Answer:
Step-by-step explanation:
interchange x and y
y= 1/(x - 2)
x = 1 / (y - 2) Multiply both sides by y - 2
x(y - 2) = 1 Remove the brackets
xy - 2x = 1 Add x to both sides
xy = 1 + 2x Divide by x
y = (1 + 2x)/x
The brackets have been destroyed. The answer is as I've given it.
y = (1/x) + 2
let $p$ be the set of $42^{\text{nd}}$ roots of unity, and let $q$ be the set of $70^{\text{th}}$ roots of unity. what is the smallest positive integer $n$ for which all the elements in $p$ and all the elements in $q$ are $n^{\text{th}}$ roots of unity?
The smallest positive integer \($n$\) for which all the elements i n\($p$\) and all the elements in \($q$\) are \($n^{\text{th}}$\) roots of unity is $70 \cdot 42 = 2940$.
The smallest positive integer \($n$\) for which all the elements in p and all the elements in q are \($n^{\text{th}}$\) roots of unity can be determined by finding the least common multiple (LCM) of the two sets. The set p contains all \($42^{\text{nd}}$\)roots of unity and the set q contains all \($70^{\text{th}}$\) roots of unity. The LCM of 42 and 70 is 2940, so all elements in both sets are \($2940^{\text{th}}$\) roots of unity. This means that 2940 is the smallest positive integer for which all the elements in p and all the elements in q are \($n^{\text{th}}$\) roots of unity.
The LCM of 42 and 70 is found by listing the prime factors of each number and then taking the product of each factor the greatest number of times it occurs in either number.
42 = 2 x 3 x 7
70 = 2 x 5 x 7
LCM = 2 x 3 x 5 x 7 = 420
Learn more about integer here
https://brainly.com/question/15276410
#SPJ4
1. find the interval of convergence for the following series. make sure to also check the endpoints when applicable. a) [infinity]x k=1 kkxk b) [infinity]x k=1 xk k! c) [infinity]x k=1 xk 7k√k
The interval of convergence of [infinity]x k=1 kkxk is [0, 1). The interval of convergence of [infinity]x k=1 xk k! is (-infinity, infinity). The interval of convergence of [infinity]x k=1 kkxk is [-1, 1).
For the series
∑ (k=1 to ∞) k^2 x^k
we can use the ratio test to find the interval of convergence:
lim as k approaches infinity of |(k+1)^2 x^(k+1) / (k^2 x^k)|
= lim as k approaches infinity of |(k+1)x / x| = lim as k approaches infinity of (k+1) = infinity
Therefore, the series diverges for all values of x when x is not zero.
To check the endpoints, we can test x=0 and x=1:
when x=0, the series clearly converges to 0.
when x=1, the series becomes
∑ (k=1 to ∞) k^2
which is a p-series with p=2, so it diverges.
Therefore, the interval of convergence is [0, 1).
For the series
∑ (k=1 to ∞) x^k / k!
we can also use the ratio test:
lim as k approaches infinity of |x^(k+1) / (k+1)!| / |x^k / k!|
= lim as k approaches infinity of |x| / (k+1)
= 0 if |x| < infinity
= infinity if x = infinity
= undefined if x = -infinity
Therefore, the interval of convergence is (-infinity, infinity), which means the series converges for all x.
For the series
∑ (k=1 to ∞) x^k 7k√k
we can use the root test to find the interval of convergence:
lim as k approaches infinity of |x 7√k|^(1/k)
= |x| lim as k approaches infinity of (7√k)^(1/k)
= |x|
Therefore, the series converges when |x| < 1, and diverges when |x| > 1 or x= -1 or x=1.
To check the endpoints, we can test x=-1, x=1, and x=0:
when x=-1, the series becomes
∑ (k=1 to ∞) (-1)^k 7k√k
which does not converge, since the terms do not approach zero.
when x=1, the series becomes
∑ (k=1 to ∞) 7k√k
which also does not converge, since the terms do not approach zero.
when x=0, the series clearly converges to 0.
Therefore, the interval of convergence is [-1, 1).
