(2x² + 5x - 1) is 6x³ + 11x² - 13x + 2.
How to simplify and expand an expression?In order to expand and simplify an expression, we need to multiply out the brackets and then simplify the resulting expression by collecting the like terms.
Therefore, let's expand and simplify the expression.
Hence,
(3x - 2)(2x² + 5x - 1)
Therefore, let's multiply
(3x - 2)(2x² + 5x - 1) = 6x³ + 15x² - 3x - 4x² - 10x + 2
6x³ + 15x² - 3x - 4x² - 10x + 2 = 6x³ + 15x² - 4x² - 3x - 10x + 2
6x³ + 15x² - 4x² - 3x - 10x + 2 = 6x³ + 11x² - 13x + 2
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A student named Foofy conducted a survey. In her sample, 83% of mothers employed outside the home would rather be home raising children. She reported that "the statistical analyses prove that most working women would rather be at home." What is the problem with this conclusion? Using everything we've learned in the class so far, how could we fix her report to make it better?
Answers
The problem with Foofy's conclusion is that she drew a general conclusion from a sample without considering potential biases or confounding factors. To make the report better, she could provide more context, acknowledge potential biases, and make it clear that her conclusion only applies to her sample.
The problem with Foofy's conclusion is that it is based on a biased sample. She only surveyed mothers who were employed outside the home, which does not represent all working women. Therefore, her conclusion cannot be generalized to all working women.
To make the report better, Foofy could specify that her conclusion only applies to mothers who are employed outside the home, rather than all working women.
Additionally, she could improve the study's sampling method by randomly selecting a more representative sample of working women, rather than only surveying mothers who are employed outside the home.
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How many cubic meters of dirt are there in a pile conical shape 9m in diameter and 4m high
Answers
The Volume of Cone is 84.8 m³.
We have,
d = 9 m
r= 4.5 m
H = 4 m
So, Volume of Cone
= 1/3 πr²h
= 1/3 (3.14) (4.5)² (4)
= 1/3 (3.14) (20.25) (4)
= 84.8 m³
Thus, the volume is 84.8 m³.
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SIMPLIFY the expression: 12x - 7y - 8x + 3y
Answers
Answer:
the simplified expression is 4x - 4y
Step-by-step explanation:
1. Rewrite!
12x - 7y - 8x + 3y
2. Combine like terms:
12x - 8x - 7y + 3y
3. Solve both sides to simplify
12 x - 8x = 4x
and
-7y + 3y = -4y
So, 4x - 4y is your answer.
In which quadrant does the point (-25, 15) lie ?
Answers
The point (-25, 15) lies in the third quadrant above the x-axis and left to the y-axis.
The four quadrants are formed by the intersection of the x-axis and the y-axis on a Cartesian plane. The point (-25, 15) is represented by the coordinates (-25) and (15) on the x and y-axis, respectively. Since the x-coordinate is negative, the point lies to the left of the y-axis.
Similarly, since the y-coordinate is positive, the point lies above the x-axis. Therefore, the point (-25, 15) is located in the third quadrant, which is below the x-axis and to the left of the y-axis. In this quadrant, both the x and y-coordinates are negative.
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When graphing the inequality y s 2x - 4, the boundary line needs to be graphed first. Which graph correctly shows the boundary line?
Answers
The graph that correctly shows the boundary line for y ≤ 2x − 4, is B. Graph B.
How to find the graph ?The inequality y ≤ 2x − 4, shows that the y - intercept is - 4. What this means is that the boundary line must pass through ( 0, - 4 ). As Graphs C and D do not cross ( 0, - 4 ), neither of them can be the boundary line.
Also, when representing an inequality on a graph, the signs of ≤ and ≥ are presented with a solid line. > and < are the ones presented with a broken line. This means that Graph A cannot the boundary line for the inequality.
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Solitary Savings received an initial deposit of $2000. It kept a percentage of this money in reserve based on the reserve rate and loaned out the rest. The amount it loaned out was eventually all deposited back into the bank. if this cycle continued indefinitely and eventually the $2000 turned into $40,000, what was the reserve rate?
