1.1.1 To determine how much grass seeds they will need, the caretaker measure the length and breadth of the area of the sports field. He measured the length to be 162m and the breadth 160m. Calculate the area where the grass will be planted. You may use the formula: Area of rectangle = length x breadth (2)​

After answering the presented question, we can conclude that As a equation result, the system of equations solution is [tex]x = 64/3 \\and \\y = 62/3.[/tex]

In mathematics, an equation is a statement that states the equality of two expressions. An equation consists of two sides separated by an algebraic equation (=). The argument "2[tex]x + 3 = 9,"[/tex] for example, states that the sentence "2x Plus 3" equals the value "9." The goal of solving equations is to find the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, linear or nonlinear, and contain one or more parts. In the equation [tex]"x^2 + 2x - 3 = 0,"[/tex] the variable x is raised to the second power. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.

[tex](a) x + y = 34[/tex]

[tex]2x - y = 30[/tex]

The matrix of coefficients is | 1 1 | | 2 -1 |

This matrix's determinant is 130 - 342 = -62.

We can obtain the values of x and y using Cramer's Rule as follows:

[tex]x = det(A1)/det(A) = (-64)/(-3), = 64/3.[/tex]

[tex]y = det(A2)/det(A) = (-62)/(-3), = 62/3.[/tex]

As a result, the system of equations solution is [tex]x = 64/3 and y = 62/3.[/tex]

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Answer: To graph the linear equation x - y = 1, we can find its intercepts by setting one of the variables to zero and solving for the other.

Step-by-step explanation:

Setting x = 0, we get:

0 - y = 1

Solving for y, we get:

y = -1

So the y-intercept is (0, -1).

Setting y = 0, we get:

x - 0 = 1

Solving for x, we get:

x = 1

So the x-intercept is (1, 0).

Now we can plot the intercepts on a coordinate plane and draw a straight line passing through them:

    |

    |    .

    |        .

    |             .

    |                  .

    |                        .

    |                             .

------------------------------------------

    |         |         |         |         |

   -2        -1         0         1         2

Therefore, the graph of the linear equation x - y = 1 is a straight line passing through the points (0, -1) and (1, 0).

Step-by-step explanation:

a parallel line has the same slope. they just have different y-intersects (the y- value when x = 0).

the slope is the factor of x : -53

the y-intercept is given with the provided point (0, 2).

so, line j is

y = -53x + 2

Answer:

Rounding to the nearest hundredth of a foot, the change in altitude is approximately 514.77 feet.

Step-by-step explanation:

To solve this problem, we can use trigonometry. The angle of climb is 15 degrees, which means that the ratio of the change in altitude to the horizontal distance traveled is the tangent of 15 degrees:

tan(15°) = change in altitude / horizontal distance

We can rearrange this equation to solve for the change in altitude:

change in altitude = horizontal distance x tan(15°)

Substituting the given values, we get:

change in altitude = 2 miles x tan(15°)

We can convert the distance to feet by multiplying by 5280:

change in altitude = 2 miles x 5280 feet/mile x tan(15°)

Using a calculator, we get:

change in altitude ≈ 514.77 feet

Rounding to the nearest hundredth of a foot, the change in altitude is approximately 514.77 feet.

Step-by-step explanation:

So first of all u going to make sure all the base is the same so it 's easier for u to simplify

and then after that in order to make all the base the same so u need to multiple (x²-4) ...

Answer:

e

Step-by-step explanation:

5(4x +3)=-4(5-2x)

5×4x +5×3=-4 ×5 -4 × -2x

20x +15=-20+8x

The firm should produce good  x₁ = 4 and x₂ = 8 to minimize cost of C = x₁² + x₂² .

What is Lagrange multipliers ?

Lagrange multipliers is a method used in optimization problems to find the maximum or minimum value of a function subject to one or more constraints. The method involves introducing a Lagrange multiplier, which is a scalar variable, to the objective function and the constraint(s). This forms the Lagrangian function, which is then optimized with respect to the original variables and the Lagrange multiplier.

To minimize the cost C = x₁² + x₂²

We can use the method of Lagrange multipliers to solve this problem. Let's define the Lagrangian function L as:

L(x₁, x₂, λ) = x₁²+ x₂² + λ(400 - 5x₁²- 8x₁x₂ - 15x₂²)

Taking partial derivatives of L with respect to x₁, x₂, and λ, we get:

∂L/∂x₁ = 2x₁ - 10λx₁ - 8λx₂ = 0

∂L/∂x₂ = 2x₂ - 30λx₂ - 8λx₁ = 0

∂L/∂λ = 400 - 5x₁² - 8x₁x₂ - 15x₂² = 0

Solving these equations simultaneously, we get:

x₁ = 4

x₂ = 8

λ = 1/20

Hence, the firm should produce a combination of x₁ = 4 and x₂ = 8 to minimize the cost of C = x₁² + x₂² while satisfying the production quota of 400.

