Reggie made a scale drawing of a house. In real life, the garage is 3 meters wide. It is 6 millimeters wide in the drawing. What is the drawing's scale factor?

The system y = 3x + 4 and 6x - 2y = 8 has no solutions.

A system of equations is a set of equations with multiple variables. To determine the number of solutions for a system of equations, one can use the following methods: graphing, substitution, or elimination. In this case, we can use the elimination method by adding or subtracting the equations to eliminate one of the variables.

If we add the two equations, we get y = 3x + 4 + 6x - 2y = 8, which results in 3x + 4 = 8. This is an inconsistent equation and does not have any solutions. Therefore, the system y = 3x + 4 and 6x - 2y = 8 has no solutions.

This shows that the system is inconsistent, which means that there's no solution that satisfies both equations.

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A 30-60-90 triangle is a right triangle where the three interior angles are 30°, 60°, and 90°.

Let, the shorter leg of a 30 60 90 triangle is equal to a. Then:

If we know the shorter leg length, we can find out that:

In the 30 60 90 triangles :

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The difference of the two polynomials (9x² + 8x) - (2x² + 3x) is 7x² + 5x.

To find the difference of these two polynomials, we need to subtract the second polynomial from the first. This is done by subtracting each term of the second polynomial from the corresponding term of the first polynomial. In this case, we have:

So, the difference of the two polynomials (9x² + 8x) - (2x² + 3x) is 7x² + 5x.

The terms that are being subtracted are the terms that have the same degree, meaning the same exponent of the variable.

It's worth noting that the order of subtraction doesn't change the result and that we can subtract polynomials of any degree and size, and it will work the same way.

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The probability that exactly 4 cars will enter the car wash in an hour is 0.195

Generally, This is a Poisson process, where the mean number of cars entering the car wash is 4 cars per hour. The probability of exactly 4 cars entering in an hour is given by the Poisson probability mass function:

P(X = 4) = (e^(-4) * 4^4) / 4!

where e is approximately 2.71828, and 4! is

4 * 3 * 2 * 1 = 24.

Plugging in the values, we get:

P(X = 4) = (2.71828^(-4) * 4^4) / 24

P(X = 4) =0.195

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The probability of choosing  a shade of blue and carpet is 1/6 greater than that of choosing a shade of yellow and wood flooring.

The total number of possible paint colors Daria can choose is 5 shades of blue + 2 shades of yellow + 2 shades of purple = 9 shades

The total number of flooring options Daria can choose from is carpet or wood = 2 options

The probability of choosing a shade of blue is 5/9 and the probability of choosing carpet is 1/2. So, the probability of choosing a shade of blue and carpet is (5/9) * (1/2) = 5/18.

The probability of choosing a shade of yellow is 2/9 and the probability of choosing wood flooring is 1/2. So, the probability of choosing a shade of yellow and wood flooring is (2/9) * (1/2) = 2/18

The probability of choosing a shade of blue and carpet is 5/18, and the probability of choosing a shade of yellow and wood flooring is 2/18. So, the probability of choosing a shade of blue and carpet is (5/18) - (2/18) = 3/18 or 1/6 greater than the probability of choosing a shade of yellow and wood flooring.

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The statement that correctly describes the graph is given as follows:

C. The graph represents a linear function with a constant rate of change.

A function is classified as linear or non-linear depending on the rate of change of the function.

If the rate of change of the function is constant, that is, when x changes by one amount, y always changes by the same amount, then the function is classified as linear.

Conversely, if the rate of change of the function is different for different intervals, then the function is classified as non-linear.

As the graph presented at the end of the answer shows a linear function with constant slope, it has a constant rate of change, thus it is linear and option c is correct.

The graph is given by the image presented at the end of the answer.

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If the ratio of cars to truck in Main Street Auto Leasing  Company is 9 to 4 and in the airport Auto Leasing Company is 5 to 3 , then the Main Street Auto Leasing Company has more number of cars .

The Ratio of cars to truck in Main Street Auto Leasing Company is = 9:4 ;

the ratio of cars to truck in Airport Auto Leasing Company is = 5:3 ;

the number of trucks in each Leasing Company is = 24 trucks ;

Case (i)  : Main Street Auto Leasing Company  ;

Since the ratio is = 9:4 ,

So , the number of cars is = 9x   and

the number of trucks = 4x ;

That means , [tex]4x = 24[/tex] ;

[tex]x = 6[/tex] ;

the number of cars in Main Street company is = [tex]9 \times 6[/tex] = 54 cars .

