find the coordinates of the circumcenter of ABC with vertices A (4,6), B (6,-2) and C (0,-2)

True. The order in which the vectors A and B are drawn does not affect the resultant vector when they are added graphically.

When adding vectors graphically, you represent each vector as an arrow with its magnitude and direction. To find the resultant vector, you place the tail of vector B at the head of vector A (or vice versa), forming a triangle. The resultant vector is then drawn from the tail of the first vector to the head of the second vector. The order in which you draw the vectors does not alter the resulting triangle or its sides.      

Mathematically, vector addition is commutative, which means that the order of addition does not change the result. In this case, adding vector A first and then vector B is equivalent to adding vector B first and then vector A. The resultant vector will have the same magnitude and direction regardless of the order in which the vectors are added.

Therefore, whether you draw vector A first or vector B first, you will obtain the same vector sum (resultant) when adding them graphic ally.

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Answer:

x² - 1

Step-by-step explanation:

The product

(x - 1)(x + 1)

= x(x + 1) - 1(x + 1) ← distribute both parenthesis

= x² + x - x - 1 ← collect like terms

= x² - 1

Answer:

25%

Step-by-step explanation:

Since there are 24 apples, and 6 are bad, to find the percentage of the bad apples, you do bad apples/total apples

6/24=.25

0.25 is 25%

The solution is Option A.

The translation of the center of circle is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

Let the equation for the circle A be represented as

( x - 7 )² + ( y - 1 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( 7 , 1 )

Let the equation for the circle A be represented as

( x + 8 )² + ( y - 2 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( -8 , 2 )

So , the translation of circle A to B is given by

( 7 , 1 ) to ( -8 , 2 )

So , the x coordinate is translated by 15 units to left and the y coordinate is translated by 1 unit up

Hence , the translation is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

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The ratio equivalent to 1cm/50mi is 1/8053.6. To find the equivalent ratio to 1cm/50mi, we need to convert either the numerator or the denominator to the same unit of measurement.

Let's convert 1cm to miles:
1 cm = 0.00000621371 miles
Now we can write the ratio as:
0.00000621371 miles/50 miles
Simplifying this ratio by dividing both the numerator and denominator by 0.00000621371, we get:
1/8053.6
Therefore, the ratio equivalent to 1cm/50mi is 1/8053.6.
To find a ratio equivalent to 1cm/50mi, you can simply multiply or divide both terms by the same number. For example, you can multiply both by 2:
(1cm * 2) / (50mi * 2) = 2cm / 100mi
So, an equivalent ratio to 1cm/50mi is 2cm/100mi.

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Answer:

what that person said

Step-by-step explanation:

Answer: One abutment

Step-by-step explanation: When a fixed bridge is created, there must be at least one abutment of the bridge.

The rate of interest per annum will be 3.6%.

The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.

Given, Isabelle takes out a loan that gathers compound interest.

At the start, the loan amount is £5500

after the 1-year loan amount is £5698.00

After the 2-year loan amount is £5903.13

thus,

P = 5500

For t = 1 year A = 5698.00

since interest is annually thus, the value of n is 1

So, from the formula

5698 =  5500( 1 + r)

5500r = 5698 -5500

r = 198/5500

r = 0.036

or

rate of interest, r = 3.6%

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Answer:

5/6 = 1/12x

Step-by-step explanation:

x represents the amount of times you can can drive to or from work with the gas in the tank

5/6 = 1/12x

- Multiply both sides of equation by 12

10 = x

The lifetime cost of the model is $765.

Kate is re-modelling her kitchen.

She is going shopping for a refrigerator.

The model price is $405, and the estimated energy cost per year is $36.

If the model has an estimated lifetime of 10 years,

Lifetime cost of the model:

The lifetime cost of the model is $765

Explanation: Given, The model price is $405

Estimated energy cost per year is $36.

The model has an estimated lifetime of 10 years.

Lifetime cost of the model can be calculated as follows:

Total lifetime cost = Initial cost + (Estimated energy cost per year × Estimated lifetime)

Initial cost = $405

Estimated energy cost per year = $36

Estimated lifetime = 10 years

Total lifetime cost = $405 + ($36 × 10)

Total lifetime cost = $405 + $360

Total lifetime cost = $765

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A theorem which is used to find the rational solutions of a polynomial equation is known as the rational root theorem.

A polynomial expression is given and after solving them we get the two values known as the roots of the function.

