Consider the following system of two linear equations:

3y + 2x = 15
x – y = 0

Select the graph that correctly displays this system of equations and point of intersection.

Answer:

n = 15

Step-by-step explanation:

the equation for inverse variation is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

to find k use the point (5, 3 ) , that is y = 3 when x = 5 , then

3 = [tex]\frac{k}{5}[/tex] ( multiply both sides by 5 )

15 = k

y = [tex]\frac{15}{x}[/tex] ← equation of variation

substitute (1, n ), that is x = 1, y = n into the equation

n = [tex]\frac{15}{1}[/tex] = 15

According to the graph, the value of the constant in the equation below is 2. The correct option is B.

A constant function in mathematics is one whose (output) value is constant regardless of the input value.

We are given the equation for the height.

On the graphic, height, and width are related. By choosing a point, we can find the value of the constant.

To find a constant in a graph, the width is multiplied by height.

(Height)(Width) = Constant.

Multiply any of the coordinate values shown, and you will see the constant is 2.

 3 × 1.5 = 2 × 1 = 8 × 4 = 7 × 3.5 =

we will take only one variable which is 2 x 1 = 2, so the constant is 2

Therefore, the correct option is B, 2.

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The simplified expression when a polynomial is divided by a monomial is [tex]y^3 / u^3 (8u^4 - 3y^2u^4 - 3y^2).[/tex]

A polynomial expression can be represented as a product of other, smaller polynomial expressions through the algebraic process of factoring. The process of factoring can be used to simplify expressions and solve problems. A polynomial equation's roots can be found by factoring, as can the common factors in an expression that can be eliminated. Factoring occasionally enables us to spot trends and connections between several expressions.

Depending on the kind of polynomial and the degree of the terms involved, there are several ways to factor. S

For the given expression [tex](12y^7u^2-32y^5u^6+15y^7u^6) / (-4y^2u^5)[/tex] factor the common term.

[tex](12y^7u^2-32y^5u^6+15y^7u^6) / (-4y^2u^5)\\-4y^5u^2(3y^2 - 8u^4 - 3y^2u^4) / (-4y^2u^5)[/tex]

Cancelling the -4:

[tex]= y^3 / u^3 (8u^4 - 3y^2u^4 - 3y^2)[/tex]

Hence, the simplified expression is [tex]y^3 / u^3 (8u^4 - 3y^2u^4 - 3y^2).[/tex]

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Rounded to the nearest tenth, the approximate duration for one swing of a pendulum with a length of 13.69 meters is 7.7 seconds.

We are given that the time, t, in seconds it takes for a pendulum to swing back and forth once is given by:

t = 2.01√L

where L is the length of the pendulum in meters.

We are asked to find the time it takes for a pendulum of length 13.69 meters to swing back and forth once. So we can substitute L = 13.69 into the equation above to get:

t = 2.01√(13.69) ≈ 2.01 × 3.7 ≈ 7.7

Therefore, the time it takes for a pendulum of length 13.69 meters to swing back and forth once is approximately 7.7 seconds (rounded to the nearest tenth).

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To calculate the minimum amount of wrapping paper needed to wrap the gift, Naomi would be finding the Surface Area.

The Surface Area of a three-dimensional object is the sum of the areas of all its faces. In this case, the gift is a rectangular prism with dimensions of length 10 inches, height 2 inches, and depth 3 inches.

To wrap the gift, Naomi would need to cover all six faces of the rectangular prism with wrapping paper. The formula for the Surface Area of a rectangular prism is:

Surface Area = 2lw + 2lh + 2wh

where l, h, and w are the length, height, and width of the rectangular prism, respectively.

Substituting the values for the length, height, and depth of the gift, we get:

Surface Area = 2(10 x 2) + 2(10 x 3) + 2(2 x 3)

Surface Area = 20 + 60 + 12

Surface Area = 92 square inches

Therefore, Naomi would need at least 92 square inches of wrapping paper to cover the gift, which is the Surface Area of the rectangular prism.

Let the side length of the square base be x cm and the height of the box be h cm. Then the volume of the box is given by:

V = x^2 * h = 13,500 cm^3

We want to minimize the amount of material used, which is the surface area of the box. The surface area A is given by:

A = x^2 + 4xh

We can use the volume equation to solve for h in terms of x:

h = 13,500 / x^2

Substituting this into the surface area equation gives:

A = x^2 + 4x(13,500 / x^2) = x^2 + 54,000 / x

To minimize A, we take the derivative with respect to x and set it equal to zero:

dA/dx = 2x - 54,000 / x^2 = 0

Solving for x, we get:

x^3 = 27,000

x = 30

Substituting this back into the volume equation gives:

h = 13,500 / (30^2) = 15

Therefore, the dimensions of the box that minimize the amount of material used are 30 cm by 30 cm by 15 cm.

