Suppose that x and y vary inversely, and x = 12 when y = 8 . Write the function that models the inverse variation.

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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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 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?

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.

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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Answer:

I think its two

Step-by-step explanation:

If I am wrong sorry

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:

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

The way to change improper fractions to mixed numbers for kids is solved by using the division operation.

In math the term called fraction is defined as a part of a whole number, and a way to split up a number into equal parts

Here we need to identify the way to change improper fractions to mixed numbers for kids.

As from the definition of fraction we have identified that the way to solve the improper fraction into mixed fraction is written as follows:

Here we have to convert an improper fraction to a mixed number,

Then we have to work out how many whole numbers there are by dividing the numerator by the denominator.

And then we have to make the remainder the new numerator and leave the denominator as it was.

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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

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 :>

Mandy will catch up Rita at 0.5 hour after they start walking.

As per data given are Mandy start = 1, Rita start = 2, Mandy speed = 5 and Rita speed = 2. Based on this explanation we can determine the formula for Mandy time to catch up Rita as follow

s1 = s2

Rita start + Rita speed x t = Mandy start + Mandy speed x t

2 +3 x t = 1 + 5 x t

2 + 3t = 1 + 5t

2 - 1 = 5t - 3t

1 =  2t

t = 0.5 h

Hence, Mandi will catch up with Rita at 0.5h after start.

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The nth partial sum of a geometric sequence can be calculated using the first term a1 and common ratio r as follows: Sn=a1(1−rn)1−r. The infinite sum of a geometric sequence can be calculated if the common ratio is a fraction between −1 and 1 (that is |r|<1) as follows: S∞=a11−r.

In arithmetic, a chain is an enumerated series of gadgets in which repetitions are allowed and order matters. Like a hard and fast, it consists of contributors (additionally referred to as elements, or terms). The quantity of elements (possibly endless) is called the duration of the series.

Unlike a fixed, the same factors can appear a couple of times at distinct positions in a chain, and unlike a fixed, the order does be counted. formally, a chain can be described as a function from herbal numbers (the positions of elements inside the collection) to the factors at each position. The belief of a sequence may be generalized to a listed family, defined as a character from an arbitrary index set.

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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 zeros of the given function y = x²-4 are 2 and -2.

The zeros of a function are defined as the values of the variable of the function such that the function equals 0.

Given is a function, y = x²-4

To find the zeros, equate the function to 0,

x²-4 = 0

x² = 4

x = ±2

Hence, the zeros of the function are 2 and -2.

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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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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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In an experiment, there is a H 0.08 probability that a player will move both two and five spaces during a game.

Player movement during a turn is determined by a spinner. It displays the outcomes of 10 spins.The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities. chances in multiples.

A (1): the probability that a particular occurrence will take place. (2): the proportion of the number of outcomes in a comprehensive set of equally likely options that result in a specific event to the total number of conceivable outcomes. How likely something is to occur is known as its probability. when we are unsure of how an event will turn out.

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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.

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 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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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.

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 slope of the equation 3x + 4y = -12 is -3/4

Slope in math is defined as the ratio of the amount that y increases as x increases some amount

Here we have given the equation 3x + 4y = -12.

As we all know that the general form of the equation of the line is written as,

y = mx + c

here m refers the slope of the line and c refers the y intercept of the line.

Now, we have to convert the given equation into the general form then it can be look like the following,

=> 4y = -12 - 3x

=> y = -12/4 - 3x/4

It can be rewritten as,

=> y = -3x/4 - 12/4

Then the resulting slope is -3/4.

Complete Question:

What is the slope of the equation 3x + 4y = -12?

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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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Answer:

65° or 115°

Step-by-step explanation:

there is no picture but if

mEDB looks like mCDB then its 65°

but if they dont look alike then

180-65=115

straight line is 180°

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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 questions 18, 19, and 20 have the values of x for the bisected angle to be 6, 15, and 8 respectively.

If line UW bisects m∠TUV then;

m∠TUW = m∠WUV

13x - 5 = 7x + 31

13x - 7x = 31 + 5 {collect like terms}

6x = 36

x = 36/6 {divide through by 6}

x = 6

If line MO bisects m∠PMN then;

2(m∠OMN) = m∠PMN

2(2x + 7) = 74 {divide through by 2}

2x + 7 = 37

x = (37 - 7)/2 {make x the subject}

x = 15

If line EF bisects m∠CEB then;

m∠FEB = m∠CEF

10x - 3 = 7x + 21

10x - 7x = 21 + 3 {collect like terms}

3x = 24

x = 24/3 {divide through by 3}

x = 8

Therefore 6, 15, and 8 are the values of x for questions 18, 19, and 20 respectively for the bisected angles.

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