please help ∠a is opposite

When a circle with the equation  (x - 1)² + (y - k)² = 50 travels through the location (2,3), the possible values of k are -4 and 10.

A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Additionally, it is rotationally symmetric about the center at every angle. Every pair of points in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally symmetric about the center at every angle.

given

The equation of a circle is (x - 1)² + (y - k)² = 50

The equation of the circle passes through the point (2, 3) = (x, y).

Now,

(2 - 1)² + (3 - k)² = 50

1 + (3 - k)² = 50

(3 - k)² = 50 - 1

3 - k = √49

3 - k = ±7

Now,

3 - k = 7

3 - 7 = k

k = -4

3 - k = -7

3 + 7 = k

k = 10

When a circle with the equation  (x - 1)² + (y - k)² = 50 travels through the location (2,3), the possible values of k are -4 and 10.

To know more about circle visit:

https://brainly.com/question/29142813

#SPJ1

Answer:

90

Step-by-step explanation:

[tex]\frac{gray}{color}[/tex] = [tex]\frac{gray}{color}[/tex]

[tex]\frac{9}{2}[/tex] = [tex]\frac{x}{20}[/tex]

If you multiply 2 x 10 = 20 ,so

9 x 10 = 90

The required number is rounded off as 18.3 is 18.29 and 18.299.

Given that,

To determine the two different numbers that when rounded to the nearest tenth with give you 18.3.

What do rounding values mean?

The rounding of values is the replacement of a number with an approximate value that has a more transient, straightforward, or direct expression.

When a number is rounded to the closest tenth, the result is 18.3, which implies that there must be a number greater than 5 in each position following the tenth position after the decimal place.

Thus, 18.29 and 18.299 are the numbers.

The required number is then rounded off to 18.3, which is 18.29 and 18.299, respectively.

Learn more about round the decimal here;

brainly.com/question/867784

#SPJ4

The two congruent base angles' measurements ∠D = 14.36 and

∠E = ∠F = 82.9

A triangle with two sides that have the same length is said to be isosceles. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.

As per the data given in the above question are as bellow,

As seen in the picture below, we have D, E, and F as well as sides D, E, and F.

We determine the angle D using the cosine rule.

[tex]d^2=e^2+f^2-2(e)(f) \cos (D) \\3^2=12^2+12^2-2(12)(12) \cos (D)[/tex]

9=144+144-288 cos(D)

9=288-(288 cos(D))

9-288= -288 cos(D)

-279 = -288 cos (D)

-279/288 = cos (D)

[tex]D=\cos ^{-1}\left(\frac{279}{288}\right)[/tex]

D=14.26

Triangle DEF is an isosceles triangle, allowing us to calculate E and F using the triangle's angles.

180°-14.36 = 165.64°, rounded to 1 dp;

165.64°2=82.9°

We now get

D = 14.36,

E = 8, and F = 82.9.

For such more question on isosceles triangle.

https://brainly.com/question/11884412

#SPJ4

Note: The missing diagram is as bellow.

The smallest angle, angle E, measures is 82 degrees.

Given that DE = DF = 12 and FE = 3, we can see that DE and DF are equal, which means that angles D and F are congruent.

Additionally, EF is the unequal side, so angle E will be the smallest angle in the triangle.

To find the angle measures, we can use the Law of Cosines, which states that in a triangle with sides a, b, and c and opposite angles A, B, and C, the following equation holds:

c²= a² + b² - 2abcos(C)

we know that DE = DF = 12, and EF = 3.

We can set up the equation for angle E:

12²= 12² + 3² - 2 × 12 × 3×cos(E)

Simplifying the equation:

144 = 144 + 9 - 72 × cos(E)

144 = 153 - 72 ×cos(E)

72 × cos(E) = 9

cos(E) = 9 / 72

cos(E) = 1 / 8

To find the measure of angle E, we need to take the inverse cosine (arccos) of 1/8:

E = arccos(1/8)

E = 82.77 degrees (rounded to the nearest degree)

Since the triangle is isosceles, angles D and F are congruent. T

Therefore, each of the base angles (angles D and F) will measure:

D = F = (180 - E) / 2

D = F = (180 - 82) / 2

D = F =98 degrees

To learn more on Triangles click:

https://brainly.com/question/2773823

#SPJ6

The solution for the equation is,

1. x = 2 and y = 1

2. no solution,

3. y = 0 and x = 11

4. x = 4/3 and y = 10/3

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

Given sets of equations,

1. x - y = 1

x + y = 3

add both the equations we get,

x - y + x + y = 1 + 3

2x = 4 (+y and -y eliminated)

x = 4/2 = 2

substitute value of  x

x + y = 3

2 + y = 3

y = 3 - 2 = 1

x = 2 and y = 1

2.  x + y = 1

x + y = 11

the equation has no solution because In this case, the two lines representing the equations are parallel to each other.

