the sum of three consecutive numbers is -6. what are the numbers

The range for the function y = x + 5, when the domain is {-2, 2}, is {7, 3}.

From the question, we have the following parameters that can be used in our computation:

y = x + 5

Domain {-2, 2}

Substitute the known values in the above equation, so, we have the following representation

When x = 2, y = 2 + 5 = 7

When x = -2, y = -2 + 5 = 3

Hence, the range for the relation y = x + 5 is {7, 3}.

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Complete question

find the range of the following function when the domain is -2 and 2

y = x + 5

Sorry I don't know good luck

Conan needs 16 tubes to store all 17 tennis balls because each tube can carry three balls.

The unit technique is a way of challenge where you first assess the value of a specific unit, than multiply that value to get the answer. Simply defined, a minimum unit value is extracted from a specified multitude using the unit method. For contrast, 40 pens will set you back 400 rupees, or $1.01.  a solitary nation. anything has a distinctive component. (Mathematics, Algebra) Its adjoint and reciprocal remain equivalent. (Hyper Algebra, Statistical Analysis, Mathematics of Matrix or Players)

given

conan fills 5 tubes with 3 balls each

2 tennis balls are left

Conan needs 16 tubes to store all 17 tennis balls because each tube can carry three balls.

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Answer:

Inequality form: -2 ≤ x ≤ 1

Interval Notation: [-2, 1]

Step-by-step explanation:

Move all terms not containing x from the center section of the inequality.

Answer:

yes

Step-by-step explanation:

yes

Answer:

yes

Step-by-step explanation:

ABCD is rhombus with  m 25 = 3x+33 and m/2 = 4x-44, the value of the x is 14.4.

In a rhombus, opposite angles are equal, and the measure of an angle is half the measure of its intercepted arc. Therefore, we have:

m ∠B = m ∠D = 2(m ∠A) = 2(m ∠C)

Also, the sum of the measures of the angles in a quadrilateral is 360 degrees, so we have:

m ∠A + m ∠B + m ∠C + m ∠D = 360

Since ABCD is a rhombus, its diagonals bisect each other at right angles. Therefore, we have:

m ∠BAC + m ∠CBD = 90

Substituting the given angle measures, we get:

2(4x-44) + 2(3x+33) = 360 (using the fact that m/2 = 2m∠A)

8x - 88 + 6x + 66 = 180

14x - 22 = 180

14x = 202

x ≈ 14.4 (rounded to the nearest tenth)

Therefore, x ≈ 14.4.

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Gauss-Jordan elimination is a method used to solve a system of linear equations by reducing the augmented matrix of the system to a reduced row-echelon form through a series of elementary row operations.

The process involves manipulating the rows of the augmented matrix to obtain a triangular matrix, where all entries below the diagonal are zero. This is achieved by applying elementary row operations such as adding a multiple of one row to another row or multiplying a row by a scalar.

Once the augmented matrix is in triangular form, further elementary row operations are used to eliminate the nonzero entries above the diagonal. This results in the augmented matrix being in reduced row-echelon form, where the pivot elements are all equal to 1 and the columns corresponding to the pivot elements are linearly independent.

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The equation of linear function which relate y to x is,

⇒ y = - 4x - 2

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (- 2, 6) and (- 1, 2).

Now,

Since, The equation of line passes through the points (- 2, 6) and (- 1, 2).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (2 - 6) / (- 1 - (-2))

m = - 4 / 1

m = - 4

Thus, The equation of line with slope - 4 is,

⇒ y - 6 = - 4 (x - (-2))

⇒ y - 6 = - 4 (x + 2)

⇒ y = - 4x - 8 + 6

⇒ y = - 4x - 2

Therefore, The equation of linear function which relate y to x is,

⇒ y = - 4x - 2

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Answer:

x = -2

x = 3

The two x's resemble to roots of the parabola.

Step-by-step explanation:

In the following, I uploaded an image with the steps to the equation.

With given expression, Fiction books will be calculated as 12.

What are expressions exactly?

