the equation of a circle is given below
(x - 2/3)^2 +y^2=36
what is the center?
what is the radius?

The required graph of the function is graph 3.

You must select x-values and insert them into the equation before you can graph a function. A y-value will be produced once those values are entered into the equation. Your coordinates for a single point are your x- and y-values.

To check the graph we will put the values of x and identify the graph from the given option.

So, we have [tex]p(x) = 6\sqrt[3]{x}[/tex]

at x = 1

[tex]p(x) = 6\sqrt[3]{1}[/tex]

[tex]p(x) = 6[/tex]

Now, we can see that i  graph 1, 2 and 4. there is no value which gives p(x) = 6 for x = 1.

and

In graph 3, at x = 1, there is a a of p(x) = 6.

So.the graph of the function is graph 3.

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The mean number of manufacturing processes that need to be performed before a commercially successful one is 8.

Probability is a way to gauge how likely something is to happen. It is a mathematical concept that measures the probability or likelihood of an event occurring. It is stated as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty.

The probability of a single manufacturing process producing a commercially successful result is 12.5%, which can be expressed as a probability of success (p) of:

p = 0.125

The probability of the first commercially successful process occurring on the first attempt is p, and the probability of it occurring on the second attempt is (1-p)p (i.e. the probability of failure on the first attempt times the probability of success on the second attempt). Similarly, the probability of it occurring on the third attempt is (1-p)²p, and so on.

The mean, or expected value, of the number of processes required to achieve a single success can be calculated using the geometric distribution, which describes the number of independent Bernoulli trials required to achieve the first success. The formula for the mean of the geometric distribution is:

mean = 1/p

Substituting the value of p, we get:

mean = 1/0.125

mean = 8

Therefore, the mean number of manufacturing processes that need to be performed before a commercially successful one is 8.

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The quadratic function in factored form can be written as:

f(x) = a(x + 5)(x - 9)

The value of a is -1/3, and the equation of f(x) in factored form is -(1/3)(x + 5)(x - 9).

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form.

The -intercepts of a quadratic function correspond to the zeros of the function, which means that the roots of the quadratic equation are -5 and 9.

Therefore, the quadratic function in factored form can be written as:

f(x) = a(x + 5)(x - 9)

where a is a constant. We can find the value of a by using the point (-2,11) that lies on f(x). Substituting x=-2 and y=11 into the function, we get:

11 = a(-2 + 5)(-2 - 9)

11 = a(3)(-11)

11 = -33a

Solving for a, we get:

a = -1/3

Therefore, the equation of f(x) in factored form is:

f(x) = -(1/3)(x + 5)(x - 9)

Completing the statements:

The value of a is -1/3, and the equation of f(x) in factored form is -(1/3)(x + 5)(x - 9).

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Based on the results of this test, there is not enough evidence to conclude that children with antisocial tendencies have greater difficulty recognizing surprise than do children without antisocial tendencies.

The null hypothesis stated using symbols is: H0: μ ≤ 11.80 (where μ represents the population mean score on the emotion recognition scale for 12-year-old children with antisocial tendencies)

The alternative hypothesis stated using symbols is: H1: μ > 11.80

This is a one-tailed test, as the alternative hypothesis is only looking for an increase in the population mean score for recognizing the emotion of surprise among children with antisocial tendencies.

Using the Distributions tool with a one-tailed test and α = 0.05, the critical region is in the right tail of the distribution and the critical value of t is 1.684.

The degrees of freedom (df) for α = 0.05 and n = 40-1 = 39 is 39.

The estimated standard error is the standard deviation of the sample divided by the square root of the sample size, which is 3.28/√40 = 0.518. The t statistic is (12.55 - 11.80) / 0.518 = 1.45 (rounded to four decimal places), which is not greater than the critical value of t. Therefore, we fail to reject the null hypothesis.

Based on the results of this test, there is not enough evidence to conclude that children with antisocial tendencies have greater difficulty recognizing surprise than do children without antisocial tendencies.

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P and q are true because 10 is in fact greater than both 7 and 5. (A) the conclusion is true if an implication of the form T T. We know this with the help of a given conditional statement.

A conditional statement is one that has the syntax "If P then Q," with P and Q denoting sentences.

P is referred to as the hypothesis and Q is referred to as the conclusion for this conditional statement.