3. x + 4y = 11

x - 6y = 11

since both equations have the common constant for x we can subtract the equations,

x + 4y -(x - 6y) = 11 - 11

4y + 6y = 0

y = 0 and x = 11

4. -3x + 3y = 6

6x + 3y = 18

subtract equation 1 from 2

6x + 3y -(-3x + 3y) = 18 - 6

6x - 3y + 3x - 3y = 12

9x = 12

x = 12/9 = 4/3

substitute value of x

-3x + 3y = 6

-3(4/3) + 3y = 6

-4 + 3y = 6

y = 10/3

Hence the solution is 1. x = 2 and y = 1

2. no solution,

3. y = 0 and x = 11

4. x = 4/3 and y = 10/3.

Learn more about linear equation;

https://brainly.com/question/29739212

#SPJ1

Theories X, Y, and Z describe very different attitudes toward motivation in the workplace. Managers tend to follow one of these approaches in their everyday struggle to motivate their teams.

So what are Theories X and Z?

According to Theory X, managers must give orders and maintain a tight eye on every employee. This is an authoritarian style of management. The personnel are unmotivated and dislike their jobs, as is to be expected. This notion holds that managers should believe that their staff members are naturally lazy and will take any opportunity to avoid working. Consequently, it is believed that your employees need to be continuously monitored and that extensive control mechanisms need to be implemented. A hierarchical structure is required for this to be managed effectively, with a small span of control at each level.

The freedom to perform at the workplace is likely to motivate people more, and Theory Z is a combination of activities that ensure a healthy blend of systems. To fully achieve this blend of behaviors, technology is typically included in your HR systems. The motivation at work Theory Y is built upon by Theory Z. Here, the emphasis is on making sure that your business has a solid set of values, offers a long-term strategy for training and development, and employs a highly participative management style.

To learn more about Management Theories, visit: https://brainly.com/question/13187309

#SPJ4

The Maclaurin series of f is  [tex]& \left|x^4 \cdot \frac{1}{1+\frac{1}{n}}\right|[/tex]. The radius of convergence R is 1.

Recollect that, the Maclaurin series for ln(1+x) is,

[tex]$$\ln (1+x)=x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+\ldots=\sum_{n=1}^{\infty} \frac{(-1)^{n+1} x^n}{n}$$[/tex]

Replace x by [tex]$x^4$[/tex] to get, the Maclaurin series for [tex]$\ln \left(1+x^4\right)$[/tex],

[tex]$$\begin{aligned}\ln \left(1+x^4\right) & =x^4-\frac{\left(x^4\right)^2}{2}+\frac{\left(x^4\right)^3}{3}-\frac{\left(x^4\right)^4}{4}+\ldots \\& =x^4-\frac{x^8}{2}+\frac{x^{12}}{3}-\frac{x^{16}}{4}+\ldots \\& =\sum_{n=1}^{\infty} \frac{(-1)^{n+1} x^{4 n}}{n}\end{aligned}$$[/tex]

Find the Radius of Convergence by Ratio Test.

A series is convergent (or converges) if the sequence. of its partial sums tends to a limit; that means that, when adding one after the other in the order given by the indices, one gets partial sums that become closer and closer to a given number.

Let [tex]$a_n=\frac{(-1)^{n+1} x^{4 n}}{n}$ $\left|\frac{a_{n+1}}{a_n}\right|=\left|\frac{(-1)^{n+2} x^{4 n+4}}{n+1} \cdot \frac{n}{(-1)^{n+1} x^{4 n}}\right|$[/tex]

[tex]$$\begin{aligned}& =\left|x^4 \cdot \frac{n}{n+1}\right| \\& =\left|x^4 \cdot \frac{1}{1+\frac{1}{n}}\right|\end{aligned}$$[/tex]

[tex]$$\begin{aligned}\lim _{n \rightarrow \infty}\left|\frac{a_{n+1}}{a_n}\right| & =\lim _{n \rightarrow \infty}\left|x^4 \cdot \frac{1}{1+\frac{1}{n}}\right| \\& =\left|x^4 \cdot \frac{1}{1+0}\right| \\& =\left|x^4\right|\end{aligned}$$[/tex]

By Ratio Test, the given series convergence if [tex]$\left|x^4\right| < 1$[/tex], that is, [tex]$|x| < 1$[/tex].

Thus, the radius of convergence is R=1.