These are also known as the zeros of polynomial as after putting these values in the equation we get the result as 0 .

We should use the rational root theorem only when the value of coefficients are small.

The theorem states that each rational solution x = p ⁄ q, when on simplified satisfies the below mentioned points,

p is an integer factor of the constant term a0, and

q is an integer factor of the leading coefficient an.

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Answer:

m= 0

Step-by-step explanation:

this is the right answer

-7-14m+49=42+7m

42-14m=42+7m

14m+7m=42-42

21m=0

m=0

Answer:

or,-14(2m-7)=7(6+m)

or,-28m + 98=42 + 7m

or,98-42=7m+28

or,56=35m

or,56/35=m

therefore,m=1.6 Ans

Answer:

a2 + 2al (or) a2 + √a24+h2 a 2 4 + h 2

Step-by-step explanation:

Answer:

SA=L²+2L√(L²/4+H²)

Step-by-step explanation:

Where H is the height and L is the length

Ensuring that data is collected the same way each time it is collected is an example of data consistency.

Therefore, ensuring that data is collected the same way each time it is collected is an example of data consistency.

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We can conclude that -

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given is that the regular price on a pair of jeans is $54. The store advertises a back-to-school sale at 40% off the regular price of the jeans. Two weeks later, the store advertises a sale at an additional off the sale price of these jeans at 5%.

Original price -

$54

Cost after 40% discount -

54 - {40% of 54}

54 - {40/100 x 54}

54 - {2/5 x 54}

54 - 21.6

$32.4

Cost after 5% discount -

32.4 - {5% of 32.4}

32.4 - {5/100 x 32.4}

32.4 - 1.62

$30.78

{ 3 } -

Calculating 60% of new price -

60% of 30.78

(60/100) x 30.78

18.5

Calculating 40% of new price -

40% of 30.78

(40/100) x 30.78

12.4

So, 60% of new price is greater than calculating 40%.

So, Manny is correct.

Therefore, we can conclude that -

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Answer:

-21/8

Step-by-step explanation:

3 (3/8) * -7/3

= 9/8 * -7/3

= 3/8 * -7

= -21/8

A distinct group of objects without regard to their arrangement is called a set. A set is a collection of distinct objects, called elements or members, that are enclosed within curly braces { }. Sets can contain any type of object, such as numbers, letters, symbols, or even other sets.

The elements of a set are not arranged in any particular order and each element appears only once in a set.Sets are used in various fields of mathematics and computer science. They are the building blocks for other mathematical structures, such as functions, relations, and graphs. Sets are also used to define and study mathematical concepts such as cardinality, intersection, union, complement, and power sets.

In computer science, sets are used to represent data structures, such as arrays, hash tables, and trees. They are used to store and manipulate data efficiently, and to perform operations such as search, insert, delete, and sort. Sets are also used in database systems, where they represent collections of records that satisfy certain criteria.

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Answer:

I don't really know but I will help you if I can

The expected value of the sample mean of mpg derived from a random sample of four passengers is 30.5 mpg.

The expected value of the sample mean can be calculated using the formula

E(x) = μ

where x is the sample mean, and μ is the population mean.

In this case, the population mean is given as 30.5 mpg. The standard deviation of the population is also given as 4.1 mpg.

The standard deviation of the sample mean can be calculated using the formula

σx = σ/√n

where σ is the population standard deviation and n is the sample size.

Substituting the given values, we get:

σx = 4.1/√4 = 2.05

So the expected value of the sample mean is

E(x) = μ = 30.5 mpg.

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Clear and complete definitions of the following concepts are stated below:

1. Continuity of a function

2. The derivative of a function

3. Critical value of a function

4. Increasing and Decreasing function

5. Upward and Downward Concavity

6. Location of possible inflection points

7. The fundamental theorem of calculus

1. Continuity of a function at a point refers to the function being able to be defined and having a finite output at that point, as well as the function's output values being "close" to each other as the input values approach the point in question. This can be formally defined using limits: a function f is continuous at a point x=a if and only if the limit of f(x) as x approaches a is equal to f(a). In other words, if we can draw the graph of the function without lifting our pencil and without any breaks or jumps, then the function is continuous at that point. To use this definition in a problem, we would need to calculate the limit of the function as x approaches the point in question and see if it equals the function's output at that point.