Answer: -2， 6

（-2）Because from 3a³ to (1)a³, it needs to subtract 2a³.

   (6)  Because from -5b³ to b³, it needs to add 6.

Step-by-step explanation:

We can start by solving the second equation for one of the variables. Let's solve for y:

3x + 3y = 6

3y = 6 - 3x

y = 2 - x

Now we can substitute this expression for y into the first equation:

9x - 19y = 74

9x - 19(2 - x) = 74 (substituting y = 2 - x)

9x - 38 + 19x = 74

28x = 112

x = 4

Now we can use this value to find y:

y = 2 - x

y = 2 - 4

y = -2

Therefore, the solution to the system of equations is x = 4 and y = -2.

Hopes this helps

Therefore, Aditi's mother requires 342 yellow tiles and 57 red tiles for the floral design on the kitchen wall.

Proportion is a statement that two ratios are equal. A ratio is a comparison of two quantities and is written in the form of a fraction. A proportion can be written in the form of a:b = c:d, where a, b, c, and d are numbers. This means that the ratio of a to b is equal to the ratio of c to d. We can also write a proportion as a fraction, where the numerator is the product of the means (ad) and the denominator is the product of the extremes (bc). Proportions are commonly used in mathematics to solve problems involving ratios and rates.

Here,

Since the floral design is made up of yellow and red hexagonal tiles, we need to determine the proportion of yellow tiles and red tiles in the design. Let's assume that the design consists of x yellow tiles and y red tiles. Each flower in the design consists of 7 hexagonal tiles - 6 yellow tiles and 1 red tile. Therefore, the total number of tiles in the floral design is:

Total number of tiles = 57 flowers x 7 tiles per flower

Total number of tiles = 399 tiles

Since each flower consists of 6 yellow tiles and 1 red tile, the total number of yellow tiles in the design is:

Number of yellow tiles = 6 x Number of flowers

Number of yellow tiles = 6 x 57

Number of yellow tiles = 342

Similarly, the total number of red tiles in the design is:

Number of red tiles = 1 x Number of flowers

Number of red tiles = 1 x 57

Number of red tiles = 57

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Complete question:

Aditi's mother is renovating her kitchen. One of the walls of kitchen is entirely made up of tiles. She wants to have a row of floral designs made up of yellow and red hexagonal tiles in the middle of the wall as shown in the adjoining figure. If there are 57 flowers in a row, find out how many yellow-and red-coloured tiles she requires for that wall.

To measure a straight angle, Shirley could use any combination of pattern blocks that adds up to 180 degrees.

What are the pattern block angle combinations Shirley could use to measure the angle?

As a result, the pattern block angle combinations that Shirley could use to measure the angle are:

Incomplete question provided, below is the complete question -
Shirley measures the straight angle using pattern blocks. Choose every possible combination of angle possibilities for pattern blocks Shirley could use to calculate the angle.

# The tan pattern block has six minor angles.

# On the red pattern block, there are two angles: one large and one small.

# On the red pattern block, there is one large angle and three small angles.

# The tan pattern block has four tiny angles, and the red pattern block has one tiny angle.

# The red pattern block has two sharp angles.

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Triangle (B) is a comparable number that you must drag into the table.

An angle is formed when two straight lines or beams meet at a singular endpoint.

The intersection of two locations is known as the vertex of an arc.

The word "angle" is derived from the Latin word "angulus," which means "corner."

But there are some basic viewpoints.

Combining different shots greatly expands your camera options.

The most confusing of the five angles involves taking a scene from straight overhead.

So, the following:

Using the provided figure, we obtain:

A 60-degree equilateral triangle is depicted in the image.

And as can be seen in figure B, we obtain an equilateral triangle with a 60-degree inclination on each side.

Therefore, triangle (B) is a comparable number that you must drag into the table.

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Answer:

247700% I'm not sure

I'm not good I'm maths

The equation of the axis of symmetry of the quadratic function is given by y = -2x² + 8x - 5.

x = 4 is the x-coordinate of the vertex.

x = 0 and x = 4 are the x-coordinates of the x-intercepts.

y = -5 is the y-coordinate of the y-intercept.

