How do you find the Circumcentre of a triangle?.

The solutions of the system are x = 1, y = 2 and z = -1.

And we solve the system with the help of Jordan-canonical form.

A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the numbers.

Given:

A system of equations,

x + y - 2z = 5

-x + 2y + z = 2

2x + 3y - z = 9

In the matrix form;

[tex]\left[\begin{array}{ccc}1&1&-2\\-1&2&1\\2&3&-1\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}5\\2\\9\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}1&1&-2\\0&0&-10/3\\0&1&3\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}5\\10/3\\-1\end{array}\right][/tex]

That means,

x = 1, y = 2 and z = -1.

Therefore, the solutions of the system are x = 1, y = 2 and z = -1.

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Answer: Similar by SAS, and ABC ~ AVU

Step-by-step explanation:

AV = 77 - 66 = 11

AU = 42 - 36 = 6

6/36 = 1/6

11/66 = 1/6

Therefore, these two triangles ABC and AVU are similar by SAS similarity.

ABC ~AVU :>

The degree of the polynomial 5x2 + 4x2 - 7x is 3.

5x2 and x2 are the same power value is 4 and 7x contain the power value 1 so the difference of the degree of polynomial we find is 3. When they don't already, unite all the different phrases in the expression to make it simpler.

The phrases that are not associated with a variable, like 3 or 5, are referred to as constant terms.  The terms associated with the variable are known as coefficients. Either intentionally disregard these terms or check them off the list while looking for the degree of a polynomial.

The polynomial is represented in standard form in this manner. First should be the phrase with the highest exponent, and last should be the word with the lowest exponent. This will enable you to determine which term's exponent has the highest value.

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The distance that light travels in 12.3 nanoseconds is 37.9 meters.
What is speed?
Speed is the rate of change of an object's position relative to a given frame of reference. It is a scalar quantity, meaning it has both magnitude and direction. Speed is usually measured in meters per second (m/s) or kilometers per hour (km/h). Speed is an important factor in many activities, including travel, sports, and transportation.

This can be calculated by multiplying the speed of light (3.0 x 108 m/s) by the time (12.3 nanoseconds), which yields a result of 37.9 meters. This answer is rounded to the correct number of significant figures, which is two.

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The best answer (and only correct answer) among the options given is: option [C]:    y⁻¹ = (x+6) / 3  .

What is the inverse function?

The inverse function returns the original value for which a function gave the output. If you consider functions, f and g are inverse, f(g(x)) = g(f(x)) = x.

Given the original function:  y = 3x - 6 ;

To find the "inverse equation" of said function; we change the "x" to a y"; and the "y" to an "x"; and rewrite:

x = 3y − 6 ;

Now, rewrite in "slope-intercept form" ; or y = mx + b ;

    that is, with y as "single, isolated" variable on the left-hand side of the equation (with an "implied coefficient of positive one", only);  then an "equal sign, then "mx + b" ; in which: "m" is the coefficient of the variable, "x"; and in which "m" refers to the "slope";  and "b" refers to the 'y-intercept".

So, we have the inverse function:

x = 3y − 6  ;  we want to write in slope-intercept form;

Add "6" to each side of the equation:

x + 6 = 3y − 6 + 6 ;

x + 6 = 3y ;  

Rewrite as:   3y = x + 6 ;

Divide EACH side of the equation by "3" ; to isolate "y" one side of the equation; specifically, the left-hand side of equation; and to write in "slope-intercept form:

3y / 3 = (x + 6) / 3  ;

to get:

y = (x + 6) / 3 ;

y = (x/3)  + (6/3) ;

y = (x/3 ) + 2 ;

or;  write as: y = (1/3)x + 2 ;

Now, let us examine the answer choices given:

Note that all the answer choices begin with "y-1" ;

(except "answer choice: [B]" , which begins with "x-1").  This seems confusing; however, in reality, this does not mean, "y minus 1"; or "x minus 1".  Rather, it mean y⁻¹  or x⁻¹  as notation for the "inverse" (not to be confused with the exponent notation.  The confusion stems from the fact that it can be difficult to make such notations on the "Brainly" system.

That being said, we can write the aforementioned "rewritten equations" (see above in THIS VERY ANSWER) as:

y⁻¹ = (x + 6) / 3 ;

y⁻¹ = (x/3)  + (6/3) ;

y⁻¹ = (x/3 ) + 2 ;

or;  write as: y⁻¹ = (1/3)x + 2

That being said:

Therefore, the best answer (and only correct answer) among the options given is:  option  [C]:  y⁻¹ = (x+6) / 3  .