2. The derivative of a function f at a point x is a measure of how the function is changing at that point. It is formally defined as the limit of the difference between f(x+h) and f(x) as h approaches 0, or:

f'(x) = lim h->0 [f(x+h) - f(x)]/h

The derivative tells us the slope of the tangent line to the function at that point. It can be interpreted as the rate of change of the function at that point, or the amount by which the function is increasing or decreasing as the input value changes.

3. A critical value of a function is a value of the input at which the derivative of the function is 0 or is undefined. At a critical value, the function may have a local minimum, a local maximum, or neither. To determine which of these is the case, we can use the second derivative test. If the second derivative of the function at the critical value is positive, then the function has a local minimum at that point. If the second derivative is negative, then the function has a local maximum at that point. If the second derivative is 0, then we cannot determine whether the function has a local minimum or maximum at that point.

4. To determine where a function is increasing or decreasing, we can look at the sign of the derivative at different points. If the derivative is positive at a point, then the function is increasing at that point. If the derivative is negative, then the function is decreasing at that point. If the derivative is 0, then the function is neither increasing nor decreasing at that point.

5. To determine where a function is concave upward or concave downward, we can again look at the sign of the derivative at different points. If the derivative is increasing (i.e., the derivative of the derivative is positive), then the function is concave upward at that point. If the derivative is decreasing (i.e., the derivative of the derivative is negative), then the function is concave downward at that point. If the derivative is constant (i.e., the derivative of the derivative is 0), then the function is neither concave upward nor concave downward at that point.

6. To locate possible inflection points of a function, we can look for points where the concavity of the function changes. This occurs when the derivative of the derivative changes sign. To determine whether a function really has an inflection point at a possible inflection point, we can use the second derivative test as described above. If the second derivative is 0 at the point, then the function has an inflection point there. If the second derivative is positive or negative, then the function does not have an inflection point at that point.

7. The fundamental theorem of calculus is a theorem that relates the concept of the derivative of a function to the concept of the function's integral. It states that if f is a continuous function on the interval [a, b], then the function F defined by

F(x) = ∫a^x f(t) dt

is continuous and has a derivative at every point in the interval (a, b), and that the derivative of F at a point x is equal to f(x).

The fundamental theorem of calculus is important because it allows us to evaluate definite integrals, which are used to compute the area under a curve or the volume of a solid of revolution. It also provides a connection between the concepts of the derivative and the integral, which are both fundamental tools in calculus. This connection allows us to solve problems involving both concepts more easily, and it helps us to understand the relationship between the two concepts.

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Answer:

What graph?

Step-by-step explanation:

According to the sample data, the best conclusion supported by the sample data is that approximately 30% of all largemouth bass in the pond weigh more than 2 pounds. The answer is (D) Approximately 30% of all largemouth bass in the pond weigh more than 2 pounds.

The conclusion that is best supported by the sample data is that approximately 30% of all largemouth bass in the pond weigh more than 2 pounds, which is based on the fact that the sample contained 150 largemouth bass, of which 30% weighed more than 2 pounds.

Therefore, options A and C are incorrect. The sample data does not provide enough information to determine the average weight of all fish in the pond, so option B is also incorrect.

The correct answer is D) Approximately 30% of all largemouth bass in the pond weigh more than 2 pounds. This conclusion is supported by the sample data because the study specifically included a sample of 150 largemouth basses, of which 30% weighed more than 2 pounds. The other options are not supported by the sample data because the study does not include data on any other types of fish or the average weight of all fish in the pond.

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Answer:

(-3,5)

Step-by-step explanation:

To solve using substitution, first isolate one variable in one of the given equations. Then, substitute the value you received from that equation for the matching variable in the second equation. Finally, substitute that value back into any of the equations to have both the x and y values.

1) The y in y = x + 8 is already isolated, so let's substitute that value for the y in x + y = 2. Substitute x + 8 for y in x + y = 2, then solve:

\(x + y = 2\\x + (x + 8) = 2 \\x + x + 8 = 2\\2x + 8 = 2 \\2x = -6\\x =-3\\\)

Therefore, the x-value of the solution is -3.

2) Substitute the x value back into any of the one equations to find the value. Any choice is fine - in my work, I chose to substitute -3 for the x in y = x + 8:

\(y = x + 8 \\y = (-3) + 8\\y = -3 + 8\\y = 5\)

Therefore, the y-value of the solution is 5.

3) Thus, the solution is (-3, 5).  

