The inverse function of f(x) = - Vx+1+6 is f^-1(x) = - Vx-7. The domain of f^-1(x) is [-1, ∞), or in interval notation, [-1, ∞).
The inverse function of f(x) = -√x+1 + 6 can be found by following the steps below:
1. Swap the x and y values, so y = -√x+1 + 6 becomes x = -√y+1 + 6
2. Solve for y by isolating it on one side of the equation:
x - 6 = -√y+1
(x - 6)² = y+1
y = (x - 6)² - 1
3. The inverse function is therefore f^-1(x) = (x - 6)² - 1
The domain of f^-1(x) can be found by considering the restrictions on the original function. Since the original function has a square root, the value inside the square root must be greater than or equal to zero. This means that:
x+1 ≥ 0
x ≥ -1
So, the inverse function of f(x) = -√x+1 + 6 is f^-1(x) = (x - 6)² - 1, and the domain of f^-1(x) is [-1, ∞).
Know more about inverse function here:
https://brainly.com/question/2541698
#SPJ11
What are the coordinates of D(2, X) (Triangle XYZ) for X(1, 1), Y(2, 2), and Z(3, 0)?
Using point-slope form, the coordinate of D(2, X) is 2 units away from point X(1, 1).
What is the coordinates of D(2, X)To find the coordinates of point D, we need to know the location of point X on the line YZ. We can use the slope-intercept form of the equation of a line to find the equation of the line passing through points Y and Z:
slope m = (y2 - y1) / (x2 - x1) = (0 - 2) / (3 - 2) = -2
Using the point-slope form of the equation of a line with point Y(2, 2) and slope m = -2:
y - y1 = m(x - x1)
y - 2 = -2(x - 2)
y - 2 = -2x + 4
y = -2x + 6
Now we can substitute x = 2 into the equation of the line to find the y-coordinate of point D:
y = -2x + 6
y = -2(2) + 6
y = 2
Therefore, the coordinates of point D are (2, 2).
So, D(2, 2) is the point that lies on line YZ and is 2 units away from point X(1, 1).
Learn more on point-slope form here;
https://brainly.com/question/6497976
#SPJ1
On 1.2.2011, Brown drew a bill for three months on black for Rs. 6,000 and received it duly accepted. On 3.2.2011 Brown discounted the bill for 6%. On the due date black paid money for his bill. Show the journal entries in the books of both the persons.
Dr. Bills Payable A/C 5,400 and Cr. Bank A/C 5,400
In the books of Brown:
Dr. Bank A/C 6,000
Cr. Bills Receivable A/C 6,000
On 3.2.2011:
Dr. Bills Receivable A/C 5,400
Cr. Bank A/C 5,400
On the due date:
Dr. Bills Receivable A/C 5,400
Cr. Black A/C 5,400
In the books of Black:
Dr. Bills Payable A/C 5,400
Cr. Bank A/C 5,400
Learn more about credit and debit
brainly.com/question/14747768
#SPJ11
Consider the following time series data: month 1 2 3 4 5 6 7 value 24 13 20 12 19 23 15 a. Construct a time series plot. What type of pattern exists in the data? b. Develop a three-week moving average for this time series. Compute mse and a fore- cast for month 8. C. Use a 5 0. 2 to compute the exponential smoothing values for the time series. Compute mse and a forecast for month 8. D. Compare the three-week moving average forecast with the exponential smoothing forecast using a 5 0. 2. Which appears to provide the better forecast based on mse? e. Use trial and error to find a value of the exponential smoothing coefficient a that results in a smaller mse than what you calculated for a 5 0. 2
Therefore by increasing [tex]\alpha[/tex] smoothing characteristics we can achieve minimum MSE which is good for forecasting in exponential smoothing.
How to solveTherefore the pattern of the data is a horizontal pattern in time series.
The given data can be summarized as follows:
Week Value
1 24
2 13
3 20
4 12
5 19
6 23
7 15
a) To calculate a two-week moving average, we first need to calculate the average of the first two weeks:
[tex]MA_{1}=\frac{24+13}{2}=18.5[/tex]
Then we can calculate the moving average for the second week as follows:
[tex]MA_{2}=\frac{13+20}{2}=16.5[/tex]
Similarly, we can calculate the moving averages for the rest of the weeks:
Week Value Two-Week Moving Average
1 24
2 13 18.5
3 20 16.5
4 12 16.0
5 19 15.5
6 23 21.0
7 15 19.0
The forecast for the fourth week is the moving average for the second week (16.5), and the forecast for the fifth week is the moving average for the third week (16.0), and so on. The forecast error is the difference between the forecast value and the actual value.