In mathematics, expressions are mathematical claims that consist of at least two sentences that contain numbers, variables, or both, and are linked by an operator in between. Mathematical operations include addition, subtraction, multiplication, and division. For instance, x + y is an equation in which the words x and y are separated by an addition operator. In mathematics, there are two types of expressions: numerical expressions, which include only numbers, and algebraic expressions, which contain both numbers and variables.

e.g. A number is 6 more than half of another number, x. This proposition can be stated mathematically as x/2 + 6. Mathematical expressions are used to answer complex problems.

Now,

According to given conditions

Let non-fiction books=n

then fiction books are=3/8n

given that n+3/8n=44

11n/8=44

n=32

then 3/8n=12

hence,

        Fiction books will be 12.

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Right Question:-

   In the library at Lenape Elementary School, there are 3/8 as many fiction books as there are nonfiction books. There are 44 books in the school library. How many books are fiction books?

If the temperature decreased by 15°F, Pilar would expect to sell 15 fewer cups of hot chocolate.

What is an equation?

An equation is a statement that shows the equality of two expressions by using an equal sign (=). It expresses a mathematical relationship between two or more variables or quantities.

Regarding the second question, to find out how many more cups of hot chocolate Pilar would expect to sell if the temperature decreased by 15°F, we can plug in t = 15 into the equation c = -t + 120 and calculate the difference between the original value of c and the new value.

c(Original) = -15 + 120 = 105

c(New) = -(15+15) + 120 = 90

The difference is:

c(New) - c(Original) = 90 - 105 = -15

Therefore, if the temperature decreased by 15°F, Pilar would expect to sell 15 fewer cups of hot chocolate.

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A circle cannot be the shape of the cross section because a circle has a shape that is parallel to its bases (not perpendicular). Moreover, it cannot be a triangle or a trapezoid. Rectangle (B) is the correct response.

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. As a result, it is also known as a parallelogram or an equiangular quadrilateral.

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Answer:

The rate at which the tank is being emptied is 25 gallons per minute, which means that the change in the amount of oil in the tank per minute is -25. Let's assume that the initial amount of oil in the tank is 2500 gallons and the capacity of the tank is 3000 gallons.

The equation that relates the amount of oil in the tank, V, and time, t, is given by:

V = 2500 - 25t

This equation represents a linear relationship between the amount of oil in the tank and time. As time increases, the amount of oil in the tank decreases linearly at a rate of 25 gallons per minute.

The capacity of the tank, c, is 3000 gallons, which means that the tank will be completely emptied after:

t = (3000 - 2500) / 25 = 20 minutes

After 20 minutes, the amount of oil in the tank will be:

V = 2500 - 25(20) = 2000 gallons

The conversion of 27cm to inch is 10.63 inches.

A centimeter is a metric unit of measurement equal to one-hundredth of a meter. It is commonly used in many countries for measuring small distances, such as the length of an object or the height of a person. One centimeter is equal to 0.3937 inches.

To convert 27 centimeters to inches, we can use the following formula:

1 inch = 2.54 centimeters

Therefore, to convert 27 centimeters to inches, we can divide 27 by 2.54:

27 cm ÷ 2.54 = 10.63 inches (rounded to two decimal places)

So, 27 centimeters is approximately equal to 10.63 inches.

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On converting the length , 151 centimeter is equivalent to 4.954 feet .

The Units of measuring the length are used to measure the distance between two points of an object. There are several units of measuring length , which are : meter , centimeter , kilometer , feet .

We have to convert 151 cm to feet,

So , we use the conversion factor of 0.03281 feet per centimeter  , which means that there are approximately 0.03281 feet in 1 centimeter.

So , to convert 151 cm to feet, we multiply the number of centimeters by this conversion factor ;

Using this method, we get ;

⇒ 151 cm × 0.03281 feet/cm = 4.954 feet ;

Therefore, 151 cm is equal to approximately 4.954 feet.

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Answer:

4x+12 ≤ 0 or 4x+1>3

4x ≤ -12 or 4x+1 > 3

x ≤-3 or x >1/2

The inscribed angles are  3°, 5°, and 2.5°.

It is the angle inscribed on the arc of a circle.

The measure of the angle is half of the intercepted arc.