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The cost of one cookie is 1. This value can be determine from the eliminate methods or substitution methods.

As per data given is a two different formula of pizza and cookie, we can determine it by elimination methods or substitution methods. Let do it by elimination methods. As per formula given are first buy 3 pizza + 2 cookie =  6.50 and the second buy 1 pizza + 1 cookie = 2.50. The calculation will be:

3 pizza + 2 cookie =  6.50

1 pizza + 1 cookie = 2.50     multiply with 3 because we want eliminate pizza

3 pizza + 2 cookie =  6.50

3 pizza + 3 cookie = 7.50       -

0 pizza - 1 cookie = - 1

1 cookie = 1

Hence the price of one cookie will cost you 1.

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Answer:

  28.5 m/s

Step-by-step explanation:

Given that power is 1400 W when speed is 25 m/s, and power is proportional to the square of speed, you want the speed when the power is 1820 W.

Since power is proportional to the square of speed, the ratio of speed squared to power is a constant:

  s²/P = 25²/1400 = x²/1820

where x is the unknown speed.

We can find the value of x by multiplying by 1820 and taking the square root:

  x² = 25²(1820/1400)

  x = 25√(1820/1400) = 25√1.3 ≈ 28.5 . . . . m/s

The speed is 28.5 m/s when the power is 1820 watts.

The new coordinates after reflection will be (4,2) (-2,1) (-1,-3).

A reflection is a type of transformation that involves flipping a shape, known as the preimage, across a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you turned the form across the line to graph a reflection.

The general guidelines for the reflection over x-axis equation are as follows: The reflection equation of the new reflected graph will be y=f(x) y = f (x) given an equation, y=f(x) y = f (x). In other words, the function is just multiplied by 1, which results in a curve that crosses the x-axis.

The new coordinates after reflection will be -

(4,2) (-2,1) (-1,-3)

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Answer:

D- 5hrs

Step-by-step explanation:

If the family can hike 3 miles per hour,
for 15 miles: 15/3 = 5 hours.

Every hour they cover 3 miles per hour, so to cover 15 miles, they will take 5 hours

Answer:

D. 5 hours

Step-by-step explanation:

3 miles per 1 hour so 3/1

15 miles per x hours so 15/x

3/1 = 15/x or 3 = 15/x

get x by itself so

3 divided by 3 and 15 divided by 3

x = 5 hours

Answer: Number 3, which is √73

Step-by-step explanation:

Use the distance formula:

Distance (d)

= √(8 - 0)2 + (3 - 0)2

= √(8)2 + (3)2

= √73

= Number 3 :>

A perfect square trinomial is a polynomial of the form (x + b)^2 = x^2 + 2bx + b^2. It is called a "perfect square" because when it is multiplied out, the resulting polynomial is a square of a binomial.

To find the perfect square trinomial of 36, we need to find two numbers that when added, give us b and when multiplied give us b^2=36.

Those two numbers are 6 and -6, since 6*-6 = -36 = 36.

So, the perfect square trinomial of 36 is (x + 6)(x - 6) = x^2 - 36

Another way to find the perfect square trinomial is to take the square root of the constant term (36) and then add and subtract that value to the variable.

√36 = 6

then x^2 + 6x - 6x + 36 = x^2 - 36

So, the perfect square trinomial of 36 is x^2 - 36.

[tex]36[/tex] is the square of [tex]6[/tex]. The square of a binomial is called a perfect square trinomial. [tex]X^2+12x+36[/tex] is a perfect square trinomial.

The credit utilization ratio would be 11.7%.

What is credit utilization?

The credit utilization ratio is a measure of how much of a person's credit limit is being used. It is calculated by dividing the total credit card balances by the total credit limit.

In Mary's case, the total credit card balances are $150 + $200 = $350

The total credit limit is $2000 + $1000 = $3000

To find the credit utilization ratio, we divide the total credit card balances by the total credit limit:

$350 / $3000 = 0.117 or 11.7%.

Hence, the credit utilization ratio would be 11.7%.

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The equation y = 400x represents the relationship as shown in the table.

The correct option is table d.

What is the proportional relationship?

A proportional relationship is a relationship between two expressions, where changes in one expression mean some constant change in another expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.

Given:

A table is shown in the attached image.