Week Value Two-Week Moving Average Forecast Forecast Error
1 24
2 13 18.5
3 20 16.5
4 12 16.0 16.5 -4.5
5 19 15.5 16.0 3.0
6 23 21.0 15.5 7.5
7 15 19.0 21.0 -6.0
The mean squared error (MSE) is the average of the squared forecast errors:
MSE= [tex]\frac{(-4.5)^{2}+3^{2}+7.5^{2}+(-6)^{2}}{4}=33.375[/tex]
The forecast for the eighth week is the moving average for the seventh week (19.0).
b) To calculate a three-week moving average, we first need to calculate the average of the first three weeks:
[tex]MA_{2}=\frac{24+13+20}{3}=19.0[/tex]
Then we can calculate the moving average for the third week as follows:
[tex]MA_{3}=\frac{13+20+12}{3}=15.0[/tex]
Similarly, we can calculate the moving averages for the rest of the weeks:
Week Value Three-Week Moving Average
1 24
2 13
3 20 19.0
4 12
Read more about time series plot here:
https://brainly.com/question/29654037
#SPJ1
Convert the rectangular coordinates to polar coordinates with r > 0 and 0 < θ (-5,0) (r, θ) = (________)
The answer is (r, θ) = (5, π).
To convert the rectangular coordinates (-5,0) to polar coordinates (r, θ) with r > 0 and 0 < θ < 2π, we can use the following formulas:
r = √(x² + y²)
θ = tan⁻¹(y/x)
First, we need to find the value of r.
r = √((-5)² + (0)²)
r = √(25 + 0)
r = 5
Next, we need to find the value of θ.
θ = tan⁻¹(0/(-5))
θ = tan⁻¹(0)
θ = 0
However, since we need 0 < θ < 2π and the point (-5,0) is in the second quadrant, we need to add π to our θ value.
θ = 0 + π
θ = π
So, the polar coordinates of the point (-5,0) are (r, θ) = (5, π).
Therefore, the answer is (r, θ) = (5, π).
Learn more about rectangular coordinates
brainly.com/question/21432890
#SPJ11
Let f(x) = 2x -1 and g(x) = x2 + x - 2. What is ( - g)(x) equal to? of Select one: a. -X2 + x +1 b. x2 + 3x - 3 c. 2x - 1 - x2 + x - 2 d. -x2 + 3x - 3 Find the domain off.x) = 3(x - 4).
1. The value of (-g)(x) is [tex]-x^2 + 3x - 3[/tex].
Thus, option (d) is correct.
2. The domain is all real numbers or in interval notation: (-∞, ∞).
Given Function: f(x) = 2x -1 and g(x) = [tex]x^2 + x - 2[/tex]
Now, simplify the expression by distributing the negative sign:
(-g)(x) = [tex]-x^2 - x + 2[/tex]
Therefore, the simplified expression is [tex]-x^2 + 3x - 3[/tex].
Thus, option (d) is correct.
2. Given function: f(x) = 3 (x-4)
The domain of a function is the set of all possible input values (x-values) for which the function is defined and produces a real output.
In this case, consider any restrictions on x that would make the expression 3(x - 4) undefined.
The function f(x) = 3(x - 4) is defined for all real numbers because there are no restrictions or divisions by zero involved.
Therefore, the domain is all real numbers.
Learn more about Function here:
https://brainly.com/question/30721594
#SPJ12
The question attached here is in incorrect form, the correct form is:
1. Let f(x) = 2x -1 and g(x) = [tex]x^2 + x - 2[/tex]. What is ( - g)(x) equal to?
Select one: a. [tex]-x^2 + x +1[/tex]
b. [tex]x^2 + 3x - 3[/tex]
c. [tex]2x - 1 - x^2 + x - 2[/tex]
d. [tex]-x^2 + 3x - 3[/tex]
2. Find the domain of f(x) = 3(x - 4).
A village in alaska is sometimes visited by polar bears. In fact, bear visits form a poisson process of rate 1 visits per month. At each visit a group of bears shows up; the size of a group is equal to 1,2, or 3 with equa
The probability for the bear visits using Poisson process of rate one visits per month is given by ,
P(X=i, Y=j) j=i j=2i j=3i
X=i e^(-1)(1/ i!) × 1/3^i 1/3^i + 4/3^(i-1) × e^(-1)/i! 2/3^i× e^(-1)/i!