Case (ii) : Airport Auto Leasing Company ;

the ratio is = 5:3 ;

So , the number of cars is = 5x   and

the number of trucks = 3x ;

That means , [tex]3x = 24[/tex] ;

[tex]x = 8[/tex] ;

the number of cars in Airport Auto company is = [tex]5 \times 8[/tex] = 40 cars .

Therefore , the Main Street Auto Leasing Company has more  number of Cars .

The given question is incomplete , the complete question is

Main Street Auto Leasing has a ratio of cars to trucks that is 9 to 4. Airport Auto Leasing has a ratio of cars to trucks that is 5 to 3. If each leasing center has 24 trucks, which auto leasing company has more cars ?

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The probability of each of your three friends having an ace is 32%.

The probability of each of your three friends having an ace is calculated using the Binomial Probability Formula. The formula is P(x) = nCr * p^x * (1-p)^(n-x). Here, n = 13 (number of cards dealt to each person) , r = 1 (number of aces you want to calculate the probability of), p = 4/52 (probability of getting an ace from a deck of 52 cards) and x = 1 (number of aces each of your three friends have).

Therefore, the probability of each of your three friends having an ace is P(x) = 13C1 * (4/52)^1 * (48/52)^(13-1) = 0.32.

This means that the probability of each of your three friends having an ace is 32%.

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The light cream milk product have approximately 15.36 grams of milk fat in an 80-gram serving.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Let n be the percentage of milk product to have approximately 15.36 grams of milk fat in an 80-gram serving.

Using percentage formula,

15.36 = n x 80 / 100

n = 1536 / 80

n = 19.2%

Therefore, the product is light cream milk.

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Since Mary and Max are playing a game with complex numbers, Max's score must be equal to 1/(3 + 2i), so that the product of their score is one.

A reciprocal function simply refers to a type of function which comprises a constant on its numerator and an algebraic expression or complex number in its denominator such as: f(x) = 2/3 + 7i.

In Mathematics, a reciprocal function is typically used when describing relationships that are inversely proportional to one other.

Let the variable n represent Max's score. Therefore, a mathematical expression which models the product of both Mary and Max's score is given by the following:

Product = 3 + 2i × n = 1

Making n the subject of formula, we have the following as Max's score;

n = 1/(3 + 2i)

Check:

3 + 2i × 1/(3 + 2i) = 1

(3 + 2i)/(3 + 2i) = 1

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The linear expression that is not equivalent to the other three is D) (-5x-1)+(6x + 7).

A linear expression is an algebraic expression which is composed of constants, variables, and coefficients that are related by only addition and multiplication operations. It usually takes the form of ax + b, where 'a' and 'b' are constants and 'x' is a variable. Linear expressions can be used to describe various mathematical and physical phenomena, such as the slope of a line or the volume of a cylinder.

This linear expression is not equivalent to the other three because it does not have the same coefficient for the x terms and the constant terms. The other three expressions all have the same coefficients for the x terms and the constant terms, making them equivalent.

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The diameter of the circle C/13

The formula provides the circumference of a circle.

The circumference of any shape in mathematics designates the path or limit that surrounds the shape. In other words, the circumference, sometimes referred to as the perimeter, aids in figuring out how long the contour of a shape is. The size and perimeter of a circle are, as we all know, its two most important properties.

C = pi * d, where d is the diameter and c is the circumference.

C = pi * 13 gives the diameter as 13.

Subtract 13 from each side, C/13 = d.

Dimensions are C/13.

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The equation is y = 2x and the constant of variation k = 2

Therefore, the correct answer is option d.

Here, we can clearly see that y varies directly with x, because as x increases, y increases with the same proportion and vice versa. The constant of variation, k, is the coefficient of proportionality between x and y. To find the constant of variation, we can divide the value of y by the value of x for any one of the given points.

For example, for the point (-2, -4) we have:

k = -4 / -2 = 2

So the equation relating x and y is: y = kx = 2x

Hence, the equation is y = 2x and the constant of variation k = 2

Therefore, the correct answer is option d.

