What is the equation of a circle with radius 4 and center (0,8)? А (x-8)2 + y2 = 4 B x2 + (y+8)2 = 16 C + С x2 + (y-8)2 = 16 D x2 + (y-8)2 = 4

Answer:

\(\angle N\cong \angle Z\)

Step-by-step explanation:

Given:

In ΔLMN and ΔXYZ, \(MN=3\,,\,LN=2\,,\,YZ=9\,,\,XZ=6\)

To find: criteria that needs to be shown to prove ΔLMN \(\sim\) ΔXYZ using SAS similarity theorem

Solution:

According to SAS Similarity Theorem, if two sides in one triangle are proportional to two sides in another triangle and the included angle between the sides are congruent, then the two triangles are said to be similar.

In ΔLMN and ΔXYZ,

\(\frac{LN}{XZ}=\frac{2}{6}=\frac{1}{3}\\\frac{MN}{YZ}=\frac{3}{9}=\frac{1}{3}\\\therefore \frac{LN}{XZ}=\frac{MN}{YZ}\)

So, ΔLMN \(\sim\) ΔXYZ by SAS similarity theorem if \(\angle N\cong \angle Z\)

For both triangles to be proven to be similar by the SAS similarity theorem, the additional information needed to be shown is a pair of congruent included angles, which is: a. ∠N ≅ ∠Z

The SAS Similarity Theorem states that two triangles are similar to each other if they have two pairs of corresponding sides that are proportional to each other and a pair included angles that are congruent.

△LMN and △XYZ have:

two pairs of corresponding sides that are proportional (YZ/MN = XZ/LN = 3)

Therefore, for both triangles to be proven to be similar by the SAS similarity theorem, the additional information needed to be shown is a pair of congruent included angles, which is: a. ∠N ≅ ∠Z

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If you're just factorizing, you can do so by grouping.

cot³(x) + cot²(x) + cot(x) + 1

= cot²(x) (cot(x) + 1) + cot(x) + 1

= (cot²(x) + 1) (cot(x) + 1)

Put another way, if y = cot(x) + 1, then

cot²(x) y + y = (cot²(x) + 1) y

We can simplify this somewhat. Recall the Pythagorean identity,

sin²(x) + cos²(x) = 1

Dividing through both sides of the equation by sin²(x) reveals another form of the identity,

sin²(x)/sin²(x) + cos²(x)/sin²(x) = 1/sin²(x)

1 + cot²(x) = csc²(x)

Then we end up with

cot³(x) + cot²(x) + cot(x) + 1 = csc²(x) (cot(x) + 1)

Given:\(cot^{3} x+cot^{2} x+cotx+1\)

Factor:

\(cot {}^{2} (x)(cot(x) + 1) + 1(cot(x) + 1\)

\((cot {}^{2} (x) + 1)(cot(x) + 1)\)

Substitute \( \cot {}^{2} (x) + 1 = csc {}^{2} (x):csc {}^{2} (x)(cot(x) + 1)\)

Answer:

X = 10 Unknown Side:  30 and 21

Step-by-step explanation:

Answer:

there are 10 possible combinations when selecting three photos out of five.

Step-by-step explanation:

The formula to calculate combinations is given by:

C(n, r) = n! / (r! * (n - r)!

In this case, we have 5 photos (n = 5) and we want to select 3 photos (r = 3). Plugging these values into the formula,

C(5, 3) = 5! / (3! * (5 - 3)!)

C(5, 3) = (5 * 4 * 3!) / (3! * 2 * 1)

C(5, 3) = (5 * 4) / (2 * 1) = 10

Answer:97

Step-by-step explanation:

Answer:

k = 62

Step-by-step explanation:

x + 97 + 149 + 55 = 360  {sum of all angles of quadrilateral}

x + 301 = 360

x = 360 - 301

x = 59

l // m and AB is transversal.

∠1 = x   {alternate interior angles}

∠1 = 59

ΔABC is an isosceles triangle.

m∠1 =  m∠2 = 59

In ΔABC ,

59 + 59 + k = 180  {angle sum property of triangle}

118 + k = 180

k = 180- 118

k = 62

Mr. Brown picks out the time that appears the most to find the mode.

He arranges the times in increasing order and picks the middle value to find the median.