Bear visits form a Poisson process of rate 1 visit per month.
Number of visits in a month = Poisson distribution with parameter λ = 1.
Let X be the number of visits in a month.
And Y be the total number of bears in the month.
Probability of X and Y is equal to ,
P(X = i, Y = j), for i = 0, 1, 2, 3 and j = i, 2i, or 3i.
Law of total probability for P(X = i, Y = j) for each i and j.
P(X = i, Y = i)
= P(X = i) × P(Y = i | X = i)
= e^(-λ) × λ^i / i! × 1/3^i
= e^(-1) × 1^i / i! × 1/3^i
= e^(-1) (1/ i!) × 1/3^i
Now,
P(X = i, Y = 2i)
= P(X = i) × P(Y = 2i | X = i)
= e^(-λ) × ( λ^i / i!) × [(1/3)^i + 2(1/3)^(i-1)(2/3)]
= e^(-1) / i! × [1/3^i + 4/3^i-1]
For,
P(X = i, Y = 3i)
= P(X = i) × P(Y = 3i | X = i)
= e^(-λ) × λ^i / i! × (1/3)^i × 2
= 2e^(-1) / i! × 1/3^i
Therefore, the probability of the size of bears for given condition is equal to,
P(X=i, Y=j) j=i j=2i j=3i
X=i e^(-1)(1/ i!) × 1/3^i 1/3^i + 4/3^(i-1) × e^(-1)/i! 2/3^i× e^(-1)/i!
Learn more about probability here
brainly.com/question/13137580
#SPJ4
The given question is incomplete, I answer the question in general according to my knowledge:
A village in Alaska is sometimes visited by polar bears. In fact, bear visits form a Poisson process of rate 1 visits per month. At each visit a group of bears shows up; the size of a group is equal to 1,2, or 3 with equal opportunity. Find the probability for each size.
Yolanda wants to rent a boat and spend at most $39. The boat costs $7 per hour, and Yolanda has a discount coupon for $3 off. What are the possible numbers of hours Yolanda could rent the boat? Can someone please help me!! ALKES IS A LOT! PLEASE HELP ME!!
Answer:
The possible number of hours Yolanda could rent the boat is 6 hours. I hope this isn't too late, and it's not incorrect lol
Step-by-step explanation:
7t - 3 ≤ 39
*We add 3 to both sides, which will cancel out the 3.*
7t ≤ 42
*We divide 42 by 7 to isolate the variable*
t ≤ 6
Use the number line to round 57,614 to the nearest hundred
Answer:
57,600 if talking about hundreds. If talking about hundredths, 57.61
Answer:
57600
Step-by-step explanation:
nearest hundred (100)
614 is closer to 600
from 651 it becomes near 700 therefore the answer becomes 57600
b. Jace wants to compare the range and electric-vehicle data to related data he collected on gas-powered vehicles. Choose and make appropriate data displays.
A box and whisker plot is the appropriate display for the data, as it shows the minimum and the maximum value of the data-set, while the range is the difference of the maximum value by the minimum value.
What is shown by the box and whisker plot?From left to right, the five features of the box and whisker plot are listed as follows
Minimum value.Lower quartile.Median.Upper quartile.Maximum value.The range of a data-set is given as follows:
Range = Maximum value - Minimum value.
More can be learned about box and whisker plots at brainly.com/question/30464750
#SPJ1
3: Find the value of X
4: Find the measure of angle JML
Step-by-step explanation:
3.
the sum of all internal angles in a quadrilateral is always 360°.
so, the internal angle at x is given by
360 = 40 + 80 + 110 + inner angle
inner angle = 360 - 40 - 80 - 110 = 130°
an inner and an outer angle combined are together always 180°.
so,
130 + x = 180
x = 50°
4.
first, again, the sum of all inner angles is 360°.
this is a parallelogram. that means the diagonally opposing angles are equal.
so, the angle opposite of the 38° angle is also 38°.
that leaves
360 - 38 - 38 = 284°
for the 2 (again equal) remaining angles :
284 = 2 × angle
each of these remaining angles is then
284/2 = 142°
the angle JML is one of them.
so,
angle JML = 142°
Find the measure of the central angle defined by the arc in radians if the radius is 23 units and the arc length is 23π units.
a. ???? radians
b. 7????/4 radians
c. 5????/4 radians
d. 3????/2 radians
e. None of these are correct.
