Find all points (a, b, c) in space for which the system has at least one solution.
x + 2y + 3z = a
4x + 5y + 6z = b
7x + 8y + 9z = c

The function that maps the  trapezoid FGHI to trapezoid F'G'H'I' is

B. (x, y) → (1/2 x - 5, 1/2 y)

The change of shape as seen in the two objects was reduction in size and  linear movement to the left.

The reduction is size is reduction by half and this is dilation with a scale factor of 1/2. This is represented by the formula

(x, y) → (1/2 x, 1/2 y)

Then linear movement to the left is translation to the left and this id 5 units to the left. The formula to show this as below

(x, y) → (1/2 x - 5, 1/2 y)

This is equivalent to B and hence the correct option

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The number of hours Natalie worked babysitting last week is 6hrs and the number of hours she worked landscaping last week is 2 hrs.

Let x be the number of hours Natalie worked babysitting and y be the number of hours she worked landscaping. Then, the total earnings were 11x + 10y = $86.

Also, x = 3y, because she worked 3 times as many hours babysitting as she did landscaping.

Substitute x = 3y into the first equation:

11(3y) + 10y = $86

Expanding the first term we get,

33y + 10y = $86

Combining terms,

43y = $86

Dividing both sides by 43 we get,

y = $2

So, Natalie worked y = 2 hours of landscaping.

To find the number of hours she worked babysitting, substitute y = 2 into x = 3y as follows -

x = 3(2) = 6

So Natalie worked x = 6 hours babysitting.

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Superior segway tours provide sightseeing tours around chicago, illinois. it charges a one-time fee of $55 with $15 per hour.  The slope of the situation is 15.

The slope of a situation represents the rate of change of one quantity with respect to another. In this case, the quantity being considered is the cost of the sightseeing tour, and the independent variable is the number of hours the tour lasts. The cost of the tour can be expressed as a linear equation: C = 55 + 15h, where C is the cost and h is the number of hours. The slope of this equation is 15, meaning that for every hour the tour lasts, the cost increases by $15.

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The probability that a student chosen at random plays both football and cricket is 7/20.

The probability that a student chosen at random plays both football and cricket can be found by using the formula for conditional probability:

P(football and cricket) = P(football | cricket) * P(cricket), where P(football | cricket) is the probability of playing football given that the student plays cricket, and P(cricket) is the probability of playing cricket.

Out of the 21 students who play cricket, 14 of them play football as well, so P(football | cricket) = 14/21.

The probability of playing cricket is P(cricket) = 21/40 since there are 40 students in total and 21 of them play cricket. So, the probability that a student chosen at random plays both football and cricket is P(football and cricket) = (14/21) * (21/40) = 14/40 = 7/20.

Therefore, the main answer is the probability that a student chosen at random plays both football and cricket is 7/20.

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Correct question:

In a class, there are 10 students who play football and cricket

7 who do not play football or cricket

14 students who play football

21 students who play cricket

find the probability that a student chosen at random plays football and cricket.

Three student that hare a townhouse find that their electric bill for October, each owe in September is amount $20.31.

Let amount that September's bill was, be S

Then October's bill was: S - $2.32

Therefore, we get: S + S - 2.32 = 119.56

2S - 2.32 = 119.56

2S = 119.56 + 2.32

2S = 121.88

S, or September's bill was: 121.88/2 or $60.94

Amount each owed for September: 60.94/3 = $20.31

We consume electricity produced for our use by a corporation whenever we switch on a light, plug in a device, or let our refrigerator run. You can purchase this company's electricity by the Kilowatt-hour to power your home. When the firm requests payment for the electricity you consumed, they send a letter outlining the amount of electricity you consumed, the rates they charge, and the amount owed to the company.

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For Z/6Z and Z/7Z, the multiplication tables are 1-5 and 0 and 1-6 and 0 correspondingly. The elements 1, 2, 3, 4, 5 and 1, 3, 5, 6 respectively have multiplicative inverses.

The multiplication table is as follows for the group Z/6Z:

1 * 1 = 1\s2 * 1 = 2\s3 * 1 = 3\s4 * 1 = 4\s5 * 1 = 5\s0 * 1 = 0

1, 2, 3, 4, and 5 are the elements with multiplicative inverses.