The times in seconds for the 100-meter dash are as follows: 12.5, 12.4, 12.4, 12.3, 12.6, and 12.4.

The mode is the value or values that appear most frequently in a dataset.

In this case, the time that appears the most is 12.4, which occurs three times.

Therefore, the mode is 12.4.

The median is the middle value in a dataset when arranged in increasing or decreasing order.

When we arrange the times in increasing order, we have: 12.3, 12.4, 12.4, 12.4, 12.5, 12.6.

The middle value is 12.4, so the median is 12.4.

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The horizontal asymptote of the function is y=36 and vertical asymptote is x = 6 and its end behavior is f(x)→6.

As the independent variable approaches a certain value, the function approaches asymptotes, but does not cross them. They could be angled, vertical, or horizontal.

ascending asymptotes

There will be a vertical asymptote at x=a if the denominator factor of a rational function, (x - a), is not matched by the same factor in the numerator.

horizontal asymptotes:

When x is large, the value of a rational function approaches the ratio of the highest-degree terms in the numerator and denominator.

Given the function is f(x) = 6x/x-36

limx→±∞ 6x/x-36

= limx→±∞ 6/1-36/x

= 6 ⇒ horizontal asymptote: y = 6

Consider denominator = 0 ↔ x-36 = 0 ↔ x=36

limx→₊₂₅ 6x/x-36

= 6×36/0⁺ = ∞ ⇒ vertical asymptote: x = 36

End behavior of f(x):

As x → -∞ or x → ∞, f(x) → 6.

Hence we get the asymptote and the end behavior of the function.

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Circumference of circle = 2πr

= 2 × 22/7 × 14

= 2 × 22 × 2

= 44 × 2

= 88 mm²

Easyyy!

radius(r)- 15mm

______________

Circumference of circle.

______________

Circumference of circle.= 2πr

\(2 \times \pi \times r \\ \\ = 2 \times \frac{22}{7} \times 14 \\ \\ = 2 \times \frac{22}{ \cancel7} \times \cancel{14} \\ \\ = 2 \times 22 \times 2 \\ \\ = 88mm\)

The correct answer is option E. 900. Thye match can be scheduled in 900 different ways.

We can begin by assigning person A an opponent for each of the six games. Label the players on the first team as A, B, and C, and the players on the second team as X, Y, and Z.  Since A has to play each of X, Y, and Z twice, there are \($\frac{6!}{2!2!2!} = 90$\) ways to do this. We can multiply by 90 after assuming that A's opponents in the six rounds are X, X, Y, Y, Z, and Z.

It is important to keep in mind that the opponents for C are the remaining opponents after the opponents for A and B have been selected in each round, so there is only one valid assignment for them. As a result, all that is required of us is to assign the opponents to B. This is equivalent to determining the number of permutations of X, Y, and Z in which there are no Xs in the first two spots, Ys in the next two spots, or Zs in the final two spots.

Due to the fact that there is only one way to write down the Z's (the two spots that remain), we can use casework to determine this.

There is only one way to assign spots to Y if Xs are placed in the middle and last spots. There must be a Z in one of the last two spots, which is invalid if it is left empty.

Finally, if one X was placed in one of the middle two spots and one X was placed in one of the last two spots, there are  \($2\cdot2\)  ways to assign spots to X and \($2\cdot1$\)  ways to assign spots to Y (one of the first two spots and the remaining spot in the last 2). If Xs are placed in the last two spots, then there is only one way to assign spots to Y.

There are \($1+1+2\cdot2\cdot2\cdot1 = 10$\) ways to assign opponents to B and \($90\cdot10 = 900$\) ways to order the games.

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Complete Question:

Central High School is competing against Northern High School in a backgammon match. Each school has three players, and the contest rules require that each player play two games against each of the other school's players. The match takes place in six rounds, with three games played simultaneously in each round. In how many different ways can the match be scheduled?