Therefore, the radius of convergence R is 1.

For more such questions on series convergence

https://brainly.com/question/15415793

#SPJ4

The formula to find the distance between the two points is [tex]d=√((x2 – x1)² + (y2 – y1)²)[/tex] therefore the length of the line IJ would be: 29.

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²).  This formula is used to find the distance between any two points on a coordinate plane or x-y plane.

Given I = -16 and J = 13

∴ intercepts of I are (x1,y1)=(-16,0)  and intercepts of J are (x2,y2)=(13,0)

To calculate length of IJ :

Using distance formula:

IJ =

[tex]\sqrt{(x2-x1)^2+ (y2-y1)^2} \\\\\sqrt{[13-(-16)^2+0} \\\\\sqrt{29^2}[/tex]

∴ IJ = 29

To know more about distance formula, check out:

brainly.com/question/661229

#SPJ1

The data set that could be represented by the box plot would be = 32,36,27,30,35,39,28,34. That is option D.

The box plot is defined as the type of data representation that is used in descriptive statistics to show the distribution of numerical data such as the number of hours Judy takes to complete a quilt.

The characteristics of the box plot is that is shows the outliers, the median, and the mode of the given numerical data.

Therefore, the data set that could be represented by the box plot would be = 32,36,27,30,35,39,28,34.

Learn more about median here:

https://brainly.com/question/26177250

#SPJ1

No, the given pair of coordinates as required to be assessed is not a solution to the equation; y = x.

It follows from the task content that the verdict which is true about whether the given pair of coordinates ( -3, 1 ) is a solution to the equation; y = x.

Since the given equation is; y = x and the given pair of coordinates is; ( -3, 1 ).

Recalling that it follows from convention that coordinate pairs are written as; ( x, y ).

On this note, for the given pair of coordinates; ( -3, 1 ), it follows that; x = -3 and y = 1.

Therefore, by substitution; since; 1 ≠ -3, it follows that the given pair of coordinates is not a solution for the equation.

Read more on solution pairs of an equation;

https://brainly.com/question/20884066

#SPJ1

Answer:

its 87 feet per second

Step-by-step explanation:

The value of the expression x²-2(x-y)-z³ is 24.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given;

Expression x²-2(x-y)-z³

To find the value of the expression:

If x = -3, y=4 and z = -1.

Substituting the values to the expression,

x²-2(x-y)-z³

= (-3)²-2(-3-4)-(-1)³

= 9 + 14 - (-1)

= 9+14+1

= 24

Therefore, 24 is the value of the expression.

To learn more about the expression;

brainly.com/question/24242989  

#SPJ1

∫ 8 0 f ( x ) d x if f ( x ) = { 6 if x < 6 x if x ≥ 6 is ∫ 8 0 f ( x ) d x = 12.

∫ 8 0 f ( x ) d x = ∫ 8 0 { 6 if x < 6 x if x ≥ 6 } d x

= ∫ 6 0 6 d x + ∫ 8 6 x d x

= (6x)|6 0 + (1/2)x²|8 6

= (6*6) - (1/2)(8² - 6²)

= 36 - (1/2)(48)

= 36 - 24

= 12

Sure, the expression ∫ 8 0 f ( x ) d x is an integral, which represents the area under the curve of a function f(x) over a specific interval. The notation ∫b a f(x)dx means the definite integral of function f(x) from a to b.

Integration is a fundamental concept in calculus that deals with the problem of finding a function that represents the total amount of some changing quantity. The process of integration is the reverse of differentiation, which is the process of finding the rate of change of a function. An integral, the result of integration, is a mathematical object represented by a symbol such as ∫ (integral sign) and can be computed using various techniques such as substitution, integration by parts and partial fractions. The most common use of integration is in finding the area under a curve, which is known as definite integral, but integration can also be used to solve a wide range of problems in physics, engineering, and other fields.

Learn more about Integral Expression here:

https://brainly.com/question/27286394?referrer=searchResults

#SPJ4

If f(x) is an even function, then the function that also must be even is given as follows:

f(x) + 3.

Regarding translations, we have that:

This is because the translation up or down changes the values of the function, while the translation left or right changes the position of the function, and to verify if the function is even or odd we look at the position.

The only translation that is only up or down in this problem is given as follows:

f(x) + 3.

Meaning that it is the function that is also even, and thus the second statement is the correct statement.

The options are given as follows:

More can be learned about even functions at https://brainly.com/question/23934926

#SPJ1

A. SAS Inequality Theorem , theorem can be used to prove triangle congruence, as congruent sides and angles can be used to determine the length of the third side, thereby proving congruence.