The multiplication table is as follows for the group Z/7Z:

1 * 1 = 1\s2 * 1 = 2\s3 * 1 = 3\s4 * 1 = 4

5 * 1 = 5\s6 * 1 = 6\s0 * 1 = 0

1, 3, 5, and 6 are the elements with multiplicative inverses.

The group members in a group Z/NZ are the remainders after dividing the integers by N. For instance, the elements in Z/6Z are 0, 1, 2, 3, 4, and 5. The product of each element is shown in the multiplication table.by itself when multiplied. The multiplication table for Z/6Z is as follows: 0 * 1 = 0; 1 * 1 = 1, 2 * 1 = 2, 3 * 1 = 3, 4 * 1 = 4, 5 * 1 = 5. 1, 2, 3, 4, and 5 are the elements with multiplicative inverses. The multiplication table is also the same for Z/7Z: 1 * 1 = 1, 2 * 1 = 2, 3 * 1 = 3, 4 * 1 = 5, 6 * 1 = 6, 0 * 1 = 0. 1, 3, 5, and 6 are the elements with multiplicative inverses.

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The 'e' value of 6e12 means 6 x 10^12, which is equal to 6000000000000. It is a scientific notation used to represent a very large number.

The 'e' value of 6e12 is a scientific notation used to represent a very large number. 6e12 is shorthand for 6 x 10^12, which means 6 multiplied by 10 to the power of 12. To calculate the value of 6e12, first note that 10 to the power of 12 is equal to 1000000000000. Then, multiply 6 by 1000000000000 to get 6000000000000. Therefore, 6e12 is equal to 6000000000000. This notation is commonly used to represent very large numbers without having to write out all of the zeros. It is also useful when dealing with large numbers in scientific calculations.

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A rational expression seems to be undefined when ever the denominator is zero.

Here given expression, 5/(x - 10)

The expression becomes undefined when denominator becomes 0.

So here, if x = 10 then the denominator becomes 0.

That is 5/10-10

= 5/0

which is undefined, when x = 10.

Given expression, 15/(y² + 4)

To a expression to be undefined denominator has to be 0.

But here denominator cannot become zero.

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For [tex]log_{10}{\frac{1}{x} }=-6.34[/tex], the value of x is  2187761.6

We know that logarithm of a number is nothing but the power to which a number must be raised to get some other values.

i.e., if  [tex]b^y=a[/tex] then [tex]log_b{a}=y[/tex]

similarly if  [tex]log_b{a}=y[/tex] then  [tex]b^y=a[/tex]  

Where, a and b are two positive real numbers

y is a real number

Here, a is called argument, and b is called the base of the logarithm.

Consider logarithmic equation,

[tex]log_{10}{\frac{1}{x} }=-6.34[/tex]

Comparing above equation with  [tex]log_b{a}=y[/tex] we get,

a = 1/x, b = 10 and y = -6.34

From definition of logarithm [tex]log_b{a}=y[/tex] then  [tex]b^y=a[/tex]  we get,

⇒ [tex]10^{-6.34}=\frac{1}{x}[/tex]

⇒ x = [tex]\frac{1}{10^{-6.34}}[/tex]

⇒ x = 10^(6.34)

⇒ x = 2187761.6

Therefore, the value of x is 2187761.6

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If we take a sample of 50 students from your school and measure their height , then (c) The mean of the sample data. will be a Random Variable .

A Random Variable is a defined as a variable whose value depends on the outcome of a random event.

Option (c) : the random event is the selection of 50 students from the school to measure their height. The mean height of this sample of 50 students is a random variable because it can vary depending on the specific students who are selected.

Option (a) : The true mean height of all students from your school is a population parameter and is a fixed value, so it cannot be called as a random variable.

Option (b) : The mean of the sampling distribution of mean heights for samples of size 50 is a population parameter as well, and it represents the average of all possible sample means of size 50 taken from the population. So,  it is a fixed value and not a random variable.

Therefore , The mean of the sample data will be a random variable .

The given question is incomplete , the complete question is

Suppose you take a sample of 50 students from your school and measure their height.  Which one of the following is a random variable?

(a) The true mean height of all students from your school.

(b) The mean of the sampling distribution of mean heights for samples of size 50.

(c) The mean of the sample data.

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The values of x are 18 or -14.

What is an equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions written on the left and right sides. We have LHS = RHS (left-hand side = right-hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it contains no "equal to" symbol. It will be regarded as a phrase.

Exponents that are fractions with power as the numerator and a root as the denominator are said to be rational exponents.