\($\textbf{(A)}\ 540\qquad\textbf{(B)}\ 600\qquad\textbf{(C)}\ 720\qquad\textbf{(D)}\ 810\qquad\textbf{(E)}\ 900$\)

Answer:

\(3\)

Step-by-step explanation:

\(\mathrm{The\ slope\ of\ a\ line\ passing\ through\ the\ points\ (x_1,y_1)\ and\ (y_2,y_1)\ is\ given\ by:}\\\mathrm{Slope(m)=\frac{y_2-y_1}{x_2-x_1}}\\\\\mathrm{According\ to\ the\ question,}\\\mathrm{(x_1,y_1)=(0,-2)}\\\mathrm{(x_2,y_2)=(-2,-8)}\)

\(\mathrm{Therefore\ the\ slope=\frac{-8-(-2)}{-2-0}=\frac{-8+2}{-2}=3}\)

Answer:

D. y= 4x + 13

Step-by-step explanation:

the slope would have to be 4 to be parallel

so plug the points in

1=4(-3) + b

1= -12 +b

13 = b

On solving the provided question, we can say that  Here, 21 and 22 only share a single element, which is 1. Since they are co-prime factor, their HCF equals 1.

Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.

21 and 22:

1, 3, 7, and 21 are the factors of 21.

1, 2, 11, and 22 are the factors of 22.

Here, 21 and 22 only share a single element, which is 1. Since they are co-prime, their HCF equals 1.

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Answer:

102in2

Step-by-step explanation:

The formula for surface area is 2(wl+hl+hw). So plug in the measurements of the prism into the formula to get 102.

The line passes through the points (4,19) and (9,24) is y=x+15.

A linear function is a polynomial function whose degree is utmost zero or one.  It is represented as a straight line in the graph.

A line passes through the points (4,19) and (9,24)

The slope of a line passing through the two points \(P=(x_{1},y_{1})\)and \(Q=(x_{2},y_{2})\) is given by

\(m =\frac{y_{2} - y_{1} }{x_{2} -x_{1} }\)

We have that \(x_{1}=4, x_{2} =9,y_{1} =19, y_{2} =24\)

Substitute values in the formula we get slope as follows,

\(m=\frac{24-19}{9-4}, m=1.\)

Now, the y-intercept is

\(b= y_{1} - mx_{1} ,b=15\).

The equation of the line can be written in the form y=mx+b.

⇒y=x+15

Hence, the equation of line is y=x+15.

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Answer:

 \(\frac{x-7}{4} =f^{-1}( x)\)

Step-by-step explanation:

→ Replace f(x) with y

y = 4x + 7

→ Minus 7 from both sides

y - 7 = 4x

→ Divide both sides by 4

\(\frac{y-7}{4} =x\)

→ Replace y's with f⁻¹(x)

\(\frac{x-7}{4} =f^{-1}( x)\)

1.3338 is the likelihood, The probability of anything occurring is known as probability.

The probability of anything occurring is known as probability. To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur.

The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.

Explanation:

Mean (m) = 25

The standard deviation is 13

Sample size (n) is 95.

Chance that x will fall between 22 and 27.

Zscore = x - mean / s / n

If x = 22, Zscore is equal to (22 - 25) / (13/95).

For x = 27, Zscore is equal to (27 - 25) / (13/95) / n = 13 / 95, which is 1.3338.

1.3338 is the likelihood.

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a) To maximize its net savings, the company should use the new machine for 7 years.  b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar).  c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).

Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.

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Answer:  9v=162

Step-by-step explanation:

If you need the answer, Victors height is 18.

9v = 162

/9       /9

V = 18

Step-by-step explanation:

we are given a variable of victors height as v

according the expression

9 × v = 162

9v = 162

divide both sides by 9

v = 18

The Quadratic Factoring solutions to the equation \(2x^2\) + x - 10 = 0 are x = -5/2 and x = 2.

To solve the quadratic equation \(2x^2\) + x - 10 = 0 by factoring or finding square roots, we need to express it in the form (ax + b)(cx + d) = 0, where a, b, c, and d are constants.

Let's try factoring the quadratic equation:

\(2x^2\)+ x - 10 = 0

To factor it, we look for two numbers whose product is ac = 2(-10) = -20 and whose sum is b = 1.

The factors of -20 that add up to 1 are 5 and -4.

