For a given arithmetic sequence, the first term, 47, is equal to 26, and the 37 th term, a37, is equal to 278. th Find the value of the 4th term, a4.​

The formula is written as (3x+9)(x+9) of + 36x + 81 = 0. A second-degree polynomial equation can be used to define quadratics.

Multiplying a variable by itself is the mathematical operation known as "squaring," which is frequently used to refer to a quadratic issue. This vocabulary is based on the notion that a square's area is equal to the sum of its side lengths. The word "quadratic" derives from the Latin quadratum, which meaning square.

here ,

[tex]= + 36x + 81 = 0\\= 3x^2 + 27x + 9x + 81\\= 3x(x+9) + 9(x+9)\\= (3x+9)(x+9)\\= 3(x+3)(x+9)[/tex]

factorized form is [tex](3x+9)(x+9) of + 36x + 81 = 0 .[/tex]

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Answer:

9 months

Step-by-step explanation:

1 quarter is 3 months

3 quarters is 3 times 1 quarter, so it is 3 times 3 months.

3 x 3 months = 9 months

Answer: 9 months

Therefore , the solution of the given problem of angles comes out to be equation :  x+ y =85°.

'

In Euclidean geometry, an angle is a shape that is made up of two rays, known as the tone's flanks, that meet at a midpoint known as such angle's vertex. Two rays may combine to form an angle there in plane where they are positioned. When two planes collide, an angular is also generated. They are referred to as dihedral angles. An angle in plane geometry is the possible configuration of two rays of lines that share a termination. The origin of the English term "angle" is the Latin phrase "angulus," which meaning "horn." The vertex is the point in which the two vectors, also known as that of the faces of the angle, converge.

Here,

Given :

Let two angles be x and y  is

=> x+ y =85°

So, the equation is represented as  x+ y =85°.

Therefore , the solution of the given problem of angle comes out to be equation :  x+ y =85°.

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The inequality to represent the number of stamps Keshia can buy with $10.00, considering that each stamp costs 49 cents, can be written as:

0.49x + 7.65 <= 10.00

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

The inequality to represent the number of stamps Keshia can buy with $10.00, considering that each stamp costs 49 cents, can be written as:

0.49x + 7.65 <= 10.00

This inequality can be read as "the cost of x number of stamps plus the cost of the package is less than or equal to Keshia's budget of $10.00."

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The given statement “if the slope of a line is 3, then the slope of a parallel line is 4” is false because parallel lines have equal slopes

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

Slope of a line = 3

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = 3

This means that the slope is 3

The slopes of parallel lines are equal

This means that the slope of the other line is 3

Hence, the statement is false

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On solving the provided question, we can say that F= The lifting force is 27135 0.003357*250*180*180 = F=27135, surface area

The total area that all of a 3D object's faces cover is the surface area. The surface area of a cube is its surface area, for instance, if we are trying to determine how much paint is needed to paint it. Always expressed in square units.

The entire surface of a three-dimensional shape is referred to as its surface area. A cuboid with six rectangular faces has a surface area equal to the sum of the areas of each face. Alternatively, you can label the cuboid's length, width, and height (l, w, and h), then calculate its surface area (SA) using the formula: SA=2lw+2lh+2hw.

F= k*a*v^2

a= 250

v=190

30300=k*250*{190^2}

k= 0.03357

F= 0.003357*250*180*180

F=27135

The lifting force is 27135

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Answer:

3 feet

Step-by-step explanation:

To solve this problem, we can use the Pythagorean theorem. Let's call the distance from the tent pole to the rope x. We can set up the following equation:

x^2 + 12^2 = 15^2

Solving for x, we get:

x = sqrt(15^2 - 12^2)

x = sqrt(9)

x = 3

Therefore, the distance from the tent pole to the rope is 3 feet.

As a result, the necessary linear equations for the rectangle's area and perimeter are y = 18[x - 1] and z = 6[x + 1], respectively.