Given equation is

3 ⁴√(x-2)³ - 4 = 20                          given

3 ⁴√(x-2)³ - 4 + 4= 20 + 4                Add 4

3 ⁴√(x-2)³ = 24

⁴√(x-2)³ = 24/3                                Divide by 3

⁴√(x-2)³ = 8

(x-2)^(3/4) = 8                                 Applying the formula [tex]\sqrt[m]{x^n} = x^\frac{n}{m}[/tex]

(x-2)^[(3/4)×(4/3)] = 8^(4/3)                Cancel Rational exponent

|(x-2)|= (2³)^(4/3)

x-2 = ±16

x -2 = 16    or       x - 2 = -16

x = 18         or        x = -14                   Add 2

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The value of the equation of is x are 18 or -14.

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign. It shows that the expressions written on the left and right sides have an equal relationship. In every mathematical equation, LHS = RHS (left hand side = right hand side) is used. Equations can be solved to find the value of an unknown variable that represents an unknown quantity. If there is no "equal to" symbol in a sentence, it is not an equation. We'll consider that to be a term.

Exponents are referred to as rational exponents if they are fractions with a power as the numerator and a root as the denominator.

Given equation is

3 [tex]\sqrt[4]{x-2} ^{(3)}[/tex]- 4 = 20                          given

3 [tex]\sqrt[4]{x-2} ^{(3)}[/tex] - 4 + 4= 20 + 4                Add 4

[tex]3 \sqrt[4]{x-2}^{(3)} = 24[/tex]  

[tex]\sqrt[4]{x-2}^{(3)} = 24/3[/tex]                            Divide by 3

[tex]\sqrt[4]{x-2}^{(3)} = 8[/tex]

[tex](x-2)^{(3/4)}[/tex] = 8                                 Applying the formula

[tex](x-2)^{[(3/4) \times(4/3)] }[/tex] = [tex]8^{(4/3)}[/tex]             Cancel Rational exponent

|(x-2)| = [tex](2^3)^{(4/3)}[/tex]

x-2 = ±16

x -2 = 16    or       x - 2 = -16

x = 18         or        x = -14                   Add 2

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The required number of miles he walked in one hours is  3(2/3) miles.

Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. In other words, velocity is a vector, whereas speed is a scalar value.

We have,

ella walked 11 miles in 3 hours

We need to find how many miles he walked in 1 hour, Which is called as Speed.

= 11/3 = Speed

= 3(2/3) miles

Thus, required Miles are 3(2/3).

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Answer:

25%

Step-by-step explanation:

If 3/5 of the flowers are red, then 2/5 of them are white. Since 9/20 of the roses are white, then 9/20*2/5=3/20 of all of the flowers are white roses. Subtracting the number of white roses from the total amount of white flowers will give us the fraction of how many of the flowers are white carnations. 2/5-3/20=5/20=1/4 of all of the flowers, which is 25% as a percentage.

The percent of all the flowers are white carnations is 255.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. With the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

3/5 of the flowers are red.

2/5 of them are white.

and, 9/20 of the roses are white.

fraction of white roses of all flower

= 9/20 x 2/5

=3/20

Fraction of Flowers that are white Carnations

= 2/5 - 3/20

= 5/20

= 1/4.

Then, the percent of all the flowers are white carnations is

= 1/4 x 100

= 25%

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Answer: for x=1, it would be y=50

Step-by-step explanation:

Answer: Function 1 is 45 and Function 2 is 50 I think

Step-by-step explanation:

If the numbers cannot be repeated, there can be 5040 possible codes. The probability to select the correct code in first try will be 1/5040. If the digits can be repeated then there can be 10000 possible combinations.

The code can be of digits between 0 to 9. Hence we have a choice of 10 digits

If the number cannot be repeated then the first digit of the code can be selected in

10 ways.

Similarly the second, third and fourth can be selected in 9, 8, and 7 ways.

Hence the code can be formed in

10 X 9 X 8 X 7 ways

= 5040ways

Now out of these 5040 codes, there can be only one code.

The probability to select it in first try i

1/5040

If the digits can be repeated, then we can use 10 digits for every specific number. Hence there can be

10 X 10 X 10 X 10 ways

= 10000 codes.

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The required number of students could be participating in the art show are 110.