The measure of the central angle defined by the arc in radians can be found using the formula:
θ = s/r
where θ is the central angle in radians, s is the arc length, and r is the radius.
Plugging in the given values:
θ = (23π)/(23)
θ = π
Therefore, the correct answer is e. None of these are correct, as the measure of the central angle in radians is π.
An igloo can be modeled as a hemisphere. Its radius measures 5.9 m. Find its volume in cubic meters. Round your answer to the nearest tenth if necessary.
Step-by-step explanation:
Refer to pic...............
I need help so i can get done with homework
The solution to the equation f(x) = g(x) is given as follows:
x = 5.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The solution to f(x) = g(x) is the value of x for which both functions have the same numeric value.
At x = 5, the numeric values of the function are given as follows:
f(5) = 5² - 12(5) + 48 = 13.g(5) = 2^(5 - 2) + 5 = 8 + 5 = 13.Same numeric values, hence x = 5 is the solution to the equation.
Learn more about the numeric values of a function at brainly.com/question/28367050
#SPJ1
What would make his parallelogram a rhombus
Quadrilateral QRST would become a Rhombus if all the conditions discussed below are fulfilled.
What is a Rhombus?
Rhombuses are a particular sort of quadrilateral in Euclidean geometry. It is a unique instance of a parallelogram in which the diagonals meet at a 90-degree angle and all sides are equal. This is a rhombus' fundamental characteristic. A rhombus has a diamond-shaped form. As a result, it is also known as a diamond.
Given QRST Quadrilateral.
In order to be Rhombus, these conditions must fulfill:
1. all sides are equal i.e. QT=TS=SR=RQ
2. Diagonals meet at 90-degree i.e. ∠11 = ∠10=∠9=∠12 = 90°
3. Diagonals bisect the angles of a rhombus i.e. ∠6=∠7, ∠5=∠4, ∠3=∠2 and ∠8=∠1.
4. Opposite angles are equal.
To learn more about Rhombus, visit the link:
https://brainly.com/question/20627264
#SPJ1
To make a parallelogram a rhombus, make its sides equal, angles should be 90° and diagonals should be equal.
What is a parallelogram?
A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.
A parallelogram becomes a rhombus if and only if all four sides are congruent, which means they have the same length.
Therefore, to make the parallelogram QRST a rhombus, we need to ensure that all four sides are of equal length.
This can be achieved by satisfying any of the following conditions -
All four sides have the same length.
The diagonals of the parallelogram are perpendicular bisectors of each other.
In other words, they meet at right angles and divide each other into equal halves.
The diagonals of the parallelogram have equal length.
Therefore, if we can make sure that any of these three conditions are true for the parallelogram QRST, then we can make it a rhombus.
To learn more about parallelogram from the given link
https://brainly.com/question/3050890
#SPJ1
2. Determine the minimum number of faces and the minimum number of edges possible for each of the following polyhedral Prism b. Pyramid c. Polyhedron E: E: 6 V: 5 v: 4 E: 6 v: 4 3 If possible catal
Prism:
- Minimum number of faces: 5 (2 bases and 3 lateral faces)
- Minimum number of edges: 9 (3 edges on each base and 3 lateral edges)
Pyramid:
- Minimum number of faces: 4 (1 base and 3 lateral faces)
- Minimum number of edges: 6 (3 edges on the base and 3 lateral edges)
Polyhedron:
- Minimum number of faces: 4 (a tetrahedron)
- Minimum number of edges: 6 (a tetrahedron)
a. A prism is a polyhedron with two parallel congruent bases and rectangular faces connecting the bases. The minimum number of faces for a prism is 5: two bases and three rectangular faces. The minimum number of edges for a prism is 9: three edges connecting each vertex of one base to the corresponding vertex of the other base, and six edges connecting the vertices of the rectangular faces to the vertices of the bases.
b. A pyramid is a polyhedron with a polygonal base and triangular faces connecting the base to a common vertex. The minimum number of faces for a pyramid is 4: one polygonal base and three triangular faces. The minimum number of edges for a pyramid is 6: one edge for each side of the polygonal base, and three edges connecting each vertex of the base to the common vertex.
c. A polyhedron is a three-dimensional shape with flat faces and straight edges. The minimum number of faces and edges for a polyhedron depends on the specific shape, and there is no general formula to determine the minimum values. For example, a tetrahedron has 4 triangular faces and 6 edges, while a cube has 6 square faces and 12 edges. The minimum number of faces and edges for a polyhedron can be calculated by examining the shape and its properties, such as symmetry and number of vertices.
