Write the given statement using symbols. The product of 7 and y
is the sum of 9 and 6

the equation of the circle is (x + 2)^2 + (y - 3)^2 = 45.

To find the equation of a circle, we need the coordinates of the center and the radius. We can use the distance formula to find the radius of the circle, which is the distance between the center and the point on the circle.

Let (h, k) be the center of the circle, and let (x, y) be any point on the circle. Then the distance formula gives us:

r = √[(x - h)^2 + (y - k)^2]

where r is the radius.

Using the given information, we have:

Center = (-2, 3)

Point on circle = (4, 6)

So the center is (h, k) = (-2, 3), and the point on the circle is (x, y) = (4, 6). Plugging these values into the distance formula, we get:

r = √[(4 - (-2))^2 + (6 - 3)^2] = √[6^2 + 3^2] = √45 = 3√5

Therefore, the equation of the circle with center (-2, 3) and point (4, 6) on it is:

(x - (-2))^2 + (y - 3)^2 = (3√5)^2

Simplifying this equation, we get:

(x + 2)^2 + (y - 3)^2 = 45

what is equation?

An equation is a mathematical statement that shows the equality of two expressions, typically separated by an equal sign (=). Equations are used to represent relationships between variables or quantities, and they are a fundamental tool in many areas of mathematics, science, and engineering.

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Answer:

x = 5*sqrt(2)

Step-by-step explanation:

Equation

Use the Pythagorean Theorem to get the value of x. If the triangle is isosceles, it means that both lets are equal to x.

x^2 + x^2 = 10^2

2x^2 = 100

x^2 = 50

x^2 = 5 * 5 * 2

sqrt(x^2) = sqrt(5*5*2)

x = 5*sqrt(2)

There is no denominator to rationalize. The answer is given as a irrational root.  The only other way to present it is in an approximate decimal form.

Answer:

x = \(5\sqrt{2}\) (or \(\frac{5\sqrt{2}}{1}\) if it has to have a rational denominator)

Step-by-step explanation:

We know;

1.) This triangle is isosceles (two of the sides are congruent).

2.) Hypotenuse is the biggest side in a right triangle. Therefore, that un-labeled side can't be 10, it has to be x as well.

So;

A² + B² = C²

x² + x² = 10²

2x² = 100

x² = 100/2

x² = 50

x = \(\sqrt{50}\)

Simplifying this would result in;

\(\sqrt{50}\) = \(\sqrt{25} * \sqrt{2}\)

\(\sqrt{50}\) = \(5\sqrt{2}\) (or \(\frac{5\sqrt{2}}{1}\) if it has to have a rational denominator)

Hope this helps!

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Do you do flvs?

Bicarbonate ions are formed when carbon dioxide combines with water. This reaction neutralizes the hydrogen ions, keeping the pH within the proper range. In conclusion, the bicarbonate ion is formed when carbon dioxide reacts with water. The bicarbonate buffer system is important in maintaining the body's pH balance.

Bicarbonate is a polyatomic anion with the chemical formula HCO₃−. Bicarbonate can form by combining water with carbon dioxide (CO2). The bicarbonate ion, HCO₃-, is formed when CO2 reacts with water, which causes a small amount of it to become bicarbonate ions. This reaction is extremely important in maintaining the pH of blood, and thus the proper functioning of the body.Bicarbonate ions play a significant role in buffering the body's pH balance. They act as a pH regulator in blood and other bodily fluids. The body needs to maintain a pH between 7.35 and 7.45 in order to maintain optimal health. When carbon dioxide in the body mixes with water, it produces carbonic acid, which can lead to a decrease in pH. The bicarbonate buffer system maintains the pH within the healthy range. The system works by converting carbon dioxide into bicarbonate ions, which then bind with excess hydrogen ions to form carbonic acid. This reaction neutralizes the hydrogen ions, keeping the pH within the proper range.