Canvas is a very sturdy plain-woven fabric that is used to make sails, tents, marquees, backpacks, shelters, supports for oil paintings and other goods that require toughness, as well as in shoes, handbags, and other items of fashion.

The college purchases 465 canvases. They want to provide teachers 24 canvases. For every student, they ordered at least 4 canvases.

Then, it can be expressed as

Let the number of students = x

4x + 24 = 465

4x = 441

x = 110.25

Thus, there are 110 students in the school.

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The length of the side opposite this angle of the hypotenuse is 12.51°.

A right triangle consists of the hypotenuse (longest side), the opposite(length of the leg) and the adjacent.

The angle at the corner is 90degrees

In a right triangle, the hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle. We use special words to describe the sides of right triangles. The hypotenuse of a right triangle is always the side opposite the right angle.

Given that,

Length of the leg = 10cm

angle opposite the side = 53.1 degrees

To get the hypotenuse,

sin θ = opposite/hypotenuse

sin 53.1 = 10/hypotenuse

hypotenuse = 10/sin53.1°

hypotenuse = 10/0.799

hypotenuse = 12.51

Therefore,

The length of the side opposite this angle of the hypotenuse is 12.51°.

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There are no values of x that would make both equation 1 and equation 2 true at the same time.

To solve for the variables x in this system of linear equations, we need to find the values of x that satisfy both equation 1 and equation 2 simultaneously.

One way to do this is to use the substitution method. We can isolate x in equation 1 and substitute it into equation 2.

Starting with equation 1:

22x - 1 = -23

Adding 1 to both sides:

22x = -22

Dividing both sides by 22:

x = -1

Now, substitute x = -1 into equation 2:

11x + 121 = -1

Substituting x = 1:

11(-1) + 121 = -1

Expanding:

-11 + 121 = -1

Simplifying:

111 = -1

Since 111 is not equal to -1, we can conclude that there is no solution to the system of linear equations. In other words, there are no values of x that would make both equation 1 and equation 2 true at the same time.

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24) The value of factors of the expression 25x² - 64 is, (5x - 8) (5x + 8).

25) The value of factors of the expression 216x³ - 8 is,

⇒ (6x - 2) (36x² + 12x + 4)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

1) The expression is,

⇒ 25x² - 64

2) The expression is,

⇒ 216x³ - 8

Now, We can factors as;

1) The expression is,

⇒ 25x² - 64

⇒ (5x)² - 8²

⇒ (5x - 8) (5x + 8)

2) The expression is,

⇒ 216x³ - 8

⇒ (6x)³ - 2³

⇒ (6x - 2) ((6x)² + 6x × 2 + 2²)

⇒ (6x - 2) (36x² + 12x + 4)

Thus, We get;

24) The value of factors of the expression 25x² - 64 is, (5x - 8) (5x + 8).

25) The value of factors of the expression 216x³ - 8 is,

⇒ (6x - 2) (36x² + 12x + 4)

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Note that given the diagram showing joined Rectangles with the total area of the compound shape given as: ABCDEF = 36cm², the value of length AB = 4.5 or 9/2

A compound form is created by combining simple shapes. It's also known as a "composite" or "complex" form.

To solve for the value of AB,  lets start form the given:

Given that:

The area of the shape ABCDEF is 36 square centimeters.

From the given figure:

In the smaller rectangle, length of sides AB is x and BC is (2-4) cm.

In the larger rectangle, length of the sides DE is (x-2) and EF is 3x cm.

thus the area if the Smaller Rectangle is:

A(Small) = x(x-4)

= x² - 4x

The area of the larger rectangle will be:
A(Large)  = 3x(x-2)

= 3x² -6x

The total area of the shape will be:

A(Small) + A(Large) = 36

X²-4x+3x²-6x = 36
⇒ 4x² - 10x - 36 = 0; Divide both sides by 2

⇒2x² - 5x - 18 = 0

solving the above using the factoring method, we have:

⇒2x2-5x-18=0

⇒2x2-9x+4x-18=0

⇒x(2x-9)+2(2x-9)=0

⇒(2x-9)(x+2)=0

⇒(2x-9)=0or(x+2)=0

⇒ 2x = 9or x= -2

Thus, x = 9/2 or -2

Since the value of AB cannot be a negative value, thus the correct answer is: 9/2 or 4.5

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Full Question:

See image attached

The x and y-intercept of the function 2x - 3y = 6 are (3,0) and (0,-2) respectively.