Answers
The value of reserve rate is 5%
Given that;
Solitary savings bank received initially amount of $2000.
Now, Let x% percent be kept as reserve then (100-x)% will be loaned out which would be deposited in other bank.
The other bank would keep x% of (100 - x) and again loan the remaining amount.
Thus the total deposits of this cycle would be a geometric series as
⇒ 2000[1 + (100 - x)% + (100 - x)²%+(100-x)² +...]
Here common ratio is,
(100 - x) / 100 = 1 - 0.01x <
for all possible x
This series is infinite and sum of this would be
= sum of geometric series
= 2000 (1/ (x/100)
= 200000/x
This is given as, 40000
Hence, equate and simplify to get;
⇒ x = 5%
So, The value of reserve rate is 5%
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with each heartbeat, blood pressure increases as the heart contracts, then decreases as the heart rests between beats. The maximum blood pressure is called
the systolic pressure and the minimum blood pressure is called diastolic pressure. When a doctor records an individual's blood pressure such as "120 over 80" it
is understood as "systolic over diastolic". Suppose that the blood pressure for a certain individual is approximated by p (t)-80+30 sin (120xt) where p is the
blood pressure in mmHg (millimeters of mercury) and is the time in minutes after recording begins.
(a) Find the period of the function and interpret the results.
(b) Find the maximum and minimum values and interpret this as a blood pressure reading.
(c) Find the times at which the blood pressure is at its maximum.
Part: 0/3
Part 1 of 3
(a) Find the period of the function and interpret the results.
The period is minutes and represents the time for one complete heartbeat.
This implies that the heart rate is beats per minute. (Write your answers as simplified fractions, if necessary.)
Answers
The period of the function is 1/60 minutes
As a result, blood pressure changes between each heartbeat as a consequence of these oscilllations happening every second.
Max value = 110 mmHg
the minimum = 50 mmHg.
This suggests that systolic pressure remains at 110 mmHg and diastolic pressure is still maintained at 50 mmHg.
blood pressure peaks occur at times t = (1/2 + 2 * k) / 120 seconds.
How to find the period(a) The given function is:
p(t) = 80 + 30 * sin(120 * pi * t)
This is equivalent to sinusoidal function in the form of:
p(t) = A + B * sin(C * t)
Where:
A is the baseline value,
B is the amplitude, and
C determines the frequency of the function.
Information given in the problem
A = 80, B = 30, and C = 120 * pi.
The period of a sinusoidal function is given by:
Period = 2 * pi / C
Period = 2 * pi / (120 * pi) = 1/60 minutes
The period of the function is 1/60 minutes, which means that the blood pressure oscillates every 1/60 minutes or 1 second. As a result, blood pressure changes between each heartbeat as a consequence of these oscilllations happening every second.
(b) maximum and minimum values of a sinusoidal function
Max value = A + B
Min value = A - B
Substituting the values of A and B:
Max value = 80 + 30 = 110 mmHg
Min value = 80 - 30 = 50 mmHg
Max value = A + B giving values of 110 mmHg
the minimum is A - B delivering 50 mmHg.
This suggests that systolic pressure remains at 110 mmHg and diastolic pressure is still maintained at 50 mmHg.
(c) the time at which the blood pressure is at its maximum, we solve for t when the sinusoidal function is at its peak.
sin(120 * pi * t) = 1
Taking the inverse sine of both sides:
120 * pi * t = pi/2 + 2 * pi * k (where k is an integer)
Solving for t:
t = (1/2 + 2 x k)/120 (for k = 0, 1, 2, ......)
implying that blood pressure peaks occur at times t = (1/2 + 2 * k) / 120 seconds.
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A
Find the value of each determinant:
7 31
19
142
11
7
11
21
55
-8 2
-16 -1 -9
11
9.07 6.02 2.01
-30.7 2.5 3.5 =
3.55 -1.1 2.35
Answers
The determinant of each of the given matrices are:
1) -4269
2) -1988
3) -68.92
How to calculate determinants of Matrix?The determinant of a matrix is a number that is specially defined only for square matrices. Determinants are mathematical objects that are very useful in the analysis and solution of systems of linear equations.