The SAS Inequality Theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the third side of the triangle must be greater in the triangle with the larger included angle.

The SAS Inequality Theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the third side of the triangle must be greater in the triangle with the larger included angle. This theorem is important to remember when comparing similar triangles, as it can help determine which triangle has the greater side length. This theorem can also be used to determine if a triangle is acute or obtuse, as the greater included angle will lead to the longer side being on the opposite side of the triangle. Additionally, this theorem can be used to prove triangle congruence, as congruent sides and angles can be used to determine the length of the third side, thereby proving congruence.

Learn more about triangle here

https://brainly.com/question/2773823

#SPJ4

Therefore , the solution of the given problem of triangle comes out to be x= 5/8  .

An triangle is a polygon since it has four or more parts. It is a simple geometric shape. A square having angles A, B, and C is referred to as a triangle ABC. When the sides are not collinear, Euclidean geometry generates a single plane and square. If a triangle has three sides and three corners, it is a polygon. The corners of a triangle are where its three sides meet. The sum of the angles in a triangle is 180 degrees.

Here,

Given : Similar triangle,

To find the value of x

thus ,We get

=> 3x +  5x + 12 = 6 +11

=> 8x + 12 = 17

=> 8x = 17-12

=> 8x =5

=> x =5/8

Therefore , the solution of the given problem of triangle comes out to be

x= 5/8  .

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

Answer:

answer in order from top to bottom

2

6

9

9

0

Step-by-step explanation:

that's the answer

this the the correct answer

if the answer is correct please report me as a brainalist

Step-by-step explanation:

Joe miles per hour is 141/3=47 and the same time Amy is 102/2 =51

The numbers that cannot be probabilities are: square root of 2, -53, 5/3, and 1.31.

Probability is a measure of the likelihood of a particular event occurring in a random experiment. It is a value between 0 and 1, with 0 indicating that an event is impossible, and 1 indicating that an event is certain to occur.

In statistics, probability is used to make predictions or draw inferences about a population based on a sample of data. For example, if we were to flip a coin, the probability of getting heads is 0.5, or 50%. In general probability can be defined as the ratio of the number of favorable outcomes to the total number of possible outcomes, which is the mathematical framework behind the random experiments.

From the set of numbers, 0, 0.08, and 3/5 are all possible values of probability.

Therefore, square root of 2, -53, 5/3, and 1.31 cannot be probabilities.

Learn more about probability here: https://brainly.com/question/24756209

#SPJ4

Answer:

im no sure but here you go :) unit rate = 0.05738

Step-by-step explanation:

On solving the provided question, we cans ay that the coordinates are (-5,4) (-2,-4) (5,-1) => y2 - y2 = m(x2 - x1) => m = 1/3

A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is represented by the second number. like in (12.5), when there are 12 units below and 5 above.

here,

the coordinates are

(-5,4) (-2,-4) (5,-1)

y2 - y2 = m(x2 - x1)

1-2 = m(5-2)

1 = m3

m = 1/3

To know more about coordinates  visit:

https://brainly.com/question/27749090

#SPJ1

The solution is Option A.

The output value for the function f when x = -1 and the function f ( -1 ) is given by the equation f ( -1 ) = -5

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

f ( x ) = 2x - 3   be equation (1)

On simplifying the equation , we get

when x = -1

Substitute the value of x as -1 in the equation , we get

f ( x ) = 2x - 3

f ( - 1 ) = 2 ( -1 ) - 3

f ( - 1 ) = - 2 - 3

f ( - 1 ) = -5

Therefore , the value of f ( -1 ) is -5

Hence , the function f ( x ) when x = -1 is -5

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

The amount of fruit juice and ginger ale she can use in the region comes between x + y = 32 and x ≥ 20, and the graph is attached below.

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. It is most frequently used to compare the sizes of two numbers on the number line.

Given:

Kathy is mixing fruit punch in a 32-punch bowl for a party, she plans to add at least 20 cups of fruit juice to the bowl before adding ginger ale,

Write the equation for the given phrase as shown below,

Assume x is the number of fruit juice cups, and y is the ginger ale, then,

x ≥ 20

x + y = 32

Plot the line as shown below,

Coordinates can be given as (0, 32) and (32, 0) mark the coordinates and join the line,

Thus, the region between x + y = 32 and x ≥ 20 represents the amount of fruit juice and ginger ale.

To know more about inequality:

https://brainly.com/question/2038369

#SPJ1

Answer:

A) $3720

Step-by-step explanation:

The picture tells us that employers bring 6.2% of the contribution.