A quadratic function has two variables that can be used to model real-world problems. It has a distinct shape of a parabola, which is a symmetrical U-shaped curve.

The coordinates of the vertex of the function can be calculated by taking the derivative of the given equation and setting it equal to 0.

This yields x = 4 as the x-coordinate of the vertex.

Substituting this value in the given equation gives us the y-coordinate of the vertex, which is y = 11.

The coordinates of the x-intercepts of the function can be found by setting y = 0 in the given equation.

This yields x = 0 and x = 4 as the x-coordinates of the x-intercepts. Substituting these values in the given equation gives us the corresponding y-intercepts, which are

y = -5 and y = 0 respectively.

The coordinates of the y-intercept of the function can be found by setting x = 0 in the given equation.

This yields y = -5 as the y-coordinate of the y-intercept.

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The standard form of the expression (7.2 × 10⁵) ÷ (3.4 × 10³) include the following: C. 2.12 x 10².

In Mathematics, an exponent refers to a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the law of indices for powers of the same base number and division, we have the following:

(7.2 × 10⁵) ÷ (3.4 × 10³

(7.2/3.4) × 10⁵⁻³

2.12 x 10².

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Complete Question:

The standard form of (7.2 × 10⁵) ÷ (3.4 × 10³)

a) 2.14 x 10

b) 2.11 x 10

c. 2.12 x 10²

d) 2.12 x 10​

The value of x in the right angled triangle above is 7√3.

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle. Therefore, this triangle is also called the right triangle or 90-degree triangle.

To calculate the value of x in the right angle triangle above, we use the formula below.

Formula:

Where:

Substitute these values into equation 1 and solve for x

Hence, the value of x is 7√3.

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After answering the presented question, we can conclude that Softball graphs players drink less than 4 glasses of water, 60% drink 4 to 8 glasses, and 12% drink more than 8 glasses.

Mathematicians use graphs to visually display or chart facts or values in order to express them coherently. A graph point usually represents a relationship between two or more things. A graph, a non-linear data structure, is made up of nodes (or vertices) and edges. Glue the nodes, also known as vertices, together. This graph includes V=1, 2, 3, 5, and E=1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Statistical graphs (bar graphs, pie graphs, line graphs, and so on) are graphical representations of exponential growth. A triangle-shaped logarithmic graph.

70% of track athletes drink 4 to 8 glasses of water every day.

We can observe that the blue segment, which represents the number of track athletes who drink 4 to 8 glasses of water each day, accounts for almost 70% of the whole bar. The graph does not support any of the other statements. According to the graph, approximately 25% of track athletes take less than 4 glasses of water, while approximately 5% consume more than 8 glasses. Baseball players drink less than 4 glasses of water, 35% drink 4 to 8 glasses, and 25% drink more than 8 glasses. Softball players drink less than 4 glasses of water, 60% drink 4 to 8 glasses, and 12% drink more than 8 glasses.

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The characteristic polynomial of A is λ³ - 4λ² - 3λ + 14. The eigenvalues of A are 2, 1, and 7.

According to the rational root theorem, p is a factor of the constant term and q is a factor of the leading coefficient if a polynomial with integer coefficients has a rational root of p/q, where p and q are integers without any shared factors. As the leading coefficient is 1 and the constant term is 14, the only potential rational roots in this situation are 1, 2, 7, and 14.

The characteristic polynomial of a matrix is given as

det(A - λI)

Here, λ is the eigen value.

det (A - λI)

[tex]\left[\begin{array}{ccc}1 - \lambda&0&1\\2&3 -\lambda&-1\\0&6& \lambda\end{array}\right][/tex]

Taking the determinant we have:

det(A - λI) = (1-λ)[(3-λ)(-λ) - (-1)(6)] - 0[2(-λ) - (-1)(0)] + (-1)[2(6) - (3-λ)(0)]

det(A - λI) = (1-λ)(λ² - 3λ - 6) - (-1)(12) = λ³ - 4λ² - 3λ + 14

Hence, the characteristic polynomial of A is λ³ - 4λ² - 3λ + 14.

The eigen values is the solution of the polynomial.

Using the rational roots of polynomial we have:

λ³ - 4λ² - 3λ + 14. factors as (λ-2)(λ-1)(λ-7)

Hence, the eigenvalues of A are 2, 1, and 7.

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The equation of the rational function is F(x) = 1/(x-2)(x+1). Thus, the answer is B. F(x) = 1/(x-2)(x+1).