To know more about interval of convergence:
https://brainly.com/question/30167798
#SPJ4
if the coefficient of determination is .94 what can we say about the relationship between two variable
94% of the total variation of the dependent variable is explained by the independent variable.
Coefficient of determination refers to the ratio showing the percentage of the variation in the model explained by the independent variables used to study the model.
Higher the value of R2, higher the explanatory power of the model.
In the given question, R2 = 0.94, implying 94% of the total variation in the model is explained by the independent variables.
To learn more about coefficient of determination, visit: https://brainly.com/question/28975079
#SPJ4
What is the difference of the polynomials?
(8r6s3 - 9r5s4 + 3r4s5) - (2r4s5 - 5r3s6 - 4r5s4)
8r6s3 - 5r5s4 + r4s5 + 5r3s6
The difference of the polynomials (8r^6s^3 - 9r^5s^4 + 3r^4s^5) - (2r^4s^5 - 5r^3s^6 - 4r^5s^4) simplifies to 8r^6s^3 - 5r^5s^4 + r^4s^5 + 5r^3s^6.
To find the difference of the given polynomials, we subtract the second polynomial from the first polynomial term by term.
(8r^6s^3 - 9r^5s^4 + 3r^4s^5) - (2r^4s^5 - 5r^3s^6 - 4r^5s^4)
Removing the parentheses and combining like terms, we get:
8r^6s^3 - 5r^5s^4 + r^4s^5 + 5r^3s^6
Therefore, the difference of the polynomials is 8r^6s^3 - 5r^5s^4 + r^4s^5 + 5r^3s^6. This is the simplified form of the polynomial expression obtained by subtracting the second polynomial from the first polynomial.
For more information on polynomials visit: brainly.com/question/4976118
#SPJ11
The points T, U, V and W all lie on the same line segment, in that order, such that the ratio of TU:UV:VWTU:UV:VW is equal to 2:5:5.2:5:5. If TW=24,TW=24, find UV.UV.
Answer:
\(UV = 10\)
Step-by-step explanation:
Given
\(TU : UV : VW = 2 : 5 : 5\)
\(TW = 24\)
Required
Determine UV
From the given parameters, we have that:
Ratio of TU = 2
Ratio of UV = 5
Ratio of VW = 5
First, we have to add up the total ratio;
Total = Ratio of TU + Ratio of UV + Ratio of VW
\(Total = 2 + 5 + 5\)
\(Total = 12\)
Next is to calculate the length of UV; as follows;
\(UV = \frac{Ratio\ of\ UV}{Total\ Ratio} * TW\)
Substitute 5 for Ratio of UV; 12 for Total Ratio and 24 for TW
\(UV = \frac{5}{12} * 24\)
\(UV = \frac{5 * 24}{12}\)
\(UV = \frac{120}{12}\)
\(UV = 10\)
Hence; length of UV is 10 units
in general, ______________ are more problematic than ________________ because they can produce spurious relationships.
In general, observational studies are more problematic than randomized controlled trials because they can produce spurious relationships.
Observational studies rely on the natural variation in exposures and outcomes that occur in the population, without any intervention or manipulation by the researcher.
This can lead to confounding variables, which are factors that are associated with both the exposure and the outcome and can produce a false association between them.
Randomized controlled trials, on the other hand, assign participants to different exposure groups at random, which reduces the risk of confounding and allows for a more accurate assessment of causality.
Therefore, researchers must be cautious when interpreting observational studies and consider the potential for spurious relationships.
Learn more about observation at https://brainly.com/question/15700789
#SPJ11
1. The width of a rectangle is x centimeters and its length is (x + 5) cm.
(x + 5)
Diagram not drawn to scale
(a) Write down an expression for the perimeter of the rectangle, giving your
answer in its simplest form.
The perimeter of the rectangle is 62 cm.
(b) Work out the length of the rectangle.
Step-by-step explanation:
perimeter=2(l+b)
check the picture for more clarification
What is the equation of a line in slope- intercept form that passes through the points (-2, 11) and (4, 14).