Bicarbonate is a chemical that contains three atoms: carbon, hydrogen, and oxygen. Bicarbonate is a polyatomic anion with the chemical formula HCO₃−. Bicarbonate can form by combining water with carbon dioxide (CO2).The bicarbonate ion, HCO₃-, is formed when CO2 reacts with water, which causes a small amount of it to become bicarbonate ions. This reaction is extremely important in maintaining the pH of blood, and thus the proper functioning of the body.Bicarbonate ions play a significant role in buffering the body's pH balance. They act as a pH regulator in blood and other bodily fluids. The body needs to maintain a pH between 7.35 and 7.45 in order to maintain optimal health. When carbon dioxide in the body mixes with water, it produces carbonic acid, which can lead to a decrease in pH. The bicarbonate buffer system maintains the pH within the healthy range. The system works by converting carbon dioxide into bicarbonate ions, which then bind with excess hydrogen ions to form carbonic acid.

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Answer:

3+5-9*6/2

3+5-9*3

3+5-27

8-27

-19

Answer:

5,400 mililiters

Step-by-step explanation:

5.4X1000=5400

Answer:

D

Step-by-step explanation:

1:1000

5.4:5400

Answer:

y=1

Step-by-step explanation:

we can find what w is equal to first

2w=8

/2. /2

w=4

Now we fill in w to find y

4=4y

/4. /4

1=y

Hopes this helps please mark beainliest

The correct answer is c.

The interpretation of the coefficient $0.03 in the regression of textbook retail price (PRICE) on number of pages in the book (LENGTH) is: As the length of the book increases by one page, the estimated price increases by $0.03 on average. Therefore, the correct answer is c.

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Answer:

Undefined

Step-by-step explanation:

It is undefined because the x value equals multiple y values so the slope is undefined :)

Have a great day!!

Please rate and mark brainliest!!

Answer: Choice B

Undefined

Reason:

Vertical lines always have undefined slopes.

This is because slope = rise/run, but run = 0 for vertical lines. The "run" describes how much the line moves to the right, but such a thing doesn't happen since it's stuck on one x value only.

So we could have something like slope = rise/run = 1/0 = undefined. Dividing over zero is not allowed.

The standard matrix representation of L is A = [ 1 0 -1; 0 0 2; 0 1 1 ]

To find the standard matrix representation of L for each linear transformation L, the following steps can be followed:

L : R2R2 : L(x) =

First, find the image of the standard basis vectors of R2, e1, and e2 under L. To find the image of e1, we let x = (1,0) since e1 is the standard basis vector for R2 in the x direction. We then have

L(e1) = L(1,0) = (1,0) + (0,1) = (1,1)

Next, to find the image of e2, we let x = (0,1) since e2 is the standard basis vector for R2 in the y direction. We then have

L(e2) = L(0,1) = (-1,0) + (1,1) = (0,1) + (-1,0)

Therefore, the standard matrix representation of L is A = [ 1 -1; 1 0 ]

L : R2 R2: L(x) = x1e2To find the standard matrix representation of L, we find the image of e1 and e2 under L. To find the image of e1, we let x = (1,0) since e1 is the standard basis vector for R2 in the x direction. We then have

L(e1) = L(1,0) = 1e2 = (0,1)

Next, to find the image of e2, we let x = (0,1) since e2 is the standard basis vector for R2 in the y direction. We then have

L(e2) = L(0,1) = 0e2 = (0,0)

Therefore, the standard matrix representation of L is A = [ 0 0; 1 0 ]

L: R3R3:L(x) =

First, we find the image of the standard basis vectors of R3, e1, e2, and e3, under L. To find the image of e1, we let x = (1,0,0) since e1 is the standard basis vector for R3 in the x direction. We then have

L(e1) = L(1,0,0) = (1,0,0)

Next, to find the image of e2, we let x = (0,1,0) since e2 is the standard basis vector for R3 in the y direction. We then have

L(e2) = L(0,1,0) = (0,0,1)

Lastly, to find the image of e3, we let x = (0,0,1) since e3 is the standard basis vector for R3 in the z direction. We then have

L(e3) = L(0,0,1) = (-1,2,1)

The standard matrix representation of L is A = [ 1 0 -1; 0 0 2; 0 1 1 ]

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The equation for the transformed logarithm that passes through the points (3,0) and (0,2) can be written as f(x) = -b * log(base a)(x - h) + k, where a, b, h, and k are constants to be determined.