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Answer:

Step-by-step explanation:

i cant see good

Answer:

I think it would be commutative property

Step-by-step explanation:

the commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. The commutative property only works with addition and multiplication.

Answer:

3 races

Step-by-step explanation:

(Let t = total number of races)

Each race costs $3.50, so the total cost of racing t times is 3.50 × t or 350t. Douglas wants to have at least $7.75 left on his card, so an inequality to represent this would look like this:

Solving this inequality, we get:

Or we can do this.

Therefore, Douglas can race the go-karts 3 times and still have at least $7.75 left on his card to play arcade games.

Answer:

To make the piano player's practice seem consistent, adjust the Y-axis scale, use a line graph, and add a trend line or moving average.

Step-by-step explanation:

To adjust the graph to make it seem like the piano player is pretty consistent in practicing, we can make the following changes:

Adjust the scale of the Y-axis to make the differences in the average practice times appear smaller. For example, we can change the range of the Y-axis from 0-15 to 8-14, since all the data points fall within this range. This would compress the data vertically and make the differences in the average practice times appear smaller.

Use a line graph instead of a bar graph to better show the trend of the data over time. This would allow us to see any patterns or trends in the average practice times over the course of the year.

Add a trend line or moving average to the graph to show the overall trend in the data and smooth out any fluctuations. This would further emphasize the consistency in the piano player's practice habits.

By making these adjustments, the graph would show that the piano player is consistently practicing for around 10-11 hours per week throughout the year, with some slight variations. This would convey the message that the piano player is dedicated and consistent in their practice habits.

Hope this helps! I'm sorry if it's wrong. If you need more help, ask me! :]

A graph that represent the given function include the following: graph C.

In Mathematics, a piecewise-defined function can be defined as a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

By critically observing the graph of the piecewise-defined function g shown in the image attached below, we can logically deduce the following functions;

When the domain is x < -2, we have:

f(x) = 5 (< should be used because the endpoint is an open circle).

When the domain is -2 ≤ x < 0, we have:

f(x) = 3 (< should be used because the endpoint is an open circle and ≤ for the closed circle).

When the domain is 0 ≤ x < 2, we have:

f(x) = 0 (< should be used because the endpoint is an open circle and ≤ for the closed circle).

When the domain is x ≥ 2, we have:

f(x) = -3 (≥ should be used because the endpoint is a closed circle).

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After addressing the issue at hand, we can state that We know that when  function x = 0, y = b because the function has the form y = mx + b.

Mathematicians investigate numbers and their varieties, equations and adjacent tissues, shapes but instead their locations, and potential locations for these things. The term "function" refers to the relationship here between set of inputs, each with its own output. A function is a relationship of both inputs and outputs in which each input results in a single, distinct production. Each function has its own domain, codomain, or scope. The letter f is commonly used to denote functions (x). An x represents entry. On functions, each capabilities, so several capabilities, in capabilities, and on operations are the four major types of accessible functions.

We know that the function represented by the table of values has the form y = mx + b because it is linear, where y represents the distance from Nate's starting point and x represents the time he has been travelling.

The rate of change is known to be 50 miles per hour. This means that Nate's distance from his starting point increases by 50 miles for every hour he travels. In other words, m equals 50.

We know that when x = 0, y = b because the function has the form y = mx + b.

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The portfolio depicted as a box-and-whisker plot has a random selection of one stock, with probabilities of 0.51, 0.50, and 0.50.

The probability is frequently described as the ratio of favourable results to all favourable results in the sample. The likelihood of an occurrence P(E) = (The number of favorable events) is how it is stated (Sample space).

Probability is just the possibility that something will happen. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Biostatistics seems to be the analysis of occurrences with a probability distribution.

Given the box plot,

(a)

[tex]P(X < 51) = 0.51[/tex]

(b)

[tex]P(22 < X < 51) = 0.50[/tex]

(c)

[tex]P(X \geq 30) = 0.50[/tex]

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Answer:

To find the inverse of the function p(x) = 4x - 8, we need to switch the x and y variables and solve for y.

Step 1: Replace p(x) with y.

y = 4x - 8

Step 2: Switch x and y variables.

x = 4y - 8

Step 3: Solve for y.

Add 8 to both sides:

x + 8 = 4y

Divide both sides by 4:

y = (x + 8)/4

Therefore, the inverse of the function p(x) = 4x - 8 is q(x) = (x + 8)/4.

Step-by-step explanation:

The n-th term οf the sequence is given by the fοrmula a_n = 2n + 12.