Answer:

parte 1) | Superprof

1 Indica cuáles de las siguientes expresiones son monomios. En caso de ... 4 Encuentra el valor numérico del polinomio P(x) = x^3 + 3x^2 - 4x - 12 ... d) (10x – 5/4x³ + 5/2x² – 1/2) : (5x)

Answer:

4a\(\sqrt{x}\)41

Step-by-step explanation:

12*2+9x2= Perimeter.

The perimeter P of rhombus is given as

\(\rm\bold{ P = 4\sqrt{41}a }\)

The diagonals of rhombus bisect each other at right angles and it has same perimeter as that of a square.

From this property stated above we can formulate  side of rhombus is below in equation (1)

Side and  diagonals of rhombus have following relation

\(\rm Let \; the \; side \; of\; rhombus = s\\Length\; of \; first \; diagonal = 8a\\ Length\; of \; second \; diagonal = 10a\\\\According \; to \; the \; identity\; for\; area \; of\; rhombus \\ s^2 = (p/2)^2 +(q/2)^2 ....(1) \\where \; p \; and\; q \; are\; the \; diagonals.\)

so

\(\rm s^2 = (10a/2)^2 + (8a/2)^2\\s^2 = 25a^2 + 16a^2 = 41 a^2 \\s= \sqrt{41}a ......(2)\)

Equation (2) represents side of rhombus

So the perimeter P of rhombus is given as

\(\rm P = 4\times s\)

\(\rm\bold{ P = 4\sqrt{41}a }\)

The perimeter P of rhombus is given as

\(\rm\bold{ P = 4\sqrt{41}a }\)

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Answer:

Gana 6666,67 Córdoba de los cuales

gasta 3333,33 en alimentos y 1333,33 en servicios.

Step-by-step explanation:

Se queda 2000 Córdoba

Gasta el 20% de su salario para pagar los servicios básicos de su casa.

Gasta el 50% de su salario en comida.

Suponga que gana x cantidad

luego

x = 0,2x + 0,5x + 2000

x = 0,7x + 2000

x-0,7x = 2000

0,3 veces = 2000

x = 2000 / 0,3

x = 6666,67

Gana 6666,67 Córdoba de los cuales

gasta 3333,33 en alimentos y 1333,33 en servicios.

He keeps 2000 Córdoba

He spends  20% of his salary to pay for the basic services of his hous.

He spends 50% of his salary to pay on food.

Suppose he earns x amount

then

x= 0.2x+0.5x+2000

x= 0.7x+2000

x-0.7x=2000

0.3x= 2000

x= 2000/0.3

x= 6666.67

English

He earns 6666.67  Córdoba out of which

he spends 3333.33 on food and 1333.33 on services .

Using the given ratio, we can set up a proportion to find the number of ounces of water needed if 7 teaspoons of tea are used. Let x be the number of ounces of water needed:

1 teaspoon / 6 ounces = 7 teaspoons / x + 1 teaspoon

Multiplying both sides by the denominator on the right side gives:

x + 1 = 7 teaspoons * 6 ounces / 1 teaspoon

Simplifying the right side gives:

x + 1 = 42 ounces

Subtracting 1 from both sides gives:

x = 41 ounces

Therefore, 41 ounces of water are needed if 7 teaspoons of tea are used.

In summary, to find the number of ounces of water needed if 7 teaspoons of tea are used, we can use the inverse of the given ratio and set up a proportion to solve for x. The resulting proportion shows that 41 ounces of water are needed to make the tea.

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The population of a city was 101 thousand in 1992. The exponential growth rate was 1.8% per year. We need to find the exponential growth function in terms of t, where t is the number of years since 1992.So, the formula for exponential growth is given by;\(P(t)=P_0e^{rt}\)

Where;P0 is the population at time t = 0r is the annual rate of growth/expansiont is the time passed since the start of the measurement period101 thousand can be represented in scientific notation as 101000.Using the above formula, we can write the population function as;\(P(t)=101000e^{0.018t}\)

So, P(t) is the population of the city t years since 1992, where t > 0.P(t) will give the city population for a given year if t is equal to that year minus 1992. Example, To find the population of the city in 2012, t would be 2012 - 1992 = 20.P(20) = 101,000e^(0.018 * 20)P(20) = 145,868.63 Rounded to the nearest whole number, the population in 2012 was 145869. Therefore, the exponential growth function in terms of t, where t is the number of years since 1992 is given as:\(P(t)=101000e^{0.018t}\)

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