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The complete question is -

Determine whether y varies directly with x. If so, find the constant of variation and write the equation.

x | y

-2 | -4

-4 | -8

-16 | -32

a. No

b. yes; k=-2 and y=-2x

c. yes; k=1/2 and y=1/2x

d. yes; k=2 and y=2x

The two types of units that are used for the angle measurements are (d) degrees and radians .

The two types of Units of Measurements are Radians and Degrees ,

The unit Degrees is used to measure the direction and angle size. If the object is facing north, then the object is said to be at 0°. If the object turn the opposite direction to face south, then the object turned 180°.

A full circle comprises of 360 degree .

The Radian is an S.I. unit of measuring the angles , one radian is defined as angle made at center of a circle by an arc whose length is equal to radius of circle.

The value of 1 radian is approximately equal to 57.296 degree .

The given question is incomplete , the complete question is

What are two types of angle measurements ?

(a) metrics and radians

(b) radians and metrics

(c) degrees and metrics

(d) degrees and radians

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On solving the provided question, we can say that - by the help of unitary method seconds will it take her to reach a depth of 79ft is = 39.5

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

here,

scuba diver is at a depth of  = -14 ft

elevation changes  = -2 ft per second.

seconds will it take her to reach a depth of 79ft is = 39.5

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Answer:12m,8m

Step-by-step explanation:BREAADTH

The value of each trigonometric ratio is given by :

sin A = 5/13 , cos A = 12/13, tan A = 5 / 12

cosec A = 13 /5 , sec A = 13/12 , cot A = 12 /5.

As given in the question,

Let us consider a triangle be ABC,

Figure is attached.

Side length is given by:

AC = 39

AB = 36

BC = 15

AC represents the longest side

( 36 )² + (15)² = (39)²

⇒AB² + BC² = AC²

By Pythagorean triplets ABC is right angled triangle.

All trigonometric ratio with respect to angle A is given by :

sin A = BC / AC

        = 15/39

        = 5/13

cos A = AB / AC

         = 36 /39

         = 12 /13

tan A = BC / AB

         = 5 /12

cosec A = 1/ sin A

              = 13 /5

sec A = 1/ cos A

         = 13 /12

cot A = 1 / tan A

         = 12 /5

Therefore , the value of all six trigonometric ratio is equal to

sin A = 5/13 , cos A = 12/13, tan A = 5 / 12

cosec A = 13 /5 , sec A = 13/12 , cot A = 12 /5.

The above question is incomplete , the complete question is :

Find the value of each trigonometric ratio tan A

Figure is attached.

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The four equations of uniformly accelerated motion are:

[tex]v = u + at\\s = ut + (1/2)at^2\\v^2 = u^2 + 2as\\v = u + 2as/t[/tex]

Uniformly accelerated motion is motion in which the acceleration is constant. The four equations of uniformly accelerated motion are:

These equations are derived from the basic kinematic equations of motion which relate velocity, acceleration, distance and time.

The first equation is a result of the definition of acceleration.

The second one is derived from the first equation and the definition of distance.

The third one is derived from the first and second equation by squaring the first equation and then solving for v^2.

The fourth equation is derived by dividing the distance traveled by the time taken.

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Answer:

see explanation

Step-by-step explanation:

there is a common ratio between consecutive terms, that is

12 ÷ 6 = 24 ÷ 12 = 48 ÷ 24 = 96 ÷ 48 = 2

this indicates the sequence is geometric

the nth term of a geometric sequence is

f(n) = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 6 and r = 2 , then

f(n) = 6 [tex](2)^{n-1}[/tex]

Therefore, N2 and 2N are not equal, they are different mathematical expressions.

A finite collection of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.

A mark, sign, or term that denotes, denotes, or is taken to denote a concept, an item, or a connection is known as a symbol. By connecting seemingly unrelated ideas and events, symbols let individuals look beyond the known and the visible.

No, N2 and 2N are not the same.

N2 is the square of N, which means it is N multiplied by itself. For example, if N = 5, then N2 = 5*5 = 25.

2N, on the other hand, is N multiplied by 2. For example, if N = 5, then 2N = 5*2 = 10.

So, N2 and 2N are not equal, they are different mathematical expressions.