The implication of "If P then Q" is that whenever P is true, Q must also be true.

Because 10 is indeed greater than both 7 and 5, p and q are true.

If an implication has the structure T ⇒ T, the conclusion is correct.

Consequently, even though it's not entirely apparent what they mean, I'd say the outcome is the first possibility.

By "the implication is true because both parts of the implications are true," I assume that you mean this.

Therefore, P and q are true because 10 is in fact greater than both 7 and 5. (A) the conclusion is true if an implication of the form T T. We know this with the help of a given conditional statement.

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Correct question:

Which of the following illustrates the true value of the given conditional statement? p: 10 > 7 q: 10 > 5 q → p

a. T T → T

b. T F → T

c. F T → F

d. F F → T

From the given statement, g(-13) = 0 is the the statement that could be true for g.

A function, g, has the following properties: g(0) = -2, g(-9) = 6, and its domain and range are -20 ≤ x ≤ 5, and -5 ≤ g(x) ≤ 45, respectively.

Let's examine each choice to see if it falls within the defined domain and range.

g(7) = -1

7 is not within our purview. G(7) cannot thus be true.

g(-13) = 20

Our range includes 20 and our domain includes x=-13. This holds true for g, so.

g(0) = 2

This is untrue because g(0)=-2 is a given.

g(-4) = -11

11 is outside of the acceptable range. Therefore, this claim is untrue.

From the given statement, g(-13) = 0 is true.

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The complete question is,

1. The sample mean of Diego's television data is 1.73 hours.

2. Yes, if Diego repeats the process with more random samples of 30 students and calculates the mean of each sample, his set of sample means should have a normal distribution.

To find the sample mean of Diego's television data, we add up all the hours and divide by the total number of students:

The sample mean's (summation x) is:

= 1 + 3 + 2 + 0 + 4 + 1 + 2 + 1 + 5 + 3 + 0 + 4 + 2 + 3 + 2 + 3 + 1 + 0 + 4 + 5 + 2 + 1 + 3 + 3 + 2 + 4 + 1 + 5 + 1 + 0

= 52

So the sample mean (Summation x/n) is:

= 52 / 30

= 1.73333333333

= 1.73 hours

He should have normal distribution. This is known as the Central Limit Theorem, which states that as the sample size increases, the distribution of sample means approaches a normal distribution regardless of the shape of the original population distribution, as long as the samples are selected randomly and independently.

In this case, as Diego is selecting random samples of 30 students, the Central Limit Theorem would apply, and the distribution of sample means should be normal.

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So H satisfies the three conditions of the subgroup test, and is  a subgroup of G.

Let H represent the collection of all G products of X elements and their inverses. We will demonstrate that H meets the three aforementioned requirements, demonstrating that H is a subgroup of G.

The group operation "let a and b be arbitrary elements of H" declares that H is closed. There are then finite sequences of X's elements and their inverses, such as a₁, a₂,..., a and b₁, b₂,..., bm, where a = a₁a₂...an and b = b₁b₂...bm. The result of concatenating the two sequences, a₁a₂...anb₁b₂...bm, is the product ab. As each of these products must belong to X or its inverse because X is closed under the group operation, the product ab must belong to H.

The empty product, which is the product of 0 components from X, is the identity element of H and hence contains the identity element of G.

Let a be an element of H and let a₁, a₂,..., a be a finite sequence of elements from X and their inverses such that a = a₁a₂...an. This proves that H is closed under taking inverses. If these elements are written in reverse order, then a-1 is the product of their inverses: a-1 = an-₁...a₂-1a₁-1. as we know  that each of these inverses belongs to X or its inverse because X is closed under taking inverses, Thus H owns a-1

H is a subgroup of G as a result of meeting all three requirements of the subgroup test. In addition, H is the smallest subgroup of G that contains X because it is the set of all products in G of the elements of X and their inverses.

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The income elasticity and types of goods, based on the change in demand as a result of a rise in income is:

Clubs are most likely to be classified as a luxury good.