An arithmetic prοgressiοn is a sequence οf numbers where each term is οbtained by adding a fixed value (called the cοmmοn difference) tο the previοus term. It is a type οf sequence that fοllοws a specific pattern, where the difference between cοnsecutive terms is cοnstant. Arithmetic prοgressiοns are cοmmοnly used in mathematics and variοus fields such as finance, physics, and cοmputer science.

The given sequence has a cοmmοn difference οf 2 between cοnsecutive terms. Therefοre, we can find the n-th term by adding (n-1) times the cοmmοn difference tο the first term οf the sequence.

The first term οf the sequence is 14, and the cοmmοn difference is 2.

Sο, the explicit fοrmula fοr the n-th term οf the sequence is:

a_n = 14 + 2(n-1)

Simplifying, we get:

a_n = 2n + 12

Therefοre, the n-th term οf the sequence is given by the fοrmula a_n = 2n + 12.

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The types of functions are as follows:

1) Quadratic function

2) None of the above

3) Exponential function.

What is a function?

A relation between a set of inputs and a set of allowable outputs is called a function. It has the property that every input is associated with exactly one output. A function from one set X to another allocates precisely one element of the other set Y to each element of X. Both the set X and the set Y are referred to as the function's domain and codomain, respectively. The basic conception of functions was the relationship between fluctuating quantities and other variables.

The ways to determine the different functions are  as follows:

a) If for a constant change in x-values, the y-values also change constantly, the function is linear.

b) If as the x values change constantly, the y- values also change, but the difference in differences of y-values remains constant, then the function is quadratic.

c) If the ratio between two consecutive y- values is the same, when x-values change constantly, then the function is exponential.

Let us look into each function.

1) x-values are increasing constantly by one.

The difference in y-values are:

13-7 = 6

21-13 = 8

31-21 = 10

43-31 = 12

Now the difference of difference in y-values.

8-6 = 2

10-8 = 2

12-10 = 2

This is constant. So the function is a quadratic function.

2) The difference in y-values are:

-6+21 = 15

-21+30 = 9

-33+30=  -3

-30 + 33 = 3

This function can be categorised as none of the above.

3) The ratio of the consecutive y-values are:

-12/-3 = 4

-48/-12 = 4

-192/-48 = 4

-768/-192 = 4

Since the ratio is constant, the function is an exponential function.

Therefore the types of functions are as follows:

1) Quadratic function

2) None of the above

3) Exponential function.

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The percentage of bicyclists that finished the race in less than 56 minutes is 96 %

Percentage is a ratio out of hundred

If in a​ race, 24 out of the 25 bicyclists finished in less than 56 minutes. To find what percent of bicyclists finished the race in less than 56 ​minutes, we first write it in a fraction as number/total

Since

We have that

fraction = number/total

= 24/25

Now to write it as a percentage, we multiply by 100.

So, we have that percentage = fraction × 100 %

So, we have that in percentage = 24/25 × 100 %

= 24 × 4 %

= 96 %

So, the percentage is 96 %

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"From days 3 to 5, the high temperature changed by an average of almost 4 degrees per day," is the appropriate answer.

We can determine the average rate of change from day 3 to day 5 by splitting the difference in high temperature between those two days by the distance between them (which is 2), or 2.

The highest temps on Day 3 was 85°F.

The highest temperature on Day 5 was 77°F.

Extreme temperature variation: 77°F to 85°F equals -8°F

Between day three and day five, there are two days.

(Change in maximum temperature) / (number of days) yields an average rate of change of -8°F / 2°F per day.

This leads to the conclusion that the right response is "The high temperature changed by an average of 4 degrees per day from day 3 to day 5".

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Answer:

56 muffins

Step-by-step explanation:

Since it takes  1/8 cup to make one muffin, 1 cup can make 8 times as many muffins or 8 muffins with 1 cup of raisins

With 7 cups he can make 7 x 8 = 56 muffins

Answer:

x ≈ 46.1

Step-by-step explanation:

using the sine ratio in the right triangle

sin19° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{15}{x}[/tex] ( multiply both sides by x )

x × sin19° = 15 ( divide both sides by sin19° )

x = [tex]\frac{15}{sin19}[/tex] ≈ 46.1 ( to the nearest tenth )

The factored version of the provided polynomial is (6x-1) according to the given assertion.(x-3).

An expression that consists of variables, factors, and exponents and is mixed using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial. (No division operation by a variable).

To factor the polynomial x(6x-1)-3(6x-1), we can first simplify the expression by factoring out the common factor of (6x-1):

x(6x-1)-3(6x-1) = (6x-1)(x-3)

Therefore, the factored form of the given polynomial is (6x-1)(x-3).

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Answer:

2500ml

Step-by-step explanation:

1litre=1000millilitres

2.5=?

=2.5×1000

=2500millilitres

In descending order in terms of y, the expression is -x³y⁵ - 2x²y³ + 4xy + x⁴.