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The sum of length of the parallel sides of a trapezium exists 300 cm.

A trapezoid, which is often referred to as a trapezium, is a flat, closed object with four straight sides and one set of parallel sides. A trapezium's parallel bases and non-parallel legs are referred to as its bases and legs, respectively. Also possible are parallel legs on a trapezium.

Four sides, four corners/vertices, and four angles make up a trapezium, which is a closed shape or polygon. A trapezium has parallel sides on each of its opposing angles.

One set of the sides of a trapezium is parallel only. Since no trapezium is a rectangle, they are not all the same.

Area of trapezium = (a + b)/2 × h

where h is the perpendicular height, and a and b are parallel sides.

So, (a + b) exists sum of length of bases of a trapezium.

Let the equation be

Area of trapezium = (a + b)/2 × h

substitute the values in the above equation, we get

⇒  4.2 × 100² = (a + b) / 2 × 280 {1 m = 100 cm}

simplifying the equation, we get

⇒ (84/280) × 10000 = a + b

⇒ a + b = 300 cm

Therefore, the sum of length of the parallel sides of a trapezium exists 300 cm.

The complete question is:

Find the sum of length of the parallel sides of a trapezium whose area is 4.2 m² and whose height is 280 cm.

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The sum of length of the parallel sides of a trapezium exists 300 cm.

A trapezoid, also known as a trapezium, is a closed, flat object with one pair of parallel sides and four straight sides. The parallel bases and the non-parallel legs of a trapezium are called the bases and the legs, respectively. A trapezium with parallel legs is another option.

A trapezium is a closed shape or polygon with four sides, four corners, and four angles. Each of the opposing sides of a trapezium has parallel sides.

A trapezium has only one set of parallel sides. They are not all the same since no trapezium is a rectangle.

Area of trapezium = (a + b)/2 × h

where h is the perpendicular height, and a and b are parallel sides.

So, (a + b) exists sum of length of bases of a trapezium.

Let the equation be

Area of trapezium = (a + b)/2 × h

substitute the values in the above equation, we get

⇒  4.2 × 100² = (a + b) / 2 × 280 {1 m = 100 cm}

simplifying the equation, we get

⇒ (84/280) × 10000 = a + b

⇒ a + b = 300 cm

Therefore, the sum of length of the parallel sides of a trapezium exists 300 cm.

The complete question is:

Find the sum of length of the parallel sides of a trapezium whose area is 4.2 m² and whose height is 280 cm.

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By using the unitary approach to answer the given question, we may conclude that total 28 + 40 = $68.

The unit technique is a strategy for addressing issues that entails first figuring out the value of a single unit, then multiplying that value to figure out the needed value. Simply expressed, the unit technique is used to extract a single unit value from a multiple that is provided. For example, 40 pens would cost 400 rupees, which is equal to the cost of one pen. This procedure could follow a regular procedure. a single nation. something has a distinct identity. Its adjoint and reciprocal are equal in terms of mathematics, algebra, linear algebra, mathematical analysis, or mathematics of matrices or operators.

One package of chicken costs  = $7

steaks cost  = $4 per pound.

cost of 4 chicken = 4 * 7 < $28

cost of 10 steaks = 4*10 < $40

total 28 + 40 > $ 68

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Marla is 30 years old.

Let marla age be x and Darla age be y

Given : Marla is four years less than twice as old as Darla

What is equation ?

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Marla is four years less than twice as old as Darla can be represented as : 2y - x = 4

sum of their ages is 47 can be represented as : x + y = 47

Solving both the equation using addition we got ,

3y = 51

y = 17

Substituting the value of y in x + y =47 , we get

x + 17 = 47

x = 47 -17

x = 30

Hence , Marla is 30 years old.

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The elimination method is used for solving linear equations. Here we make use of the addition property of equality, that is when same number is added on both sides of equation, it still remains equal.

Lets look into some examples.

     x + y = 10  

      x - y = 2

By adding both equations,

     x + y + x - y = 10 + 2

 + y and - y are cancelled or y term is eliminated.

      2x = 12

       x  = 6

     2x + 3y = 10

   -3x + 3y  = 15

Here to eliminate y, we have to add the additive inverse of second equation.