To compute the income elasticity of demand for each good, we use the formula:

Income Elasticity of Demand (E) = (% Change in Quantity Demanded) / (% Change in Income)

Tokens:

E = (15% increase in quantity demanded) / (13% increase in income)

E = 15 / 13

E = 1.15

Hearts:

E = (5% decrease in quantity demanded) / (13% increase in income)

E = -5 / 13

E = -0.38

Clubs:

E = (34% increase in quantity demanded) / (13% increase in income)

E = 34 / 13

E = 2.62

A luxury good is a type of normal good with a high income elasticity of demand (E > 1). In this case, clubs have the highest income elasticity of demand (E = 2.62). Therefore, clubs are most likely to be classified as a luxury good.

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The surface area of a rectangular prism is 490 in² by the area of each face and then add them up.

We refer to the prism as a rectangular prism since each face is shaped like a rectangle. A cuboid, which has six rectangular faces, and each opposite rectangular face is equal to and parallel to another rectangular face is known to have a similar shape.

To find the surface area of the right rectangular prism, we need to find the area of each face and then add them up.

Looking at the net, we can see that there are 6 faces, each with its own dimensions:

The top and bottom faces are both rectangles with dimensions 10 in by 13 in, so each has an area of 10 in × 13 in = 130 in².

The front and back faces are both rectangles with dimensions 10 in by 5 in, so each has an area of 10 in × 5 in = 50 in².

The left and right faces are both rectangles with dimensions 13 in by 5 in, so each has an area of 13 in × 5 in = 65 in².

Therefore, the total surface area of the right rectangular prism is:

2(130 in²) + 2(50 in²) + 2(65 in²) = 260 in² + 100 in² + 130 in² = 490 in²

So, the surface area of the right rectangular prism is 490 square inches.

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Answer:

  9

Step-by-step explanation:

You want the radius of a circle that has a tangent of length 12 meeting an external segment of length 6.

The given triangle is a right triangle with legs x and 12, and hypotenuse (x+6). The Pythagorean theorem tells you the relationship is ...

  (x+6)² = x² +12²

  x² +12x +36 = x² +144

  12x = 108 . . . . . . . . . . . . subtract (x²+36)

  x = 9 . . . . . . . . . . . . . divide by 12

The value of x in the figure is 9.

__

Additional comment

You can also consider what you know about Pythagorean triples. Two that might be applicable to a side length of 12 are {3, 4, 5} and {5, 12, 13}.

If the triple used here were {5, 12, 13}, that would make x=5 and the external segment 13-5=8 instead of 6.

If the triple used here were {3, 4, 5}, it would have a scale factor of 3 to become {9, 12, 15}. Then x=9 and the external segment is 15-9 = 6. This is the solution.

Another way to solve this is using the secant/tangent relation. For this, you need to extend the line 6+x across the circle. Then the relation is ...

  12² = 6(6+2x) . . . . tangent² = (segment to near)·(segment to far)

  12 = 3 +x . . . . . divide by 12

  x = 9

The slope of the line is -3, which means that Scott's delivery time decreased by 3 minutes per day on average.

(a) To find the equation of the line, we can use the point-slope form of the equation, which is:

where m is the slope of the line, and (x₁, y₁) is a point on the line. We can use the two intercepts given in the question as two points on the line.

The y-intercept is (0, 30), and the x-intercept is (10, 0). So, we have:

y - 30 = m(x - 0)

and

y - 0 = m(x - 10)

Simplifying the first equation, we get:

y - 30 = mx

Simplifying the second equation, we get:

y = mx + 0.

We can see that both equations are equivalent and represent the same line.

Therefore, the equation of the line in slope-intercept form is:

y = mx + 30

To find the value of m, we can use the formula:

where (x₁, y₁) and (x₂, y₂) are any two points on the line. We can use the intercepts given in the question:

m = (0 - 30) / (10 - 0)

m = -3

Therefore, the equation of the line in point-slope form is:

y - 30 = -3(x - 0)

Simplifying, we get:

y - 30 = -3x

(b) The y-intercept of the line is 30, which represents the delivery time on day 0. So, initially, it took Scott 30 minutes to deliver his packages.