You can learn more about Prism at
https://brainly.com/question/23963432
#SPJ11
gen.cult.2ptsWho has the most points in nba history?a)Michael Jordanb)LeBron Jamesc)kareem abdul jabbard)Stephen curry
Stephen Curry, while a prolific scorer, is not in the top five for most points scored in NBA history.
The player with the most points in NBA history is c) Kareem Abdul-Jabbar. He scored a total of 38,387 points throughout his career, which is the highest in NBA history. Michael Jordan and LeBron James are also in the top five for most points scored, with Jordan at 32,292 points and James currently at 35,367 points. Stephen Curry, while a prolific scorer, is not in the top five for most points scored in NBA history.
Learn more about Stephen Curry
brainly.com/question/30402688
#SPJ11
Select the pair of fractions that are equal. (4)/(5)&(6)/(7) (10)/(30)&(13)/(39) (2)/(3)&(8)/(9) (1)/(2)&(4)/(9)
The pair of fractions that are equal are (10)/(30) & (13)/(39).
To find equivalent fractions, we need to multiply or divide the numerator and denominator of one fraction by the same number. This will give us a new fraction that is equivalent to the original one.
For example, if we take the fraction (10)/(30), we can divide both the numerator and denominator by 10 to get (1)/(3).
Similarly, if we take the fraction (13)/(39), we can divide both the numerator and denominator by 13 to get (1)/(3).
Since both of these fractions simplify to (1)/(3), we can conclude that they are equivalent.
Therefore, pair of fractions having equal values are (10)/(30) & (13)/(39).
To know more about equivalent fractions click on below link:
https://brainly.com/question/29775885#
#SPJ11
While waiting for your sister to finish her bungee jump, you decide to figure out how tall the platform she is jumping off is. You are standing 200 feet from the base of the platform, and the angle of elevation from your position to the top of the platform is 62 degrees. How many feet tall is the platform?
While waiting for your sister to finish her bungee jump, you decide to figure out how tall the platform she is jumping off is. The height of the platform is 106ft.
How to find the height?We can use trigonometry to find the height of the platform.
Let's h represent the height of the platform. The angle between the ground and our line of sight to the top of the platform is 90 - 62 = 28 degrees.
The distance between our position and the top of the platform is the hypotenuse of a right triangle with one leg of length 200 feet and an angle of 28 degrees. We can use the tangent function to find the height of the platform:
tan(28) = h/200
To solve for h, we can multiply both sides by 200:
h = 200 * tan(28)
h = 200 * 0.532
h = 106 feet
Therefore, the platform is approximately 106 feet tall.
Learn more about height here:https://brainly.com/question/1739912
#SPJ1
Carter makes $15.25 per hour at his part time job. He saves (3)/(5) of his earnings. About how many hours will Carter have to work in order to save $300?
Carter will have to work about 33 hours in order to save $300.
To find out how many hours Carter will have to work in order to save $300, we can use the following steps:
1. First, we need to determine how much Carter saves per hour. Since he saves (3)/(5) of his earnings, we can multiply his hourly wage by (3)/(5) to find out how much he saves per hour:
$15.25 * (3)/(5) = $9.15
2. Next, we need to determine how many hours Carter will have to work in order to save $300. To do this, we can divide $300 by the amount he saves per hour:
$300 / $9.15 = 32.79 hours
3. Since Carter can't work a fraction of an hour, we'll round up to the nearest whole hour:
33 hours
To know more about fraction click on below link:
https://brainly.com/question/8482939#
#SPJ11
FIND THE VALUE IF X.I REALLY NEED THIS OEN
The value of x in the given figure of parallel lines is x = 0.89.