  2x + 3y + 3x - 3y = 10-15

    5x = -5

      x = -1

   x + 4y = 5

   3x - y = 2

To equalize the y term we multiply the second equation by 4

   12x - 4y = 8

Adding both equations,

x + 4y + 12x - 4y = 5 + 8

13x = 13

x = 1

So elimination method is used for solving linear equations.

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The sum of Annie's, Bobby's, Ciro's, and Denise's answers is $ 1140.1.

A number is simplified when it is rounded off, preserving its value while moving it closer to the next number. It is done for whole numbers as well as decimals at various places of hundreds, tens, tenths, etc.

If the number following the decimal is between 0 and 4, a number may be rounded off to its lowest value. If the number after it is between 5 and 9, the number will be rounded off to a greater value.

Annie rounds $ 280.05 to the nearest hundred

$ 280.05 will be equal to $ 300

Bobby rounds $ 280.05 to the nearest ten

$ 280.05 will be equal to = $ 280

Ciro rounds $ 280.05 to the nearest integer

$ 280.05 will be equal to = $ 280

Denise rounds $ 280.05 to the nearest tenth

$ 280.05 will be equal to = $ 280.1

Then, the sum of Annie's answer, Bobby's answer, Ciro's answer, and Denise's answer = $ 300 + $ 280 + $ 280  + $ 280.1 = $ 1140.1

Therefore,

The sum of Annie's, Bobby's, Ciro's, and Denise's answers is $ 1140.1.

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The values of x are 16, 15, and 13 respectively after balancing equations 19 - 17 = x - 13, 18 - x = 19 - 16, and 17 - 12 = 18 - x.

It is thought that a number's simplest form is represented by its smallest equivalent fraction. finding the simplest form: what to do. For shared factors, look into the numerator and denominator. Examine a fractional integer to determine if it is a prime number. An equation is a statement that has two equal sides and an equal sign in the middle. In the general form of any equation, the degrees of all the variables are listed in descending order. The common representation of a linear equation is an x + b = 0. x + b y + c = 0 is the general form of a two-variable linear equation (or something similar). Identity or conditional equations are the two categories under which equations fall. An identity holds true regardless of how the variables are valued.

given

balancing equations

a) 19 - 17 = x - 13

x = 16

b ) 18 - x = 19 - 16

x = 15

c) 17 - 12 = 18 - x

x = 13

The values of x are 16, 15, and 13 respectively after balancing equations 19 - 17 = x - 13, 18 - x = 19 - 16, and 17 - 12 = 18 - x.

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A reflex angle is an angle which measures more than 180 degrees and less than 360 degrees.

There are different types of angles in geometry, such as obtuse, acute and right angles, which all are under 180 degrees.

Assume, z is an acute or obtuse angle, and r is the reflex angle, then:

z + r = 360

r = 360 - z

Therefore, we can find the related reflex angle(r), if we know the value of the acute or obtuse angle(z).

A reflex angle equals the summation of 180 degrees and any of the primary angles (acute, right and obtuse angles). Therefore,

Reflex angle = 180° + Acute angle

Reflex angle = 180° + Right angle

Reflex angle = 180° + Obtuse angle

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The expression determines the quantity of water leaving the tank per hour is (18 1/2 gallons)/(4 1/4 hours)

Rate is the ratio of a certain number of units of one quantity to units of another quantity. Mathematically, rate is one quantity divided by the other quantity.

If a total of 18 and one-half gallons flowed out of the tank in 4 and one-fourth hours. We can write that the rate as follows:

rate = (18 1/2 gallons)/(4 1/4 hours)

rate = 4 6/17 gallons per hour

Thus, the expression determines the quantity of water leaving the tank is (18 1/2 gallons)/(4 1/4 hours)

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Equivalent fractions are those that, despite their visual differences, reflect the same value. we consumed half of a cake, for instance, if you have one, divide it into two equal pieces, and then eat one of the pieces.

Any number of equal portions, or parts of a whole, are described by fractions. Fractions in standard English indicate the number of pieces of a specific size. 8, 3/4 of .Part of an entire is a fraction. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. When a fraction is true, its numerator is smaller than its denominator.

If the denominators differ, similar fractions with a common denominator must be used. This requires figuring out the LCM of the two denominators. To be used as a denominator in fractions with various denominators, rename the fractions with a similar denominator.

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