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[tex]\qquad \textit{division of two complex numbers} \\\\ \cfrac{r_1[\cos(\alpha)+i\sin(\alpha)]}{r_2[\cos(\beta)+i\sin(\beta)]}\implies \cfrac{r_1}{r_2}[\cos(\alpha - \beta)+i\sin(\alpha - \beta)] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ z1=20[\cos(120^o)+i\sin(120^o)]~\hfill z2=4[\cos(30^o)+i\sin(30^o)] \\\\\\ \cfrac{z1}{z2}\implies \cfrac{20}{4}[\cos(120^o - 30^o)+i\sin(120^o - 30^o)]\implies 5[\cos(90^o)+i\sin(90^o)] \\\\\\ 5[0+i(1)]\implies 0+5i\implies \boxed{5i}[/tex]

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below

[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{(-6)}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{(-3)}}} \implies \cfrac{8 +6}{4 +3} \implies \cfrac{ 14 }{ 7 } \implies 2[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{ 2}(x-\stackrel{x_1}{(-3)}) \implies y +6 = 2 ( x +3) \\\\\\ y+6=2x+6\implies {\Large \begin{array}{llll} y=2x \end{array}}[/tex]

The scale of the map is that 4 inches on the drawing represents 1 mile in real life

We can use the scale formula:

scale = distance on map / actual distance

In this case, the distance on the map is 8 inches, and the actual distance is 2 miles.

Now we can plug in the values:

scale = 8 inches / 2 miles

scale = 4 inches /1 mile

Therefore, the scale of the map is 4 inches represents 1 mile

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According to the computation, each ticket is $37.5 is t = ($175 - $25)/4.

An equation is a formula that uses the equals symbol (=) to denote the equality of two expressions. Multiple languages may have somewhat distinct meanings for the term equation and its cognates.  For instance, in English, an equation is any properly constructed formula that consists of two expressions joined by the equals sign, whereas in French, an equation is any well-formed formula that contains one or more

variables 5.

Given the overall cost of parking and four tickets for a baseball game = $175.00

cost of parking = $25

The price of 4 tickets = $175 - $25

let cost of each ticket is t

t =($175 - $25)/4

cost of each ticket is $37.5

Therefore, the formula for a ticket is

t = ($175 -$25)/4, cost of ticket is $37.5.

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Therefore, Kyle's score at the tennis event is 0.74, or 74%.

Percent, denoted by the symbol %, is a way of expressing a number as a fraction of 100. Percentages can be used to compare two or more values or to express a change in a quantity over time. Percentages are commonly used to represent proportions, rates, or changes over time, and they are widely used in many fields, such as finance, statistics, and science. To calculate a percentage, we can multiply the given value by the percentage as a decimal or fraction.

Here,

To calculate Kyle's score at the tennis event, we need to use the given percentages for each category and apply them to the weight of each category. First, let's calculate Kyle's score for serves:

Kyle's serves score = 10% of 85%

= 0.1 * 0.85

= 0.085

Next, let's calculate Kyle's score for return balls:

Kyle's return balls score = 40% of 70%

= 0.4 * 0.7

= 0.28

Finally, let's calculate Kyle's score for wins:

Kyle's wins score = 50% of 75%

= 0.5 * 0.75

= 0.375

Now, we can add up all of Kyle's scores to get his overall score:

Kyle's score = Kyle's serves score + Kyle's return balls score + Kyle's wins score

= 0.085 + 0.28 + 0.375

= 0.74

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Step-by-step explanation:

[tex] \sqrt[3]{27} = 3 [/tex]

Because 3×3×3=27, or 3³=27

[tex] \sqrt[4]{81} = 3[/tex]

Because 3×3×3×3=81, or 3⁴=81

[tex] \sqrt[3]{ - 64} = - 4[/tex]

Because:

[tex] \sqrt[ 3]{ - 64} = - \sqrt[3]{ {4}^{3} } = - 4[/tex]

[tex] \sqrt[3]{1} = 1[/tex]

Because: 1×1×1=1, or 1³=1

Hope this helps!

Answer:

B

Step-by-step explanation:

B is $3.273, because the 3 at the end is less than 5, it rounds down to $3.27, which is the value that you want.

Therfore, the answer is B.

Brainliest?

I would really appreciate it!

Answer:

The answer to your problem is, C. 204 m2

Step-by-step explanation:

The surface area of square pyramid = 4 * area  of triangle

We would actually need to find the slant height of triangle(l),

√(6² + 6²) = 6√2 = Length

Formula to find:

A = bh/2 ( B = Base H = Height )

B = 12

H = 6 √2

( [12 × 6√2]/2 = 36√2 )

Equals our area ↑↑

The lateral surface is the surface of a part of the body that faces away from the midline

The lateral surface area of square pyramid = 4 * area  of triangle:

36√2 × 4 = 203.64

Since there is no option of 203.64 we will round it to 204

Thus the answer to your problem is, C. 204 m2

The rectangular cake has the largest area, Molly should buy the rectangular cake to ensure that there is enough cake for all of her guests.