It is a type of function that can be expressed in the form f(x) = p(x) / q(x), where p(x) and q(x) are polynomials and q(x) is not equal to zero. Rational functions are used in various areas of mathematics, including calculus and algebra.

The graph of a rational function is the set of points which satisfy the equation of the rational function.

In this case, the equation of the rational function is F(x) = 1/(x-2)(x+1).

The graph of this function is a line which passes through the points (2, 0) and (-1, 0) and has a vertical asymptote at x = 0.

The graph of a rational function can be determined by finding the zeroes, vertical and horizontal asymptotes, and intercepts of the function.

The zeroes of F(x) = 1/(x-2)(x+1) are x = 2 and x = -1. The vertical asymptote is x = 0 and the horizontal asymptote is y = 0.

The intercepts are (2, 0) and (-1, 0).

The graph of F(x) = 1/(x-2)(x+1) is a line which passes through the points (2, 0) and (-1, 0) and has a vertical asymptote at x = 0.

This is different from the graph of F(x) = 1/X² which is a parabola and from the graph of F(x) = 1(x+2)(x-1) which is two lines intersecting at (2, 0) and (-1, 0).

Therefore, the correct answer is B. F(x) = 1/(x-2)(x+1).

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The second piece of the function applies to x = 1, which is f(x) = -x².

Thus, f(1) = -(1)² = -1.  The correct answer is f(1) = -1.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range. In simpler terms, a function is a set of rules that takes an input value and produces a corresponding output value.

To find the value of f(1), we need to determine which piece of the function applies to x = 1.

Since 1 is greater than 0 and less than 2, the second piece of the function applies to x = 1, which is f(x) = -x².

Thus, f(1) = -(1)² = -1.

Therefore, the correct answer is f(1) = -1.

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Answer:

x = 2

y = 14

Step-by-step explanation:

{y = 4x + 6;

{y = 7x;

.

Let's replace y in the second equation with the value given in the 1st equation:

4x + 6 = 7x

4x - 7x = -6

-3x = -6 / : (-3)

x = 2

x = 2y = 4 × 2 + 6 = 8 + 6 = 14

(I THINK I USED THE RIGHT CALCULATOR)

Answer: V≈113.1

Step-by-step explanation:

V=πr2h=π·1.52·16≈113.09734

The total surface area of the square pyramid is 39 ft².

The total surface area of a square pyramid can be determined by adding the area of the lateral surfaces and the base together.  A square pyramid has four lateral sides and one base.  

Total surface area= area of the base + area of the lateral sides

Area of the base = area of a square = length² = 3² = 9 ft²

Area of the lateral sides = 2 x base x height

2 x 3 x 5 = 30 ft²

Total surface area = 30 + 9 = 39 ft²

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Answer:

24

Step-by-step explanation:

Total number of food = x

If ¾ of food = number of burgers bought

Then 3/4 times x = 3x/4

3x/4= 18

x = 24

Answer:

Por lo tanto, el segmento AM mide 26 cm.

Step-by-step explanation:

Como M es el punto medio de AB, entonces AM tiene la misma longitud que MB. Por lo tanto, la longitud de AM es:

AM = MB = AB / 2

Sustituyendo los valores dados, tenemos:

AM = MB = AB / 2 = 52 cm / 2 = 26 cm

The area of this home plate is equal to 216.5 in².

In order to determine the area of home plate, we would have to apply the law of cosine:

C² = A² + B² - 2(A)(B)cosθ

Where:

A, B, and C represent the length of side or side length of a given triangle.

By substituting the given side lengths and angle into the law of cosine formula, we have the following;

C² = A² + B² - 2(A)(B)cosθ

17² = 12² + 12² - 2(12)(12)cosθ

284 = 144 + 144 - 288cosθ

1 = -288cosθ

cosθ = (-1/288)

θ = 90.199

For the area of home plate, we have:

Area of home plate = Area of rectangle + Area of triangle

Area of home plate = 17(8.5) + 1/2(12)(12)sin90.199

Area of home plate = 144.5 + 72(0.9999940)

Area of home plate = 216.5 in².

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Answer:

The dimensions of the t r including the path are 12+3+3 and 6+3+3 which is 18x12=216 m2

If we subtract the  tr area 12x6=72m2

216m2–72m2=144m2

Step-by-step explanation:

Answer:

Step-by-step explanation:

use formula I = prt

I=Interest P=principal R=rate T=time so Interest is = to 750 x 5% or 0.05 x 4 which is 150 so after 4 years 150 interest is gained

Answer:

19 degrees

Step-by-step explanation:

hope this helps