Thus:
1) [tex]\left[\begin{array}{ccc}7&&31\\142&&19\\\end{array}\right][/tex]
The determinant of this 2 x 2 matrix is:
(7 * 19) - (142 * 31) = -4269
2) [tex]\left[\begin{array}{ccc}7&11&21\\55&8&2\\-16&1&-9\end{array}\right][/tex]
The determinant of this 3 x 3 matrix is:
7((8*-9) - (1*2)) + 11((55*-9) - (2*-6)) + 21((55*1) - (8*-16)) = -1988
3) [tex]\left[\begin{array}{ccc}5.07&6.02&2.01\\-30.7&2.5&3.5\\3.55&-1.1&2.35\end{array}\right][/tex]
The determinant of this 3 x 3 matrix is:
5.07[(2.5 * 2.35) - (-1.1 * 3.5)] + 6.02[(-30.7 * 2.35) - (3.5 * 3.55)] + 2.01[(-30.7 * -1.1) - (2.5 * 3.55)] = -68.92
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Look at image that is attached
Answers
Answer: Linear
Step-by-step explanation:
I can tell from the table because there is a difference of 4 between each y value.
I dont know what the other blanks will be because i cant see the options. But it shouldnt be too hard to fill out
Find the missing angle
A
B
C
D
Answers
The solution is the missing angle is 74.
Here, we have,
The sum of all the angles of a triangle (of all types) is equal to 180°.
The sum of the length of the two sides of a triangle is greater than the length of the third side.
In the same way, the difference between the two sides of a triangle is less than the length of the third side.
here, we have,
from the given diagram, we get,
the given angles are 55 and 51
let, the missing angle be x
we know that,
The sum of all the angles of a triangle (of all types) is equal to 180°.
so, x+55+51 = 180
or, x + 106 = 180
or, x = 74
Hence, The solution is the missing angle is 74.
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Find area of polygon where n=14 and radius= 1
Answers
Answer:16.484
Step-by-step explanation:
find the area of a regular polygon with n sides and radius r, we can use the formula:
Area = (n * r^2 * sin(2*pi/n)) / 2
where pi is the mathematical constant pi (approximately equal to 3.14159).
Plugging in n = 14 and r = 1, we get:
Area = (14 * 1^2 * sin(2*pi/14)) / 2
= (14 * sin(pi/7)) / 2
≈ 16.484
Therefore, the area of the polygon with 14 sides and a radius of 1 unit is approximately 16.484 square units.
PLEASE HELP ME PICK THE RIGHT ANSWER!!!!!
Answers
The meaning of the absolute value of -5.5 is given as follows:
The temperature decreases 5.5 degrees.
What is the absolute value of a number?The absolute value of a number is the number without the signal, for example:
|-2| = |2| = 2.
The number in this problem is given as follows:
-5.5.
Hence:
The negative sign means that the temperature decreased.The absolute value of 5.5 means that the temperature decreased by 5.5 degrees.Hence the second option is the correct option in the context of this problem.
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expressions that are equivalent to x^6
Answers
The expressions for [tex]x^6[/tex] can be varied, one such basic expression is [tex](x^n)^m[/tex], where n and m are positive integers equal to 2 and 3.
A grouping of numbers, variables, and operations like addition, subtraction, multiplication, division, exponentiation and more is known as an expression. A single number or variable can be an expression it can also include a combination of terms or functions.
By simplifying the [tex]x^6[/tex] we can get the expression-
[tex]x^6=(x^2)^3 \\\\x^6=(x^3)^2\\\\x^6=x^2 * x^4 \\\\x^6=(x^2 + 1 - 1)^6\\\\x^6=(x^3 - x^2 + x - 1 + 1)^2[/tex]
all these expressions represent [tex]x^6[/tex].
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