In mathematics, the area is a measurement of the amount of space inside a 2-dimensional shape or surface. It is usually measured in square units, such as square meters, square feet, or square centimeters. For example, the area of a rectangle is calculated by multiplying the length and width of the rectangle. The concept of area is important in many fields, including geometry, architecture, physics, and engineering.

To determine which cake is the largest, we need to compare their areas. The formula for the area of a rectangle is length x width, the formula for the area of a square is side x side, and the formula for the area of a circle is pi x radius².

For the rectangular cake, the area is:

11” x 14” = 154 square inches

For the square cake, the area is:

12” x 12” = 144 square inches

For the circular cake, the area is:

π(7”)²≈ 153.94 square inches

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The expression "2[tex]m^{3}[/tex]- 11" represents the difference of twice the cube of a number (2[tex]m^{3}[/tex]) and 11, which is option C.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations such as addition, subtraction, multiplication, and division. It represents a quantity or a relationship between quantities, and it can be simplified or evaluated by performing the indicated operations.

The expression "2[tex]m^{3}[/tex]- 11" can be broken down into two parts: "2[tex]m^{3}[/tex]" and "-11". The first part, "2[tex]m^{3}[/tex]", represents twice the cube of a number (in this case, the number is "m"). To obtain the cube of a number, you multiply the number by itself three times, so "[tex]m^{3}[/tex]" means "m x m x m". Multiplying this by 2 gives "2m x m x m" which can be written as "2[tex]m^{3}[/tex]".

The second part, "-11", simply represents the number 11 decreased by 11. Therefore, the difference between "2[tex]m^{3}[/tex]" ad "-11" is "2[tex]m^{3}[/tex] - 11".

Therefore, the expression "2[tex]m^{3}[/tex] - 11" represents the difference of twice the cube of a number (2[tex]m^{3}[/tex]) and 11, which is option C.

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Answer:

(0, -5)

Step-by-step explanation:

To solve the system of equations:

y = 3x - 5 (1)

2x - 5y = 25 (2)

We can use the substitution method or the elimination method to find the values of x and y that satisfy both equations.

Let's use the substitution method:

Start with equation (1): y = 3x - 5

Substitute this expression for y into equation (2) wherever y appears:

2x - 5(3x - 5) = 25

Distribute the -5 to both terms inside the parentheses:

2x - 15x + 25 = 25

Combine like terms:

-13x + 25 = 25

Subtract 25 from both sides to isolate x:

-13x = 0

Divide both sides by -13 to solve for x:

x = 0

Now, we can substitute the value of x we found into equation (1) to find the value of y:

y = 3(0) - 5

y = -5

So the solution to the system of equations is x = 0 and y = -5. The ordered pair representing the solution is (0, -5).

According to the profit prediction model:

Using the finite differences method, we can find the differences between consecutive profits and then the differences between those differences until we reach a constant value, which indicates that the function is a polynomial of degree one more than the number of differences it took to reach the constant value.

The table of differences is:

Year, t | 1 | 2 | 3 | 4 | 5 | 6

Profit, p | 7 | 11 | 23 | 49 | 95 | 167

First diff. | 4 | 12 | 26 | 46 | 72

Second diff. | 8 | 14 | 20 | 26

Since the second differences are constant, we know that the polynomial model is of degree 3. We can use these differences to set up a system of equations and solve for the coefficients of the polynomial.

Let p(t) = at³ + bt² + ct + d be the polynomial model. Then:

p(1) = a + b + c + d = 7

p(2) = 8a + 4b + 2c + d = 11

p(3) = 27a + 9b + 3c + d = 23

p(4) = 64a + 16b + 4c + d = 49

Solving this system of equations:

a = 1

b = -3

c = 5

d = 4

So the equation of best fit is:

p = t³ - 3t² + 5t + 4

To predict the profit after 10 years, we substitute t = 10 into the equation:

p = 10³ - 3(10)² + 5(10) + 4 = 554

Therefore, the predicted profit after 10 years is $554.