Answer:
y = (1/2)x + 12
Step-by-step explanation:
(-2, 11), (4, 14)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 14 - 11 3 3 1
m = ------------ = ------------- = ----------- = --------- = -------
x₂ - x₁ 4 - (-2) 4 + 2 6 2
y - y₁ = m(x - x₁)
y - 11 = (1/2)(x - (-2))
y - 11 = (1/2)(x + 2)
y - 11 = (1/2)x + 1
+11 +11
-------------------------------
y = (1/2)x + 12
I hope this helps!
help please RSM problem -need anwser please
Answer:
1/8 + 1/4 = 3/8
Step-by-step explanation:
Quadrilateral A has a side lengths 6, 9, 9, and 12. Quadrilateral B is a scaled copy of Quadrilateral A, with its shortest side of length 2. Draw a sketch of Quadrilateral A or make a chart.
Sides of Quadrilateral A is 6, 9, 9 and 12.
It is given that Quadrilateral B is a scaled copy of Quadrilateral A,
and have shortest side = 2
To find the length of sides of quadrilateral, first we will find the ratio of the shortest side of quadrilateral A to that of quadrilateral B as shown below :
B : A = 2 : 6 = 1 : 3
This shows that the quadrilateral B is 3 times smaller than A.
To learn more about Quadrilateral visit : https://brainly.com/question/21335636
#SPJ9
find the value of k for which the roots of the quadratic equation 5x-10x+k=0 are real and equal
The roots of the given equation is real and equal.
Given , 5\(x^{2} \\\) - 10x+ k=0
The quadratic equation is b² - 4ac = 0
Here, a= 5, b= -10, c= k
substitute in b² - 4ac = 0
(-10)² - 4 * 5* k =0
100 - 20k =0 , let this be equation (1)
100 = 20k
k = \(\frac{100}{20}\)
k = 5.
now, substitute k= 5 in equation (1)
100 -20k = 0
100 - 20*5 = 0
100 - 100 = 0
Therefore, the given equation is real and equal .
The correct question is 5x² - 10x + k =0
To learn more about Quadratic equations : https://brainly.com/question/28440540
PLEASE HELP ASAP
For her phone service, Charmaine pays
a monthly fee of $14, and she pays an
additional $0.05 per minute of use. The
least she has been charged in a month is
$75.20. What are the possible numbers
of minutes she has used her phone in a
month?
How do you find the area of a rhombus without diagonals?
The area of a rhombus can be found by multiplying the length of one of its sides by the height of a perpendicular line from the center to a side.
The height of the rhombus is the distance from the center of the rhombus to one of its sides, perpendicular to that side.
The formula for the area of a rhombus can be written as A = s*h, where A is the area, s is the length of one of the sides of the rhombus, and h is the height of the rhombus.
It's important to note that this method of finding the area of a rhombus without diagonals can only be used when the rhombus is a regular polygon, a polygon with all sides and angles congruent. When the rhombus is not a regular polygon, then you can find the area by using the diagonals.
Additionally, it's important to mention that a rhombus can be defined as a parallelogram with all sides congruent or a square with its angles not 90 degrees.
To know more about area of a rhombus on the link below:
https://brainly.com/question/12783973#
#SPJ11
help me plsss .__. ASAP will give brainliest
If m = 50, what is the value of the expression below?
0.44m + 23
A. 22
B. 45
C. 67
D. 117
SHOW YOUR WORK PLZSSSSSSSS
Answer:
B. is your answer dear
Step-by-step explanation:
0.44*50+23
22+23 = 45
hope you got it.