When a pattern of numbers in mathematics has a decreasing value, the numbers are said to be in descending order. It indicates that the numbers are sorted from highest to lowest. Information is considered to be in descending order if it is arranged from highest to lowest. For example 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 are ordered in descending order. In other terms, it is considered to be in descending order if the numbers are listed from greatest to smallest.

The given expression is:

x⁴- x³y⁵+ 4xy - 2x²y³

To arrange in descending order, place the highest value first followed by the smaller value.

Therefore, in decreasing order in terms of y, the expression is -x³y⁵ - 2x²y³ + 4xy + x⁴.

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Answer: To find the expected value of X, we need to multiply each possible value of X by its probability and then add up the results:

E(X) = Σ(x * P(X = x))

where Σ denotes the sum over all possible values of X.

Using the table given, we have:

E(X) = 0 * 0.09 + 1 * 0.29 + 2 * 0.42 + 3 * 0.15 + 4 * 0.05

E(X) = 0 + 0.29 + 0.84 + 0.45 + 0.2

E(X) = 1.78

Therefore, the expected value of pets in a randomly selected household is 1.78.

Step-by-step explanation:

The correct option is 312 cm² as the area of the composite figure calculated to be equal to 312 square centimeters.

The composite figure can be observed to be made up of two identical triangle and a rectangle, so we shall calculate for the area of one triangle, multiply the result by 2, and add the area to the area of the rectangle to get the total area of the composite figure as follows:

area of one of the triangle = 1/2 × 12 cm × 10 cm

area of one of the triangle = 6 cm × 10 cm

area of one of the triangle = 60 cm²

area of one of the two triangle = 2 × 60 cm²

area of one of the two triangle = 120 cm²

area of the rectangle = 16 cm × 12 cm

area of the rectangle = 192 cm²

total area of the composite figure = 120 cm² + 192 cm²

total area of the composite figure = 312 cm²

Therefore, the area of the composite figure is equal to 312 square centimeters.

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The triangular system has, by means of fractions, a total shaded area of 27 / 2 square centimeters.

In this problem we have the area of an entire triangle, from which we need to determine the total shaded area, this can be done by subtracting triangles from the entire triangle, by means of fractions, whose complete operation is shown below:

A = 32 - (1 / 4) · 32 - (3 / 4) · (1 / 4) · 32 - (3 / 4)² · (1 / 4) · 32

A = [1 - 1 / 4 - (3 / 4) · (1 / 4) - (3 / 4)² · (1 / 4)] · 32

A = 27 / 2 cm²

Please notice that shaded areas are positive and blank areas are negative.

By means of fractions, the total shaded area of the triangular system is equal to 27 / 2 square centimeters.

The statement is incomplete. After a quick investigation we conclude that the complete statement is the following:

The area of a complete triangle (without blank spaces) is 32 square centimeters, please compute the total shaded area, that is, the area of the composite figure seen in the figure.

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Therefore , the solution of the given problem of quadratic equation comes out to be x = 2, -3 + √(5)i, -3 - √(5)i.

Regression modelling uses the polynomial answer x = ax2 + b + c=0 for one-variable equations. The First Proposition of Algebra claims that since this proposition has a second order, there can only be one solution. There are simple and complicated solutions available variable . Even as the name suggests, a "non-linear formula" has four factors. According to this, there might be just one squared term. In the formula ax2 + bx + c = 0

Here,

The provided polynomial equation can be rewritten as follows:

=> x³ + 4x² - 7x - 28 = 0

The constant term in this situation is -28, with components of 1, 2, 4, 7, 14, and 28, and a leading coefficient of 1. Therefore, 1, 2, 4, 7, 14, and 28 are among the polynomial's potential rational solutions.

It is possible to factor the polynomial by discovering that x = 2 is one of its roots.

=> (x - 2)(x² + 6x + 14) = 0

The quadratic formula can be used to calculate the quadratic factor:

=> x = (-6 ± √(6² - 4114)) / (2*1)

=> (-6 ± √(-20)) / 2

=>  -3 ± √(5)i

Thus, the following are the answers to the algebraic equation:

=> x = 2, -3 + √(5)i, -3 - √(5)i.

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a. ΔEGF~ΔGHF~ΔEHG are the similarities between the three right triangles.

b. HF/HG = GH/EH; EF/EG = EG/EH

According to the similar right triangle theorem, if a right triangle's altitude is drawn from its right angle, two similar right triangles are created, and both similar right triangles are identical to the original right triangle. All three right triangles are essentially the same.

Similar triangles contain three pairs of comparable side lengths that are proportionate to one another, or whose ratios are identical.

The corresponding side lengths are taken into account when constructing similarity statements.

A similarity assertion linking the three right triangles is thus: ΔEGF~ΔGHF~ΔEHG.

b. They will have the following side ratios: EF/EG = EG/EH HF/HG = GH/EH

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