We have,

From the figure,

We are assuming that the intercepted arc length:

1)

Intercepted arc length = 6

Inscribed angle.

= 1/2 x 6

= 3°

2)

Intercepted arc length = 10

Inscribed angle.

= 1/2 x 10

= 5°

3)

Intercepted arc length = 5

Inscribed angle.
= 1/2 x 5

= 2.5°

Thus,

The inscribed angles are  3°, 5°, and 2.5°.

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The rank of the 4 x 5 matrix is 2 whose null space is three-dimensional

Matrix is defined as a rectangular array of rows and columns.

Rank of a matrix is defined as the maximum number of linearly independent columns (or rows ) that the matrix has.

Rank–nullity theorem is defined as a theorem described in linear algebra, which says that the dimension of the domain of a map is the sum of its rank and its nullity.

The rank-nullity theorem states that for a matrix A,

rank(A)+nullity(A)= number of pivot columns of A

That implies (the number of pivot columns) - (the null space dimension) = rank

The rank-nullity theorem states that for any matrix A, the rank of A plus the dimension of the null space of A equals the number of columns of A. In other words:

rank(A) + dim(null(A)) = number of columns of A

In this case, we have a 4 x 5 matrix A with null space of dimension 3. Therefore, we can solve for the rank of A as follows:

rank(A) + dim(null(A)) = number of columns of A

rank(A) + 3 = 5

rank(A) = 2

So the rank of the 4 x 5 matrix is 2.

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The mean value of the scores is 19.83, based on their sum and quantity of numbers.

The mean or average is calculated using the formula -

Mean = sum of all the numbers ÷ quantity of numbers.

We see that there are six numbers and hence the quantity of numbers will be 6.

Sum of all the numbers = 12 + 25 + 15 + 27 + 32 + 8

Performing addition on Right Hand Side of the equation

Sum of all the numbers = 119

Now calculating the mean of the scores by keeping the values in formula -

Mean = 119/6

Performing division on Right Hand Side of the equation

Mean of scores = 19.83

Hence, the average of scores is 19.83.

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Expect distributions of these variables are:

a) Ages of people at a Little League game are unimodal and skewed.

b) Number of siblings of people in your class is unimodal and skewed.

c) Pulse rates of college-age males unimodal and roughly symmetric.

d) Number of times each face of a die shows in 100 tosses is approximately uniform.

a) Age distribution during a Little League game is likely to be unimodal and skewed. The age range of attendees. This is because Little League has an upper age restriction and the majority of players will fall inside that range, with just a small number being outliers. As a result, the distribution is likely to be unimodal, with the majority of participants falling within a relatively small age range, and being skewed toward older ages.

b) How many siblings are in your class? The distribution of siblings in a class is probably unimodal and skewed. This is because the majority of people either have no siblings or have one or two siblings, with just a small minority having three or more. As a result, the distribution will be unimodal, with the majority of individuals falling within a very small range, and tilted in the direction of the lower numbers.

c) Males in college-age pulse rates: These men's pulse rate distributions are probably unimodal and roughly symmetric. It is doubtful that there would be different groups or outliers that would result in a bimodal distribution, even though there may be some natural variation in pulse rates. There is also no reason to assume that one tail of the distribution will be longer or more dispersed than the other, hence the distribution is probably symmetric.

d) Number of times each die face is revealed in 100 throws: The distribution of the number of times each die face is revealed in 100 throws is probably quite uniform. Each face has an equal chance of appearing on each toss, and throughout 100 tosses, each face is expected to do so roughly the same amount of times, assuming a fair die. As each face should appear nearly equally often, the distribution should be quite consistent.