To find the relationship:

We will find the common ratio,

y/x = k, where k is the proportionality constant,

400/1 =400

800/2 = 400

1200/3 = 400.

That means, the equation is,

y = 400x

Therefore, y = 400x is the equation.

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The complete question is given in the attached image.

Step-by-step explanation:

g(x) = - x² + 10x - 3

To get the g(9) substitute X in the equation for 9

g(9) = - 9² + 10(9) -3

g(9) = 81 + 90 - 3

g(9) = 171 - 3

g(9) = 168

Similarly to get g(-1)

g(-1) = - (-1)² + 10(-1) - 3

g(-1) = - 1 - 10 - 3

g(-1) = - 14

The distance on the map, in centimeters, that represents an actual distance of 4 kilometers, is 3. 2 cm

The map is such that the scale is 4 cm on the map, equals 5 km on the ground.

If we have a distance of 4 km therefore, the distance on the map would be:

= ( Distance on ground x scale on map ) / Kilometers on scale

= ( 4 x 4 ) / 5

= 16 / 5

= 3. 2 cm

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Full question is:

Scale of a map says that 4 cm represents 5 km. What distance on the map (in centimeters) represents an actual distance of 4 kilometers?

Answer:To find the unit rate in chapters per hour, we need to divide the number of chapters read by the amount of time it took to read them.

6 3/4 chapters / 1 7/8 hours = (64+3)/(18+7) chapters/hours

= (25/8) chapters/hours

To simplify this fraction, you can divide both the numerator and denominator by their greatest common factor which is 1.

25/8 chapters/hours = (25/8) chapters/hours

So the unit rate in chapters per hour is 25/8 chapters per hour.

Step-by-step explanation:

The examples of logarithmic equation are 625 = [tex]5^{4}[/tex] and 4 = [tex]log_{5}625[/tex], 100000 = [tex]19^{5}[/tex] and 5 = [tex]log_{19}100000[/tex] .

To generate a given number, a base must be raised to a particular exponent, power, or logarithm. The time needed to multiply numbers with numerous digits was drastically decreased thanks to the logarithms, which were developed in the 17th century to speed up calculations.

For more than 300 years, they served as the foundation for numerical labor, but the development of mechanical adding machines in the late 19th century and computers in the 20th century made them obsolete for large-scale calculations.

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The limit of sum formula is Sn=a(1−rn)1−r,for r≠1.

Consider a curve that lies above the x-axis. This graph's function is a continuous function with all of its values being non-negative, defined on the closed interval [a, b]. The definite integral ab f(x) dx of any such continuous function "f" is the region bound between the curve, the points "x = a" and "x = b," and the x-axis.

On the interval [a, b], the definite integral of a real-valued function f(x) with respect to a real variable x is written as,

[tex]\int\limits^b_a {f(x)} \, dx = F(b)-F(a)[/tex]

∫ = Integration symbol

a = Lower limit

b = Upper limit

f(x) = Integrand

dx = Integrating agent

A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit.

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The intensity of an earthquake generally higher near the epicenter.

Intensity is based on observed effects of ground motion on people, buildings and natural features. This varies from site to site within the fault region, depending on the observer's position relative to the earthquake epicenter. The seismic intensity of an earthquake decreases as the distance from the epicenter increases, and decreases as the distance from the epicenter increases. An epicenter is a point on the surface of the Earth directly above where an earthquake begins. Earthquakes with a moment magnitude of approximately 6.5 or less occur in a concentrated area directly below the epicenter. Therefore, apart from the effects of different rock types and different soil types, the greatest shaking occurs at the epicenter. Earthquakes with a moment magnitude greater than 6.5 cause faults at some distance from the epicenter. At these large sizes, it is common for fractures to reach the surface. In such cases, the maximum shaking may or may not occur at the epicenter..

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The first step for solving the system using substitution results in an equation is solve one equation for either x or y.

The substitution method is a quick and easy way to algebraically solve a set of linear equations and determine the variables' solutions. According to what the name implies, this method entails determining the value of the x-variable in terms of the y-variable from the first equation and then substituting or replacing the value of the x-variable in the second equation.

We can solve and determine the value of the y-variable in this method. Finally, we may use any of the above equations to obtain x by substituting the value of y. This procedure can also be switched around so that we first solve for x before solving for y.

If we take an example ,

Equation 1:  3x + 2y = 11

Equation 2:  -x + y = 3

Substituting y = 3+x in equation 1 is the first step in the equation.