So, we can rewrite the equation as:

\(2x^2\) + 5x - 4x - 10 = 0

Now, we group the terms:

(\(2x^2\) + 5x) + (-4x - 10) = 0

Factor out the greatest common factor from each group:

x(2x + 5) - 2(2x + 5) = 0

Now, we can see that we have a common factor, (2x + 5), which we can factor out:

(2x + 5)(x - 2) = 0

To find the solutions, we set each factor equal to zero and solve for x:

2x + 5 = 0 or x - 2 = 0

For 2x + 5 = 0:

2x = -5

x = -5/2

For x - 2 = 0:

x = 2

Therefore, the Quadratic Factoring solutions to the equation \(2x^2\) + x - 10 = 0 are x = -5/2 and x = 2.

So, the correct answer is:

B. 2, -5/2

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a) The estimated model relating annual salary to firm sales and market value, in equation form, is: Salary = 4.6209 + 0.1621 * log(sales) + 0.1067 * log(mktval), where log denotes the natural logarithm.

b) Calculating this expression will give us the expected salary according to the model. If the expected salary is higher than $500,000, then your friend would be asking too much.

a) The estimated model relating annual salary to firm sales and market value, in equation form, is:

Salary = 4.6209 + 0.1621 * log(sales) + 0.1067 * log(mktval)

where log denotes the natural logarithm.

b) To determine if your friend would be asking too much for an annual salary of $500,000, we need to plug the values of firm sales and market value into the model and calculate the expected salary.

Using the given values:

- Firm sales (sales) = $5,000,000

- Market value (mktval) = $20,000,000

We first need to take the logarithm of the sales and market value:

log(sales) = log(5,000,000)

log(mktval) = log(20,000,000)

Then, we can substitute these values into the equation:

Expected Salary = 4.6209 + 0.1621 * log(5,000,000) + 0.1067 * log(20,000,000)

Calculating this expression will give us the expected salary according to the model. If the expected salary is higher than $500,000, then your friend would be asking too much.

Note: Make sure to use the natural logarithm (ln) in the calculations.

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Answer:

(0, 3)

Step-by-step explanation:

The y-intercept is point on the y-axis that the line passes through.

You can see the line passes through 3 on the y-axis.

On the y-axis, every point has a 0 for the x-coordinate.

The ordered pair for the point that is 3 on the y-axis is (0, 3).

Answer:

(0, - 7 )

Step-by-step explanation:

Under a reflection in the x- axis

a point (x, y ) → (x, - y ), thus

(0, 7 ) → (0, - 7 )

A linear equation representing the data in table is t(n) = 12x + 23.

The missing values in table should be completed as follows;

n            t(n)

4             71

5             83

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

m represents the slope.

x and y are the data points.

Next, we would determine the linear equation representing the data in table which passes through the points (1, 24) and (2, 36) by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 24 = (36 - 24)/(2 - 1)(x - 1)

y - 24 = 12(x - 1)

y = 12x - 1 + 24

y = t(n) = 12x + 23

When the value n = 4, the value of t(n) can be calculated as follows;

t(4) = 12(4) + 23

t(4) = 71.

When the value n = 5, the value of t(n) can be calculated as follows;

t(5) = 12(5) + 23

t(5) = 83.

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The expression that has the element of A*B*B is Option A - (b,2,3)

Sets are groups of clearly defined objects or elements in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.

The "elements" of a set are the objects that make up the collection. Sets are equal if and only if they have the same elements, therefore a = A denotes that 'a' is one of A's elements. For sets, repetition and order are irrelevant.

Given, A={a.b} and B=[1,2,3]

Since the required expression was supposed to have the element of A*B*B the correct option would be A since it has elements b from A, 2 from B, and 3 from B, fulfilling all the required elements.

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Answer:

$207

Step-by-step explanation:

We do 1242 / 6 = 207

It costs $207 for each family member.

Answer:

207 each

Step-by-step explanation:

Take the total cost and divide by the number of family members

1242 / 6

207 each

Answer:

perpendicular planes

Step-by-step explanation:

perpendicular planes

The legend chart element will tells the category of data that each line represents the lines.

Lines:

Lines refers a one-dimensional figure, which has length but no width.

Given,

suppose that a line chart includes several lines.

Here we need to identify the chart element will tell you the category of data that each line represents.

Basically, chart is a visual representation of numeric data in a worksheet. And it helps you to identify trends, make comparisons, and recognize patterns in the numbers.

In order to get the clear information that appears in your chart, you can add a chart title, axis titles, and data labels.

The element legend or data table is used to represents the category of the data.

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