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The quadrilateral FGHI is a parallelogram

From the question, we have the following parameters that can be used in our computation:

F = (0, -6), G = (7, -4), H = (8, 4), I = (1, 2)

The lengths can be calculated as

Lengths = √[(x₂ - x₁)² + (y₂ - y₁)²]

Using the above as a guide, we have the following:

FG = √[(0 - 7)² + (-6 + 4)²] = √53

GH = √[(8 - 7)² + (4 + 4)²] = √65

HI = √[(8 - 1)² + (4 - 2)²] = √53

IF = √[(1 - 0)² + (2 + 6)²] = √65

For the slopes, we have

Slope = (y₂ - y₁)/(x₂ - x₁)

So, we have

FG = (-6 + 4)/(0 - 7) = 2/7

GH = (4 + 4)/(8 - 7) = 8

HI = (4 - 2)/(8 - 1) = 2/7

IF = (2 + 6)/(1 - 0) = 8

Based on the above computations, we have

Hence, the shape is a parallelogram

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For the circle inscribed in the triangle the value for QK is 17.34.

What is a circle?

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.

From the given figure it can be seen that XZ is bisected.

XZ = XK + KZ

Also XK = KZ

The value of XZ is 36.

So, XK = XZ/2

XK = 36/2

XK = 18

Q is the circumcentre because Q is the point of intersection of perpendicular bisectors of sides of triangle.

So, this gives -

Circumradius = QX = QY = QZ.

And QX = 25.

Use the Pythagoras theorem for ΔQXK -

QX² = XK² + QK²

25² = 18² + QK²

QK² = 25² - 18²

QK² = 625 - 324

QK = √301

QK = √301

QK = 17.34

Therefore, the value is obtained as 17.34.

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A volume of 2 liters is needed to obtain a 92 % solution.

In this problem we need to determine the volume of pure acid to be added with a volume of four liters of 88 % acid solution to get a 92 % solution. This can be done by definition of weighted average:

(88 / 100) · (4 L) + (100 / 100) · V = (92 / 100) · (4 L + V)

Where V is the volume needed of the pure acid, in liters.

3.52 L + V = 3.68 L + 0.92 · V

0.08 · V = 0.16 L

V = 2 L

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Answer: Right/complementary angles

Step-by-step explanation:

Two angles that add up to 90 degrees are called complementary angles.

Complementary angles are a pair of angles that, when added together, equal a right angle, which measures 90 degrees.

In other words, the sum of the measures of complementary angles is always 90 degrees.

Complementary angles often arise in geometry and trigonometry, and understanding their properties is important when working with angles and solving problems involving right triangles.

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Answer:

x = 24
y - 16

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\sf x = 16, \ y = 24}[/tex]

Step-by-step explanation:

Let the smaller number be x and larger number be y.

x + y = 40 ----------------(1)

x = y - 8 ------------------(2)

Put Eq. (2) in (1)

y - 8 + y = 40

2y - 8 = 40

2y = 40 + 8

2y = 48

y = 48/2

Put y = 24 in Eq. (2)

x = 24 - 8

[tex]\rule[225]{225}{2}[/tex]

Answer:

Step-by-step explanation:

eay ma boi

Only graph B represents a proportional relationship.

What is a graph ?

A graph is a visual representation of data that shows the relationship between two or more variables. It is a way of presenting information in a clear and concise manner that makes it easy to interpret and understand.

Graphs can be used to show trends over time, compare different groups or categories, or illustrate the relationship between two or more variables.

Graph A shows a non-proportional relationship because as x increases, the corresponding y values do not increase or decrease at a constant rate.

Graph B shows a proportional relationship because as x increases, the corresponding y values increase at a constant rate.

Therefore, The slope of graph B is constant and represents the constant of proportionality between x and y.

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By using the concept of interest, we can calculate the year in which the tuition will reach $10,000 as 2027

Interest is the extra money you pay for borrowing money or for an investment, and it accumulates over time.

In this case, the interest rate is 3%, so the total tuition increases by 3% each year. To calculate the year in which tuition will reach $10,000, we will need to use the following formula:

Interest = (principal × rate × time) / 100.

The principal is $8,000, the rate is 3%, and the time is the number of years it takes for the tuition to reach $10,000. Thus, the equation becomes:

Interest = (8000 × 0.03 × time) / 100.

We can solve for time by multiplying both sides of the equation by 100 and dividing by 240. This gives us the following result:

Time = ($10,000 - $8,000) / (0.03 × $8,000) = 4.17 years.

Therefore, the tuition will reach $10,000 in

(2023 + 4.17) = 2027

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