Divide 6.2 by 100 to see what will we have to multiply the 100% number (60,000) by to get out answer and you get 0.062.

Now, multiply 60,000 by 0.062 and you get $3720.

Answer:

  A.  $3720

Step-by-step explanation:

You want to know the employer's contribution to the Social Security tax on a salary of $60,000 per year. The employer's Social Security tax rate is given as 6.2%.

The amount of tax is found by multiplying the tax rate by the quantity being taxed. Here, the employer's social security tax rate is 6.2% of an employee's salary. The salary is given as $60,000, so the amount of tax the employer pays is ...

  6.2% × $60,000 = $3720

The employer contributes $3720 in Social Security tax on a salary of $60,000.

__

Additional comment

Taken together with the Medicare tax, the employer pays the US government a total of 15.3% of the employee's salary. The employer is allowed to deduct half that from the salary paid to the employee, so the employee sees a combined tax of 7.65%. The other 7.65% is an additional cost to the employer of hiring the employee.

This question is only asking about the employer's share of the Social Security tax, so the applicable tax rate is 6.2%.

The average rate of change over the interval from x = 2 to x = 4 is 2.

The average rate of change for a function over an interval is the slope of the secant line that connects the two points on the graph. The average rate of change can be found by using the formula:

Average Rate of Change = (y2 - y1) / (x2 - x1)

For the given function, the average rate of change over the interval from x = 2 to x = 4 can be found by substituting the appropriate values into the formula:

Average Rate of Change = (f(4) - f(2)) / (4 - 2)

Substituting the function values, we get:

Average Rate of Change = (6 - 2) / (4 - 2)

Simplifying, we get:

Average Rate of Change = 4 / 2

Therefore, the average rate of change over the interval from x = 2 to x = 4 is 2.

Learn more about Average Rate of Change here:

https://brainly.com/question/28744270

#SPJ4

On solving the provided question, we can say that value of tan(a) in right triangle ABC = sin(A)/cos(A) = B/P

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here,

we have a right triangle ABC

angle B = 90

so,

value of tan(a) = sin(A)/cos(A) = B/P

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

Answer:

Step-by-step explanation:

b = 4h + 3A = .5 * b * h = 11Substitute b in terms of h from the first equation into the second equation and solve for h:.5 * b * h = 11.5 * (4h + 3) * h = 11(4h + 3) * h = 224h2 + 3h = 224h2 + 3h - 22 = 0(4h + 11) (h - 2) = 0h = -11/4 OR h = 2Reject the negative answer since a length cannot be negative=> h = 2Plug h value into the first equation to solve for b:b = 4h + 3 = 4(2) + 3 = 11base = b = 11height = h = 2 (that’s what I got if it doesn’t then sorry)

The AB segment is the line connecting the midpoints of two sides of a triangle. To find it, first locate the midpoints of two sides of the triangle. Then draw a straight line between the two midpoints to form the AB segment.

The AB segment is an important line in a triangle. It is found by connecting the midpoints of two sides of the triangle. To locate the midpoints, first identify the two sides of the triangle. Then measure the length of each side and divide by two. Mark the midpoints of each side, and then connect them with a straight line. This forms the AB segment. It is important to note that the AB segment does not bisect the triangle, but instead, it is the line connecting the midpoints of two sides of the triangle. The AB segment is used to determine certain properties of the triangle, such as its area and perimeter.

Learn more about triangle here

https://brainly.com/question/2773823

#SPJ4

The process of finding the Segment AB is explained below.

The term segment in math is defined as line segment is bounded by two distinct points on a line or here we can say a line segment is part of the line that connects two points.

Here we have to find the way to identify the AB segment.

Here as we all know that Line segment that is named as AB is bound between two fixed points.

According to this case, here we have the line segment is bound between the fixed points A and B as follows:

Therefore the line segment AB starts from point A and ends at point B.

To know more about Line segment here.

https://brainly.com/question/30072605

#SPJ4

The correct option that will make the inequality expression 6 > -6/h + 11 true is when h is equal to 1.

We shall try all the values of h to know the one to make the inequality expression true as follows;

for h = 2;

6 > -6/2 + 11

6 > -3 + 11

6 > 8 is false.

for h = 6;

6 > -6/6 + 11

6 > -1 + 11

6 > 10 is false.

for h = 1;

6 > -6/1 + 11

6 > -6 + 11

6 > 5 is true.

for h = 3;

6 > -6/3 + 11

6 > -2 + 11

6 > 9 is false.

Therefore, the value for h that makes the inequality expression 6 > -6/2 + 11 true is 1.

Know more about inequality here:https://brainly.com/question/18881247

#SPJ1