Find a particular solution to the nonhomogeneous differential equation y'' +4y' 5y = -5x + 5e^-x. y_p =) x+ (e^x)/2-4/5 help (formulas) Find the most general solution to the associated homogeneous differential equation. Use c_1 and c_2 in your answer to denote arbitrary Constants, and enter them as C1 and C2.) y_h = e^(-2x)(c1cos (x)+c2sin (x)) help formulas Find the most general solution to the original nonhomogeneous differential equation. Use c_1 and c_2 in your answer to denote arbitrary constants. y = e^(-2x)(c1cos (x)+C2sin (x)) +x+(e^x)/2-4/5 help (formulas)
The particular solution to the nonhomogeneous differential equation is given by \(yp(x) = x + (e^x)/2 - 4/5\). The most general solution to the associated homogeneous differential equation is \(yh(x) = e^{(-2x)}(c1cos(x) + c2sin(x))\) . Combining the particular solution and the homogeneous solution, the most general solution to the original nonhomogeneous differential equation is \(y(x) = e^{(-2x)}(c1cos(x) + c2sin(x)) + x + (e^x)/2 - 4/5\).
To find the particular solution, we use the method of undetermined coefficients. The particular solution yp(x) contains two parts: a linear term (-5x) and an exponential term \((5e^{-x})\). Since the homogeneous equation has solutions involving exponential functions, we need to use a polynomial of degree one for the linear term and an exponential function for the exponential term. Hence, we choose \(yp(x) = Ax + Be^{-x\) and solve for the coefficients A and B by substituting this solution into the original nonhomogeneous equation. Solving for A and B, we obtain A = 1 and B = 1/2. Thus, \(yp(x) = x + (e^x)/2 - 4/5\).
For the associated homogeneous differential equation, we assume a solution of the form \(yh(x) = e^{(-2x)}(c1cos(x) + c2sin(x))\). By substituting this into the homogeneous equation, we find that it satisfies the equation for any values of c1 and c2. Therefore, \(yh(x) = e^{(-2x)}(c1cos(x) + c2sin(x))\)represents the most general solution to the associated homogeneous equation.
To obtain the most general solution to the original nonhomogeneous equation, we add the particular solution yp(x) to the homogeneous solution yh(x). Hence,\(y(x) = yh(x) + yp(x) = e^{(-2x)}(c1cos(x) + c2sin(x)) + x + (e^x)/2 - 4/5\), where c1 and c2 are arbitrary constants representing the coefficients of the homogeneous solution.
Learn more about differential equation here: https://brainly.com/question/25731911
#SPJ11
Show the calculating process by the restoring-division
algorithm for the following division case:
Divisor 00011
Dividend 1011
The quotient is 1111. The process continues until the result is less than the divisor.
To perform the division using the restoring-division algorithm with the given divisor and dividend, follow these steps:
Step 1: Initialize the dividend and divisor
Divisor: 00011
Dividend: 1011
Step 2: Append zeros to the dividend
Divisor: 00011
Dividend: 101100
Step 3: Determine the initial guess for the quotient
Since the first two bits of the dividend (10) are greater than the divisor (00), we can guess that the quotient bit is 1.
Step 4: Subtract the divisor from the dividend
101100 - 00011 = 101001
Step 5: Determine the next quotient bit
Since the first two bits of the result (1010) are still greater than the divisor (00011), we guess that the next quotient bit is 1.
Step 6: Subtract the divisor from the result
101001 - 00011 = 100110
Step 7: Repeat steps 5 and 6 until the result is less than the divisor
Since the first two bits of the new result (1001) are still greater than the divisor (00011), we guess that the next quotient bit is 1.
100110 - 00011 = 100011
Since the first two bits of the new result (1000) are still greater than the divisor (00011), we guess that the next quotient bit is 1.
100011 - 00011 = 100001
Since the first two bits of the new result (1000) are still greater than the divisor (00011), we guess that the next quotient bit is 1.
100001 - 00011 = 011111
Since the first two bits of the new result (0111) are less than the divisor (00011), we guess that the next quotient bit is 0.
011111 - 00000 = 011111
Step 8: Remove the extra zeros from the result
Result: 1111
Therefore, the quotient is 1111.
Learn more about divisor here
https://brainly.com/question/552761
#SPJ11
students are conducting an experiment to determine if the amount of sunlight affects the size of clover leaves. they plant clover in two identical pots, placing one next to a window and one inside a cupboard. they water each pot daily with 10 ml of water. which is the independent variable?
In the experiment, the independent variable is the amount of sunlight received by the clover plants.