Given the function in the question.

2x - 3y = 6

To determine the x-intercept, replace y with 0 and solve for x.

2x - 3y = 6

2x - 3( 0 ) = 6

2x = 6

2x/2 = 6/2

x = 3

Therefore, the x-intercept is (3,0).

Replace x with 0 and solve for y to determine the y-intercept.

2x - 3y = 6

2(0) - 3y = 6

-3y = 6

-3y / -3 = 6 / -3

y = 6 / -3

y = -2

Therefore, the y-intercept is (0,-2).

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The cost of putting sod in the yard is $981.75.

A trapezium is a quadrilateral with four sides where two sides are parallel to each other.

We have,

Area of a trapezium = 1/2 x (sum of the two bases) x height

Now,

Base = 80 ft and 107 ft

Height = 42 ft

Now,

Area = 1/2 x (80 + 107) x 42

Area = 1/2 x 187 x 42

Area = 187 x 21

Area = 3927 ft²

Now,

$0.25 = ft²

Multiply 3927 into both sides.

3927 x 0.25 = 3927 ft²

$981.75 = 3927 ft²

Thus,

$981.75 is the cost of putting sod in the yard.

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the orthogonal matrix for an unknown scalar α so its determinant is 1. then the value of unknown α=-1

We are aware that the number of rows and columns in a square matrix is equal. If the transpose of a square matrix with real numbers or elements equals the inverse matrix, the matrix is said to be orthogonal. Or, we may argue that a square matrix is an orthogonal matrix if the product of the square matrix and its transpose results in an identity matrix.

We know that AA'=I

[tex]\left[\begin{array}{ccc}7&0&a\\0&b&0\\-12&0&c\end{array}\right] \left[\begin{array}{ccc}7&0&a\\0&b&0\\-12&0&c\end{array}\right] =\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex]

so, after computing a= 4 , b=1 and c =-7

and the value of unknown α=-1

The complete question is :-

Complete the orthogonal matrix for unknown a so its determinate is 1.

O = a[[7,0,?][0,?,0][-12,0,?]]

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Answer:

The answer is 912

Step-by-step explanation:

Answer:

- 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

2 i think

The price of one bat when Aaryan purchased is ₹500

Let cost price of 1 bat x

Cost price of 8 bats = 8x

He sold 8 bats with 15% profit. If the net amount of profit he earned was ₹ 600

[tex]$\frac{15}{100} \times 8 x=600$[/tex]

[tex]$8 x=\frac{600 \times 100}{15}$[/tex]

[tex]$8 x=40 \times 100$[/tex]

[tex]$x=\frac{40 \times 100}{8}$[/tex]

[tex]$x=500$[/tex]

[tex]$x=500$[/tex]

The price of one bat when Aaryan purchased is ₹500

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Translating the given sentence into a variable expression, we have:

2n - 5.

we have:  n - (5 - n)

Simplifying the expression, we can use the distributive property and combine like terms:

n - 5 + n = 2n - 5

So the simplified expression is 2n - 5.

A variable is a symbol or letter used to represent a value or set of values in a mathematical expression or equation. The value of a variable can change and can be determined by the problem or context. For example, in the equation y = 2x + 3, x is a variable that represents an unknown value, while y represents a related value that depends on the value of x. Variables are used to represent unknown or changing quantities and can be used to model real-world situations in mathematics.

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The value of distance d is 240 miles.

The length of the shortest path connecting any two places in physical space is known as their distance.

Classical physics, particularly Newtonian mechanics, uses the term "distance" to refer to this.

Euclidean distance is calculated in coordinate geometry by applying the Pythagorean theorem.

This first section is

Distance = Speed * Time

Distance: (in metres (m), kilometres (km), miles, and feet

Distance: 50 multiplied by 4 equals 200 miles (50 mph; 4 hours).

In the following segment

Distance is 20 miles multiplied by two to get 40 miles (at a speed of 20 mph) in two hours.

240 miles are hence the total distance.

Assuming a six-hour trip, the average speed is 240 divided by six, or 40 miles per hour.

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Answer:

This is the answer you want

X=90°-38°

X=52°

Answer:

128°

Step-by-step explanation:

X-38°=90°

X=90°+38°

X=128°

Answer:

BCDF

Step-by-step explanation:

B. -2(4t+16)

C.-4t(2+8)

D. -4(2t+8)

F. -8(t+4)