To find the equation for the transformed logarithm, we need to use the given points (3,0) and (0,2) to determine the values of a, b, h, and k. Let's start with the point (3,0). Plugging the x-coordinate (3) into the equation, we have:

0 = -b * log(base a)(3 - h) + k

Next, we'll use the point (0,2) to obtain another equation. Plugging the x-coordinate (0) into the equation, we get:

2 = -b * log(base a)(0 - h) + k

Simplifying these equations, we have a system of equations to solve for a, b, h, and k. However, since the equation involves a logarithm, we need more information to determine the specific values of a, b, h, and k.The transformed logarithm function includes transformations such as vertical stretches/compressions (b), horizontal shifts (h), and vertical shifts (k). Without more specific information about these transformations or the base of the logarithm, it is not possible to determine the equation uniquely.

In general, the equation for a transformed logarithm can be written as f(x) = -b * log(base a)(x - h) + k, where a, b, h, and k are constants determined by the specific transformations applied to the logarithm function. It's important to have additional information or instructions to determine the values of a, b, h, and k and provide an equation that accurately represents the given transformed logarithm.

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The equation will be 6x + 5.76 = 34.14. And each bag of apples costs will be $4.73.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Autumn buys eggs and apples at the store.

Let x be the amount of each bag of apples. Then the equation will be

6x + 5.76 = 34.14

Simplify the equation, then the value of x will be

6x = 28.38

x = $4.73

Thus, each bag of apple costs will be $4.73.

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Answer:

m=-1/2

Step-by-step explanation:

(x1,y1)=(9,4)

(x2,y2)=(3,7)

m= y2−y1  / x2−x1

= 7−4  / 3−9

= 3  / −6

m= -1/2

Brainliest

Answer:

(6,5.5)

Step-by-step explanation:

(9+3)/2,4+7/2

(12/2),(11/2)

(6,5.5)

The probability of rolling a number less than or equal to 3 is 0.5.

What is the probability of rolling a number less than 3?

Event: The collection or the set of outcomes in an experiment is called as an event.

Outcomes: The possible results of a trail in an experiment are called as outcome.

Probability:

The ratio of the number of favorable outcomes to certain event and the total number of possible outcomes is called as the probability of an event.

The probability of rolling a number less than or equal to 3 is obtained by taking the ratio of the number of favorable outcomes by the total number of outcomes. It is expected about 50% of times that rolling a number less than or equal to 3.

The probability of rolling a number less than or equal to 3 is 0.5.

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The probability of a randomly selected injured wrestler visiting a physical therapist is 56%.

To calculate this probability, let's denote the probability of visiting a physical therapist as P(PT) and the probability of visiting a chiropractor as P(C). We are given that 28% of the wrestlers visit both a physical therapist and a chiropractor, so we can write this as P(PT ∩ C) = 0.28. We are also given that 8% of the wrestlers visit neither, so P(neither) = 0.08.