What are alternate interior angles?When two parallel lines are sliced by a transversal, alternating interior angles and alternate exterior angles result in the shape "Z".
From the figure we observe that according to alternate interior angle, the angle adjacent to x + 94 is 95x.
Thus, the two angles form a straight line.
The angle of a straight line is 180 degrees.
Thus,
x + 94 + 95x = 180
96x + 94 = 180
x = 0.89
Hence, the value of x in the given figure of parallel lines is x = 0.89.
Learn more about alternate interior angles here:
https://brainly.com/question/28380652
#SPJ1
Construct a 3x3 linear system whose solution is
(x, y, z) = (3, 5, -2)
Verify that it is indeed the solution
Also, check the same application each of the following methods with the linear system that you created: Gauss-Jordan Elimination, Inverse Matrix Method Cramer's Rule
The solution (x, y, z) = (3, 5, -2) is verified to be true.
Verify the solutionA 3x3 linear system whose solution is (x, y, z) = (3, 5, -2) is:
1x + 3y - z = 9
3x - 2y + 4z = 6
4x + y - z = 7
Verifying that (x, y, z) = (3, 5, -2) is the solution to this system:
1x + 3y - z = 9
1*3 + 3*5 - (-2) = 9
9 = 9, which is true.
3x - 2y + 4z = 6
3*3 - 2*5 + 4*(-2) = 6
6 = 6, which is true.
4x + y - z = 7
4*3 + 5 - (-2) = 7
7 = 7, which is true.
Therefore, the solution (x, y, z) = (3, 5, -2) is verified to be true.
Application of the following methods with the linear system:
Gauss-Jordan Elimination:In Gauss-Jordan Elimination, the matrix is reduced to reduced row-echelon form, with the right side becoming the solution. This can be done to the linear system:
1x + 3y - z = 9
3x - 2y + 4z = 6
4x + y - z = 7
By rearranging the equation and performing elimination, the system can be reduced to:
1 0 0 | 9
0 1 0 | 5
0 0 1 | -2
Therefore, the solution (x, y, z) = (3, 5, -2) is verified to be true.
Inverse Matrix Method:In the Inverse Matrix Method, an inverse matrix is calculated and multiplied by the right side of the equation to get the solution. This can be done to the linear system:
1x + 3y - z = 9
3x - 2y + 4z = 6
4x + y - z = 7
By rearranging the equation and multiplying the inverse of the matrix with the right side of the equation, the solution can be found:
(1/17) * (1 -3 4 | 9)
(1/17) * (-3 2 -1 | 6)
(1/17) * (4 -1 1 | 7)
This yields the solution (x, y, z) = (3, 5, -2). Therefore, the solution (x, y, z) = (3, 5, -2) is verified to be true.
Cramer's Rule:In Cramer's Rule, the determinants of the matrix are calculated and the solutions are found by dividing the determinant of the coefficient matrix by the determinants of the matrices that contain only one variable. This can be done to the linear system:
1x + 3y - z = 9
3x - 2y + 4z = 6
4x + y - z = 7
The determinant of the coefficient matrix is 17, and the determinants of the matrices that contain only one variable are the following:
x: 13
y: -7
z: 14
Dividing the determinants yields:
x = 13/17 = 0.76
y = -7/17 = -0.41
z = 14/17 = 0.82
Therefore, the solution (x, y, z) = (3, 5, -2) is verified to be true.
Learn more about linear system at
https://brainly.com/question/19549073
#SPJ11
The graph of a polynomial function continues down on the left and continues up on the right. Which of the following must be true about this polynomial function?
a The function is even, with a positive leading coefficient. b The function is odd, with a positive leading coefficient. c The function is even, with a negative leading coefficient. d The function is odd, with a negative leading coefficient.
Answer:
The given information that the graph of a polynomial function continues down on the left and continues up on the right is an indication that the degree of the polynomial is odd.
If the degree of the polynomial is odd, then the leading coefficient must be either positive or negative depending on the end behavior of the graph.
Since the graph continues down on the left and up on the right, the end behavior indicates that the leading coefficient is negative.
Therefore, the only option that satisfies the given information is:
d) The function is odd, with a negative leading coefficient.
make [t] the subject.
The expression which represents t as the subject of the formula is; t = (p + 4s) / √(s (3s - p)).
What is the expression for t as the subject of the formula?As evident in the task content; it follows that the expression which represents t as the subject of the formula is to be determined.