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Erika should use the coupon which gives her a discount of 15% as it will bring down the cost of the cooler to $106.25.

Given,

          The initial cost of the cooler = $125

Erika has two options: (i) 15% off coupon

                                     (ii) $15 off coupon

Cost of the cooler that Erika gets from option (i):

                                [tex]= 125 - \frac{15}{100} * 125\\= 125 - 18.75\\= 106.25\\[/tex]

Cooler costs $106.25 to Erika from option (i).

Cost of the cooler that Erika gets from option (ii):

                                [tex]= 125 -15\\=110[/tex]

Cooler costs $110 to Erika from option (ii).

We can clearly see, $106.25 < $110

Therefore, Erika should use the coupon which gives her a discount of 15%.

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Sam is now 187cm tall. When we say that Sam is now 7% taller, it means that his new height is 7% greater than his original height.

To find out how much taller he is, we can calculate 7% of his original height using the percentage formula:

percentage of original value = (part / whole) * 100

In this case, the part is the increase in height, and the whole is the original height. To find the part, we can rearrange the formula to:

part = (percentage / 100) * whole

So, to find the increase in height, we can substitute the values we know:

increase in height = (7 / 100) * 175 cm

This simplifies to:

increase in height = 12.25 cm

Now that we know how much taller Sam is, we can add this increase to his original height to find his new height:

new height = original height + increase in height

new height = 175 cm + 12.25 cm = 187.25 cm

So, Sam is now 187.25 cm tall. This number is rounded to the nearest centimeter, so his new height is 187cm tall.

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Answer:

$50678.73

Step-by-step explanation:

Answer:

103,078.73.

Step-by-step explanation:

Amount after n years = P(1 + r/100)^n       where P is amount invested, r is the percentage rate and n = number of years.

So, here we have:

Total after 10 years = 52400(1 + 7/100)^10

= 52400 * 1.967151357

= 103,078.73.

By using the diagram, each of the sentence should be completed as follows;

In Mathematics, the exterior angle theorem can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle.

By applying the exterior angle theorem, we can reasonably infer and logically deduce that the sum of the measure of both angle 2 and angle 3 in the given triangle is equal to the measure of angle 1 (∠1);

∠2 + ∠3 = ∠1

By applying the Linear Pair Postulate to the two angles formed at a point, we have the following:

∠1 + ∠4 = 180°

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Answer:

y > 7x

Step-by-step explanation:

(5xy)/7        [5 x y over 7]

["what value of y would make a product greater than 5 ?​"] can be written as:

(5xy)/7 > 5

Rearrange to find y:  

 (5xy)/7 > 5

  (5xy) > 35

   y > 35/5x

y > 7x

Answer:

24 a b c d

Step-by-step explanation:

whyats the answert

Answer:[tex]d\leq 5[/tex]

[tex]24d+20\leq 140[/tex]

Step-by-step explanation: First You do 200x0.10 which equals 20. then you put the cost per day first so 24 per day + the cost of all miles which is 20 at most means she can also spend less then 380 so we use the greater than equal symbol.

Properties of irrational number:

Here, The definition of irrational number:

An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio. If N is irrational, then N is not equal to p/q where p and q are integers and q is not equal to 0. Example: √2, √3, √5, √11, √21, π(Pi) are all irrational.

The following are the properties of irrational numbers:

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The mirror image is (4, 46) is (4, -46)

The term mirror image is defined as it is like a reflection of it either because it is exactly the same or because it is the same but reversed.

Here we have given the point (4, 46) and here need to mirror image of the points.

The rule Mirror image of (x , y ) in the x - axis is written as  ( x , -y)

Here we have the value of x as 4 and the value of y as 46.

Here we also know that it is defined as a reflected duplication of the number that appears almost identical but is reversed in the direction perpendicular to the mirror surface.

When we apply the values on the formula then we get the mirror image as (4, -46).

Complete Question:

What is the mirror image of the coordinate (4, 46)?

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Answer:

see picture

Step-by-step explanation:

Factorise for 12[tex]x^{2}[/tex]+15xy-9x is 3x (4x+5y−3)

Solution steps:

The first step is to factor out 3.

So,

3 (4[tex]x^{2}[/tex]+5xy-3x)

The second step is to consider 4[tex]x^{2}[/tex]+5xy−3x. Factor out x.

So,

x (4x+5y−3)

The third step is to rewrite the complete factored expression.

3x (4x+5y−3)

Evaluate:

3x (4x+5y−3)

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