The amount of sunlight the clover plants receive throughout the experiment serves as the independent variable, as it is being manipulated by the experimenters to determine its effect on the size of the clover leaves.
The dependent variable is the size of the clover leaves, which is being measured as a result of the change in the independent variable (amount of sunlight). The water is a controlled variable, as it is kept constant across both conditions to eliminate its effect on the outcome.
To learn more about variable here:
https://brainly.com/question/29521826
#SPJ4
Plz help ;-; I think its B...
Answer:
its C it has 4
Step-by-step explanation:
Answer:
C 4
Step-by-step explanation:
if you want to find the symmetry, you have to divide the total number with 2. So if there 8 petal divide by 2 and there are 4 lines of symmetry
Given: ∠A and ∠B are supplementary angles.
m∠A=4x−16; m∠B=2x+4
Prove: m∠B=68°
Drag and drop reasons into the boxes to correctly complete the proof.Given: ∠A and ∠B are supplementary angles.
m∠A=4x−16; m∠B=2x+4
Prove: m∠B=68°
Drag and drop reasons into the boxes to correctly complete the proof.
Answer:
Step-by-step explanation:
Statements Reasons
∠A and ∠B are supplementary Given
m∠A = (4x - 16), m∠B = (2x + 4) Given
m∠A + m∠B = 180° Definition of supplementary angles
4x - 16 + 2x + 4 = 180° Substitution property of equality
6x - 16 + 4 = 180 Simplify
6x - 12 = 180 Simplify
6x = 192 Addition property of equality
x = 32 Division property of equality
m∠B = 2(32) + 4 Substitution property of equality
m∠B = 64 + 4 Simplify
m∠B = 68° Simplify
for each sequence find the first 4 terms and the 10th term
a)10-n
b)6-2n
a) The first 4 terms of the sequence 10-n are:
- n=1: 10-1=9
- n=2: 10-2=8
- n=3: 10-3=7
- n=4: 10-4=6
The 10th term of the sequence 10-n is:
- n=10: 10-10=0
b) The first 4 terms of the sequence 6-2n are:
- n=1: 6-2(1)=4
- n=2: 6-2(2)=2
- n=3: 6-2(3)=0
- n=4: 6-2(4)=-2
The 10th term of the sequence 6-2n is:
- n=10: 6-2(10)=-14
what is the largest positive integer n for which there is a unique integer k such that 8 15 < n n k < 7 13 ?
the largest positive integer n\(\leq\)112 for which there is a unique integer k
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
Given inequality is
\(\frac{15}{8} < \frac{n+k}{k} < \frac{13}{7}\)
\(\frac{8}{15} < \frac{n}{n+k} < \frac{7}{13}\)
\(n\frac{6}{7} < k < n\frac{7}{8}\)
\(n\frac{7}{8}-n\frac{6}{7}\) > 2
n\(\leq\)112
Hence, the largest positive integer n\(\leq\)112 for which there is a unique integer k
Learn more about inequality here:
brainly.com/question/14098842
#SPJ4
Long division:
(2x² - 5x - 3) ÷ (x - 3)
Answer:
x*(2x-5)÷x - 3
Step-by-step explanation:
==>(2x² - 5x - 3) ÷ (x - 3)
==>x*(2x-5)÷x - 3
==>Done
Suppose we estimate the following regression: yt = β1 + β2x2t +
β3x3t + ut. Suppose the variance of ut is related to a known
variable zt as follows: Var(ut) = σ^2(zt). How would you transform
the
To transform the regression equation, you would divide both sides of the equation by the square root of Var(ut), which is σ√(zt). This transformation helps in obtaining the transformed regression coefficients and standard errors that account for the heteroscedasticity in the error term.
When the variance of the error term (ut) is related to a known variable (zt), it implies the presence of heteroscedasticity in the regression model. Heteroscedasticity means that the variability of the error term is not constant across different levels of the independent variables.
To address this issue, we can transform the regression equation by dividing both sides by the square root of the variance of the error term, which is σ√(zt). This transformation is known as the weighted least squares (WLS) estimation.