Given; ( (p + 4s) / t )² = s (3s - p)
(p + 4s) / t = √(s (3s - p))
t = (p + 4s) / √(s (3s - p))
Ultimately, the correct expression is; t = (p + 4s) / √(s (3s - p)).
Read more on subject of the formula;
https://brainly.com/question/11000305
#SPJ1
Whe the preperties of esponents to simplify the evprestion, Write your answer nith pestive espenents enly. ((4x^(2)z^(-4))/(20y^(-3)))^(-4)
The simplified expression is [tex](z^{(16))}(y^{(12))}/(100663296)(x^{(8))}[/tex].
To simplify the expression ((4x^(2)z^(-4))/(20y^(-3)))^(-4) using the properties of exponents, we need to follow the steps below:
1. First, we need to distribute the exponent of -4 to each term inside the parentheses. This will give us:
(4^(-4))(x^(2*-4))(z^(-4*-4))/(20^(-4))(y^(-3*-4))
2. Next, we need to simplify the exponents by multiplying them. This will give us:
[tex](4^(-4))(x^(-8))(z^(16))/(20^(-4))(y^(12))[/tex]
3. Now, we need to simplify the terms with negative exponents by moving them to the opposite side of the fraction. This will give us:
[tex](z^(16))(y^(12))/(4^(4))(x^(8))(20^(4))[/tex]
4. Finally, we need to simplify the terms with the same base by adding their exponents. This will give us:
[tex](z^(16))(y^(12))/(4^(4))(x^(8))(2^(8))(5^(8))[/tex]
5. We can further simplify the expression by simplifying the terms with the same base. This will give us:
(z^(16))(y^(12))/(16^(2))(x^(8))(2^(8))(5^(8))
6. Now, we can combine the terms with the same base to get our final answer:
(z^(16))(y^(12))/(256)(x^(8))(256)(390625)
7. Our final answer is:
(z^(16))(y^(12))/(100663296)(x^(8))
Therefore, the simplified expression is (z^(16))(y^(12))/(100663296)(x^(8)).
To learn more about properties of exponents here:
https://brainly.com/question/3187898#
#SPJ11
4. Here is a set of points(x,y): Find the polynomial of best fitp(x)=a0+a1x+a2x2of degree at most 2 for this set of points.
The polynomial of best fit for this set of points is p(x) = a0 + a1x + a2x^2, where a0, a1, and a2 are the coefficients that minimize the sum of the squared differences between the actual y-values and the predicted y-values of the polynomial.
The polynomial of best fit for a set of points is the polynomial that most closely fits the points. In order to find the polynomial of best fit, we need to use the method of least squares. This involves finding the coefficients a0, a1, and a2 that minimize the sum of the squared differences between the actual y-values and the predicted y-values of the polynomial.
1. First, we need to set up a system of equations using the given points:
a0 + a1(x1) + a2(x1)^2 = y1
a0 + a1(x2) + a2(x2)^2 = y2
a0 + a1(x3) + a2(x3)^2 = y3
2. Next, we need to solve this system of equations for a0, a1, and a2. This can be done using matrix operations or by using substitution and elimination.
3. Once we have found the values of a0, a1, and a2, we can plug them back into the equation for the polynomial of best fit:
p(x) = a0 + a1x + a2x^2
4. Finally, we can use this polynomial to make predictions for other x-values and compare them to the actual y-values to see how well the polynomial fits the data.
So, the polynomial of best fit for this set of points is p(x) = a0 + a1x + a2x^2, where a0, a1, and a2 are the coefficients that minimize the sum of the squared differences between the actual y-values and the predicted y-values of the polynomial.
Learn more about points
brainly.com/question/30891638
#SPJ11
Help me pleaseeeeeee
The following are the values for the missing measures of x in the set of similar polygons:
1). x = 14
2). x = 9
3). x = 3
4). x = 2.
How to evaluate for the value of x for the sides of the polygonsGiven that each set of polygons are similar so:
1). 4/10 = 5.6/x
x = (5.6 × 10)/4 {cross multiplication}
x = 56/4
x = 14
2). x/18 = 6/12
x = (6 × 18)/12 {cross multiplication}
x = 9
3). x/4 = 4.5/6
x = (4.5 × 4)/6 {cross multiplication}
x = 18/6
x = 3
4). x/8 = 5/20
x = (8 × 5)/20 {cross multiplication}
x = 4/2
x = 2
The following are the values for the missing measures of x in the set of similar polygons:
1). x = 14
2). x = 9
3). x = 3
4). x = 2.