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Image transcribed:

answer the following:

You have decided to start a dog-walking business. The table below shows the profits p (in dollars) of the business during your first 6 years. Use a graphing calculator and finite differences to find a polynomial model for the problem. Then use the model to predict your profit after 10 years.

Year, t | 1 | 2 | 3 | 4 | 5 | 6

Profit, p | 7 | 11 | 23 | 49 | 95 | 167

Equation of best fit:

p= ____ t³ + ____ t² + ____ t + _____

Profit after 10 years will be ______

Answer:

64.8

Step-by-step explanation:

take 77.2 + 54 = 139.7 then 21.6 x 3 = 64.8

The algebraic values of x include:

Using the same reasoning as in the previous problem:

24² + 45² = x²

576 + 2025 = x²

2601 = x²

x = ±51

Since x represents a length, discard the negative solution. Therefore, the value of x is 51.

Using the Pythagorean Theorem:

30² + 40² = x²

900 + 1600 = x²

2500 = x²

x = ±50

Since x represents a length, discard the negative solution. Therefore, the value of x is 50.

Using the Pythagorean Theorem:

18² + 80² = x²

324 + 6400 = x²

6724 = x²

x = ±82

Since x represents a length, discard the negative solution. Therefore, the value of x is 82.

Using the Pythagorean Theorem:

18² + 4² = x²

324 + 16 = x²

340 = x²

x = √340 = 2√85

Therefore, the value of x is 2√85 in simplest radical form.

Using the Pythagorean Theorem:

8² + 5² = x²

64 + 25 = x²

89 = x²

x = √89

Therefore, the value of x is √89 in simplest radical form.

Using the Pythagorean Theorem:

20² + 18² = x²

400 + 324 = x²

724 = x²

x = √724 = 2√181

Therefore, the value of x is 2√181 in simplest radical form.

Using the Pythagorean Theorem:

25² + 3² = x²

625 + 9 = x²

634 = x²

x = √634

Therefore, the value of x is √634 in simplest radical form.

Using the Pythagorean Theorem:

3² + 6² = x²

9 + 36 = x²

45 = x²

x = √45 = 3√5

Therefore, the value of x is 3√5 in simplest radical form.

Using the Pythagorean Theorem:

22² + 4² = x²

484 + 16 = x²

500 = x²

x = √500 = 10√5

Therefore, the value of x is 10√5 in simplest radical form.

To determine if a triangle is a right triangle, we can use the Pythagorean Theorem, which states that for any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Therefore:

a² + b² = c²

Substituting a = 8, b = 15, and c = 17:

8² + 15² = 17²

64 + 225 = 289

289 = 289

Since the equation is true, the triangle satisfies the Pythagorean Theorem and is therefore a right triangle.

Using the same method:

27² + 36² = 45²

729 + 1296 = 2025

2025 ≠ 2025

Since the equation is false, the triangle does not satisfy the Pythagorean Theorem and is therefore not a right triangle.

Using the same method:

9² + 11² = 4²

81 + 121 = 16

202 ≠ 16

Since the equation is false, the triangle does not satisfy the Pythagorean Theorem and is therefore not a right triangle.

To determine the classification of this triangle, compare the lengths of its sides. If all sides are less than the sum of the other two, then the triangle is acute; if one side is greater than or equal to the sum of the other two, then the triangle is obtuse; and if one side is equal to the sum of the other two, then the triangle is degenerate (a straight line).

Substituting a = 3, b = 4, and c = 6:

a + b = 3 + 4 = 7 < c

b + c = 4 + 6 = 10 > a

a + c = 3 + 6 = 9 > b

Since none of the sides are equal to or greater than the sum of the other two, the triangle is acute.

Substituting a = 9, b = 11, and c = 16:

a + b = 9 + 11 = 20 < c

b + c = 11 + 16 = 27 > a

a + c = 9 + 16 = 25 > b

Since none of the sides are equal to or greater than the sum of the other two, the triangle is acute.

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Image transcribed:

Algebra Find the value of x.

1. 12, 9, x

To start, use the Pythagorean Theorem. Then substitute 9 for a, 12 for b, and x for c.

2. 45 24 x

3. 30, 40, x

4. 80, 18, x

Algebra Find the value of x. Express your answer in simplest radical form.