The probability of visiting either a physical therapist or a chiropractor can be calculated using the principle of inclusion-exclusion:

P(PT ∪ C) = P(PT) + P(C) - P(PT ∩ C)

Since P(PT ∩ C) = 0.28, we have:

P(PT ∪ C) = P(PT) + P(C) - 0.28

We are also given that the probability of visiting a physical therapist exceeds the probability of visiting a chiropractor by 16%, so we can write this as:

P(PT) = P(C) + 0.16

Substituting this into the equation for P(PT ∪ C), we get:

P(PT ∪ C) = P(C) + 0.16 + P(C) - 0.28

P(PT ∪ C) = 2P(C) - 0.12

Since P(PT ∪ C) represents the probability of visiting either a physical therapist or a chiropractor, and we know that 8% visit neither, we can write:

P(PT ∪ C) + P(neither) = 1

Substituting the values, we have:

2P(C) - 0.12 + 0.08 = 1

2P(C) = 1.04

P(C) = 0.52

Now, using P(PT) = P(C) + 0.16, we can find:

P(PT) = 0.52 + 0.16

P(PT) = 0.68

Therefore, the probability of a randomly selected injured wrestler visiting a physical therapist is 0.68 or 68%.

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So you need 14.58 liters of 80% solution and 10.42 liters of 54% solution. To convert these to grams, you need to multiply by density of the solution.

To obtain 25 liters of a 42% solution, you would need to mix a certain amount of an 80% solution with a certain amount of a 54% solution. To determine the specific amounts, you would need to set up and solve a system of equations.

x + y = 25

(0.8x) + (0.54y) = 0.42(x + y)

x = (0.42*25) / (0.8 + 0.54) = 14.58 liters

y = 25 - x = 10.42 liters

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Answer:

25π-24

Step-by-step explanation:

from the figure,

radius of the circle(r)=diameter of the circle(d)/2

=10/2

=5

Area of the circle(A)=πr^2

=π5^2

=25π

Again,

base of the right angle triangle(b)=6

perpendicular of right angle triangle(p)=8

we also know,

the area of right angle triangle = 1/2*base*height

=1/2*6*8

=1/2*48

=48/2

=24

Now, Area of the shaded region=Area of circle - Area of right angle triangle (given in the figure)

Area of shaded region= 25π -24

You are looking for a number that is a multiple of 3, 4, 5, and 6, and is a factor of 120 divided by 7, leaving a remainder of 4.

Let's break down the problem step by step:

1. Find a number that is a multiple of 3, 4, 5, and 6.
  - The smallest number that meets this criteria is the least common multiple (LCM) of 3, 4, 5, and 6.
  - The LCM of these numbers is 60.

2. Find a number that is a factor of 120 divided by 7.
  - The result of dividing 120 by 7 is 17 with a remainder of 4.
  - The number we are looking for must be a factor of 120 divided by 7, so it must be a factor of 17.
  - The factors of 17 are 1 and 17.

3. Find a number that leaves a remainder of 4.
  - Since the number must leave a remainder of 4, we need to add 4 to the factors of 17.
  - The numbers that meet this criteria are 1 + 4 = 5 and 17 + 4 = 21.

So, the numbers that satisfy all the given conditions are 5 and 21.

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Answer:

10

Step-by-step explanation

\(\frac{a+b}{2}=20\\\frac{b+c}{2}=24\\ \frac{a+b+c}3}=18\\\)

20x2 = 40 -> a+b=40

24x2 = 48 -> b+c=48

18x3 = 54 -> a+b+c=54

solve the equations...

a=6

b=34

c=14

a+c/2 = 6+14/2 = 10

Answer:

(5, 2)

Step-by-step explanation:

\(Midpoint \: of \: segment \: CD \\\\ = \bigg( \frac{ 3+ 7 }{2}, \: \: \frac{-5+9}{2} \bigg) \\ \\ = \bigg( \frac{ 10 }{2}, \: \: \frac{4}{2} \bigg) \\ \\ = ( 5, \: \: 2)\)

Answer:well if a ice cub melts its probally gonna be 0

Step-by-step explanation:

im not so good sorry

To evaluate the integral of xdx / (7x^2+3)^5, we first need to make a substitution. Let u = 7x^2+3, then du/dx = 14x.