By dividing both sides of the equation, we can obtain the transformed regression equation with the error term divided by its standard deviation. This transformation accounts for the heteroscedasticity by giving different weights to the observations based on the variability of the error term. It allows for a more appropriate estimation of the regression coefficients and standard errors, as it gives more weight to observations with smaller error variances and less weight to observations with larger error variances.
To know more about regression equation,
https://brainly.com/question/32690163
#SPJ11
Angle C is inscribed in circle O.
AB is a diameter of circle O.
What is the measure of A?
The measure of <A = 53 degrees
How to determine the measureTo determine the measure of the angle, we need to know the following;
The sum of the interior angles of a triangle is equal to 180 degreesThe diameter of a circle is twice its radiusAngle on a straight line is equal to 180 degreesComplementary angles are pair of angles that sum up to 90 degreesSupplementary angles are pair of angles that sum up to 180 degreesFrom the information given, we have that;
AB is a diameter of circle O.
Bute m<B = 37 degrees
Then, we can say that;
<A + <B + <C = 180
<A + 90 + 37 = 180
collect the like terms, we have;
<A = 53 degrees
Learn more about circles at: https://brainly.com/question/24375372
#SPJ1
Working alone, it takes Kristen 10.2 hours to harvest a field. Kayla can harvest the same field in 16.5 hours. Find how long it would take them if they worked together.
ANSWER:
13.35 hours
EXPLANATION:
Given:
Time Kristen takes to harvest = 10.2 hours
Time Kayla takes to harvest = 16. 5 hours
Let X represent the time it would take them to work together.
Here, to find the time it would take them if they worked together, let's find their mean time, using the formula below:
\(X\text{ = }\frac{Time\text{ taken by kristen + Time taken by Kayla}}{2}\)\(\begin{gathered} X\text{ = }\frac{10.2\text{ + 16.5}}{2} \\ \\ X\text{ = }\frac{26.7}{2} \\ \\ X\text{ = }13.35\text{ hours} \end{gathered}\)It would take them 13.35 hours if they worked together.
Need help with this
“Use the law of Cosines to find the missing side length. Set up and SHOW YOUR WORK”
1: 38km
2:48km
3:41km
4:46km
Answer:
law of cosines states c^2=a^2+b^2-2abc
b^2=26^2+24^2-2(26×24)cos 134°
b^2=676+576-1248cos134°
cos134= -0.6946
b^2=1252-12(-0.6946)
12×(-0.6946)= -8.3352
b^2=1252-(-8.3352)
b^2=1252+8.3352
b^2=1260.33
b=√1260.33
b=35.50
7. The length of a rectangular swimming pool is 28 feet and the perimete
is 84 feet. What is the area of the swimming pool? *
The area is 364 because the perimeter is 84 feet, the sides are 28 times two witch it 56 and 84-56 is 26 so the other sides are 13 and 13 times 28 is 364
5. 37°. If maN = (13x)° what is the value of x and the maN?
The value of x is approximately 2.8462° and the value of maN is 37°.
To find the value of x and maN, we need to use the given information. According to the question, maN is equal to (13x)°.
To solve for x, we can set up an equation:
maN = (13x)°
Now, since we know that maN is equal to 37°, we can substitute this value into the equation:
37° = (13x)°
To isolate x, we divide both sides of the equation by 13:
37° / 13 = (13x)° / 13
This simplifies to:
2.8462° ≈ x°
Therefore, the value of x is approximately 2.8462°.
Now, let's find the value of maN. We already know that maN is equal to (13x)°. Substituting the value of x that we just found, we get:
maN = (13 * 2.8462)°
Simplifying the multiplication:
maN = 37°
So, the value of maN is 37°.
For more such questions on approximately
https://brainly.com/question/28521601
#SPJ8
Please help!
Will mark brainliest!!
Answer:
Let m = Number of months
Company A: 60+ 42.95 m
Company B: 25+49.95 m
60+ 42.95 m= 25+49.95 m
Subtract 42.95 from both sides
60 = 25 + 7m
Subtract 25 from both sides
35= 7m
Divide both sides by 7
m = 5
OAmalOHopeO