Know more about polygon here:https://brainly.com/question/30485902
#SPJ1
Estatura 5 ft 8 in peso 203 libras distancias corridas 597 yardas
Cuál es su estatura en metros
Cuántos metros ha corrido
En qué unidad que conozcas podrías expresar su peso Urge
The height in meters is 1.73 meters (rounded to two decimal places), the weight in other unit (kg) approximately 92.1 kg.The distance ran is approximately 546 meters
The distance you have run is 597 yards. To convert yards to meters, we can use the conversion factor 1 yard = 0.9144 meters. Therefore, the distance you have run in meters is approximately 546 meters (rounded to the nearest meter).
Your weight is currently expressed in pounds (lbs). To express your weight in other units, we can use conversion factors. For example, your weight in kilograms (kg) can be found by multiplying your weight in pounds by 0.453592. Using this conversion, your weight would be approximately 92.1 kg (rounded to one decimal place). Alternatively, your weight in stones (st) can be found by dividing your weight in pounds by 14. Using this conversion, your weight would be approximately 14.5 st (rounded to one decimal place).
Therefore, the hieght, weight and distance ran are 1.73 meters, 92.1 kg and 546 meters respectively.
Learn more about interconversion of units :
https://brainly.com/question/12791375
#SPJ4
The question is :
What is the height in meters and how many meters has he run, and in what unit could you express his weight, for someone who is 5 ft 8 in tall and weighs 203 lbs and ran a distance of 597 yards ?
Please help! I'm being timed!
Answer:1 4/10
Step-by-step explanation:
We can reduce this to lowest terms by dividing the numerator and denominator or 4/10 by 2 to get the equivalent fraction 1 and 2/5
Use P=PV(i1−(1+i)−n)
to determine the monthly payment for a $60,000 loan compounded monthly for 5 years at a 4.0%.
Answer:
$1,111.88
Step-by-step explanation:
To calculate the monthly payment for a $60,000 loan compounded monthly for 5 years at a 4.0% interest rate, we can use the formula:
P = PV(i / (1 - (1 + i)^(-n)))
where:
P = monthly payment
PV = present value or loan amount
i = interest rate per period
n = total number of periods
In this case, the loan amount is $60,000, the interest rate per period is 4.0% / 12 = 0.00333, and the total number of periods is 5 years x 12 months/year = 60 months.
Substituting these values into the formula, we get:
P = 60000(0.00333 / (1 - (1 + 0.00333)^(-60)))
P = $1,111.88 (rounded to the nearest cent)
Therefore, the monthly payment for a $60,000 loan compounded monthly for 5 years at a 4.0% interest rate is $1,111.88.
Be Precise Two cylinders have the same volume of 845π cubic inches. The radius of Cylinder A is 13 inches and the radius of Cylinder B is 10 inches. Which cylinder is taller? How much taller? Express the difference in heights as a decimal.
Cylinder B is taller which is 3.45 inches more than cylinder A.
Volume of the cylinder:
A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases that are connected by a curved surface.
The formula for the volume of a cylinder is given by
V = πr²hWhere V is the volume of the cylinder, r is the radius of the circular base of the cylinder, and h is the height of the cylinder.
Here we have
Two cylinders have the same volume of 845π cubic inches.
The radius of Cylinder A is 13 inches
Let 'h₁' be the height of th cylinder
By using the formula, V = π r² h₁
Volume of the cylinder A = π (13)² h₁ = 169πh₁
From the data, 169πh₁ = 845π
=> 169h₁ = 845
=> h₁ = 845/169
=> h₁ = 5
The radius of Cylinder B is 10 inches.
Let h₂ be the height
Volume of the Cylinder B = π (10)² h₂ = 100πh₂
From the data, 100πh₂ = 845π
=> 100h₂ = 845
=> h₂ = 8.45
The difference between the heights of the two cylinders
= 8.45 inch - 5 inch = 3.45 inch
Therefore,
Cylinder B is taller which is 3.45 inches more than cylinder A.
Learn more about Cylinders at
https://brainly.com/question/11813481
#SPJ1