Solving for x, we get x = sqrt((u-3)/7), which means dx = (1/(2sqrt(7(u-3))))du.

Substituting these values into the evaluation of integral, we get:

∫(x dx) / (7x^2+3)^5 = ∫[(sqrt((u-3)/7))/(2u^2)] du

Next, we need to simplify the integrand by factoring out a constant:

∫[(sqrt((u-3)/7))/(2u^2)] du = (1/2√7) ∫[(u-3)^(-1/2) / u^2] du

Using the power rule of integration, we can integrate the second term:

∫[(u-3)^(-1/2) / u^2] du = ∫u^(-5/2) (u-3)^(-1/2) du

Now, we can use the substitution method again, letting v = u-3, then dv/du = 1. Solving for u, we get u = v+3, which means du = dv.

Substituting these values into the integral, we get:

∫u^(-5/2) (u-3)^(-1/2) du = ∫(v+3)^(-5/2) v^(-1/2) dv

Using the product rule of integration, we get:

∫(v+3)^(-5/2) v^(-1/2) dv = (-2/3) (v+3)^(-3/2) (v^(1/2))

Now, we can substitute back in for u and simplify:

(-2/3) (u-3+3)^(-3/2) [(u-3)^(1/2)] = (-2/3) (7x^2)^(-3/2) [(7x^2+3)^(1/2)]

Finally, we can simplify further by factoring out constants:

(-2/3√7) (7x^2)^(-3/2) [(7x^2+3)^(1/2)] = (-2/3√7) (49x^3) / (7x^2+3)^(3/2)

Therefore, the solution to the integral of xdx / (7x^2+3)^5 is:

(-2/3√7) (49x^3) / (7x^2+3)^(3/2)

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The process of finding the derivative of a function is called differentiation.

Differentiation is a fundamental concept in calculus that involves determining the rate at which a function changes with respect to its independent variable. It allows us to analyze the behavior of functions, such as finding slopes of curves, identifying critical points, and understanding the shape of graphs.

The derivative of a function represents the instantaneous rate of change of the function at any given point. It provides information about the slope of the tangent line to the graph of the function at a specific point.

The notation used to represent the derivative of a function f(x) with respect to x is f'(x) or dy/dx. The derivative can be interpreted as the limit of the difference quotient as the interval approaches zero, representing the infinitesimal change in the function.

By applying differentiation techniques, such as the power rule, product rule, chain rule, and others, we can find the derivative of a wide range of functions. Differentiation is a powerful tool used in various areas of mathematics, physics, engineering, economics, and other fields to analyze and solve problems involving rates of change.

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Answer: x=12

Step-by-step explanation:

1/3 x -4

1/3x=4               <---- First add 4 to each side of the equation (moves the "-4")

1/3x(3)=4(3)     <---- Muliply each side by "3" to get rid of the fraction

x=12

Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Histograms are an effective way to display data graphically. They are used to show how often certain values or ranges of values appear in a data set. Visual interpretation of histograms has many strengths and limitations. Some of the strengths of visually interpreting histograms are that they are easy to read and understand, they provide a clear picture of how the data is distributed, and they can help identify outliers or gaps in the data. However, some of the limitations of visually interpreting histograms are that they can be influenced by the number of bins chosen, the way the data is grouped, and the choice of the scale used. Therefore, it is important to carefully consider these factors when interpreting a histogram. In conclusion, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

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Answer:

a) X + X + 1 = 11

Step-by-step explanation:

Em matemática, a soma de consecutivos é expressa matematicamente como:

X + (X + 1) + (X + 2) + (X + 3) .............

Na pergunta acima, somos solicitados a encontrar a expressão algébrica que indica que a soma de DOIS inteiros consecutivos é igual a 11

Portanto, esta expressão algébrica é dada como:

X + (X + 1) = 11

X + X + 1 = 11

Portanto, a opção a) X + X + 1 = 11 é a opção correta