8. 18, 4, x

9. 8, 5, x

10. 20, 18, x

11. 25, 3, x

12. 3, 6, x

13. 22, 4, x

Is each triangle a right triangle? Explain.

16. 15, 17, 8

17. 27, 45, 36

18. 9, 11, 4

The lengths of the sides of a triangle are given. Classify each triangle as acute, right, or obtuse.

19. 3,4,6

To start, compare to a+b. Substitute the greatest length for c.

20. 9, 11, 16

A 3-digit number can be formed using the digits 2,3 and 4 without repetition and with repetition 6 and 27.

What is permutation?

A permutation of a set is, broadly speaking, a rearranging of its elements if the set is already ordered, or arranging its members into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."

Here, we have

Given: 2,3 and 4

We have to find the 3-digit numbers that can be formed using the digits 2,3 and 4 without repetition and with repetition.

Without repetition: 2, 3, 4

Number of possible numbers

= 3×2×1

= 6

Hence, a 3-digit number can be formed using the digits 2,3, and 4 without repetition is 6.

With repetition

Number of possible numbers =

= 3×3×3

= 27

Hence, a 3-digit number can be formed using the digits 2,3, and 4 with a repetition is 27.

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Answer:

27

Step-by-step explanation:

b/c the formula of premeter of hexagon is P = 6s

s means sides then halved is 4.5

6*4.5=27

Therefore, a point c satisfying the conclusion of the Mean Value Theorem for f(x) = x⁻³ on the interval [1, 8] is approximately x = 2.3608.

In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. A function is often represented as an equation or a graph. It is a fundamental concept in mathematics and plays a crucial role in many areas, including calculus, algebra, and geometry. Functions are used to model real-world phenomena and solve problems in various fields, such as physics, engineering, economics, and more.

Here,

By the Mean Value Theorem, there exists a point c in the open interval (1, 8) such that:

f'(c) = [f(8) - f(1)] / (8 - 1)

where f'(x) is the derivative of f(x).

First, let's find the derivative of f(x):

f(x) = x⁻³

f'(x) = -3x⁻⁴

Now, substitute the values into the Mean Value Theorem equation:

-3c⁻⁴ = [8⁻³ - 1⁻³] / (8 - 1)

Simplify the right-hand side:

-3c⁻⁴ = (1/512) - (1/1)

-3c⁻⁴ = -511/512

Solve for c:

c⁻⁴ = (511/512) / 3

c⁻⁴ = 511/1536

c = [tex](511/1536)^{\frac{1}{4} }[/tex]

c ≈ 2.3608

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The both expressions simplify to[tex]$-\frac{16}{143}$[/tex], and they are equivalent.

Any mathematical statement with numbers, variables, and an arithmetic operation between them is an expression or algebraic expression. For instance, the expression 4m + 5 is one in which the terms 4m and 5 and the variable m are separated by the arithmetic sign +.

First, let's evaluate the expression inside the first set of parentheses:

[tex]$\begin{align*}\frac{4}{13} \div \left(\frac{-11}{12}\right) &= \frac{4}{13} \times \left(\frac{12}{-11}\right) \&= -\frac{48}{143}\end{align*}[/tex]

Now, we can substitute this result back into the original expression:

[tex]$\begin{align*}\left(-\frac{48}{143}\right) \div \frac{1}{3} &= \left(-\frac{48}{143}\right) \times 3 \&= -\frac{144}{143}\end{align*}[/tex]

Next, let's evaluate the expression inside the second set of parentheses:

[tex]$\begin{align*}\frac{-11}{12} \div \frac{1}{3} &= \frac{-11}{12} \times 3 \&= \frac{-11 \times 3}{12} \&= \frac{-33}{12} \&= -\frac{11}{4}\end{align*}[/tex]

Now, we can substitute this result back into the original expression:

[tex]$\begin{align*}\frac{4}{13} \div \left(\frac{-11}{12} \div \frac{1}{3}\right) &= \frac{4}{13} \div \left(-\frac{11}{4}\right) \&= \frac{4}{13} \times \left(-\frac{4}{11}\right) \&= -\frac{16}{143}\end{align*}[/tex]

Therefore, both expressions simplify to[tex]$-\frac{16}{143}$[/tex], and they are equivalent.

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