An object's surface area is a measurement of the total volume of space that it occupies. The entire region surrounding a three-dimensional shape is referred to as its surface area. Its surface area is the total area of a three-dimensional shape. By adding the surfaces of each of a cuboid's six rectangular sides, one may determine the cuboid's surface area. The box's dimensions could also be named using the following formula: Surface (SA) = 2lw + 2lh + 2hw. A three-dimensional shape's surface area is a measurement of the total area it occupies (a three-dimensional shape is a shape that has height, width, and depth).

given

here,

Length  = 3x + 3

Width = 6

Area of the rectangle = y, = length × width

y = [3x - 3 ] × [6]

y = 18x - 18 = 18[x -1]

Perimeter of the rectangle = 2[length + width]

z = 2 [3x + 3]

z = 6[x + 1]

As a result, the necessary linear equations for the rectangle's area and perimeter are y = 18[x - 1] and z = 6[x + 1], respectively.

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The correct question is :- Write a linear equation that represents the area and a linear equation that represents the perimeter of the rectangle (3x-3) cm and 6 cm .

The cookies that each person bake will be:

A = 4 1/2 dozen cookies

B = 6 3/4 dozen cookies

C = 15 3/4 dozen cookies.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.

Person A baked 4 1/2 Dozens of cookies for a bake sale. Person B Baked 1 1/2 as many as Person A. This will be:

= 1 1/2 × 4 1/2

= 6 3/4

Person C Baked 2 1/3 as many as Person B. This will be:

= 2 1/3 × 6 3/4

= 7/3 × 27/4

= 15 3/4

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The range of the function will be;

⇒ { 4, 2, 0, - 2, - 4 }

or, { - 4, - 2, 0, 2, 4 }

A relation between a set of inputs having one output each is called a function.

Given that;

The relation is,

⇒ (x, y) = (- 3, 4) , (- 2, 2), (- 1, 0), (0, - 2), (1, - 4)

Now,

Since, The relation is,

⇒ (x, y) = (- 3, 4) , (- 2, 2), (- 1, 0), (0, - 2), (1, - 4)

We know that;

The range of relation is the value of y.

Hence, The range of relation = { 4, 2, 0, - 2, - 4 }

Thus, The range of the function will be;

⇒ { - 4, - 2, 0, 2, 4 }

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Answer:

X < - 50

Step-by-step explanation:

5 - 1/2 x > 30

Move 5 to the other side of the inequality

- 1/2 x > 25

Multiply both sides by 2, to get rid of the denominator on the left side

-x > 50

Now switch the inequality sign and multiply to get the minus on the other side

x < - 50

[tex]5-\dfrac{1}{2} x > 30[/tex]

Simplify:

[tex]-\dfrac{1}{2} x+5 > 30[/tex]

Subtract 5 from both sides:

[tex]-\dfrac{1}{2} x+5-5 > 30-5[/tex]

[tex]-\dfrac{1}{2} x > 25[/tex]

Multiply both sides by [tex]-\dfrac{2}{1}[/tex]:

[tex]-\dfrac{2}{1} \times(-\dfrac{1}{2} x) > -\dfrac{2}{1} \times(25)[/tex]

[tex]\fbox{x} < \fbox{-50}[/tex]

A) The ratios for 2021 are as follows:

Rate of return on total asset = (Profit for the year / Total assets) * 100 = (12,605 / 29,935) * 100 = 42%

Profit margin ratio = (Profit for the year / Revenue) * 100 = (12,605 / 55,000) * 100 = 22.9%

Current ratio = (Current assets / Current liabilities) = (17,190 / 7,700) = 2.23:1

Inventory turnover ratio = (Cost of sales / Inventory) = (35,100 / 3,675) = 9.58

Accounts receivable turnover ratio = (Revenue / Receivables) = (55,000 / 4,905) = 11.22

Debt ratio = (Total liabilities / Total assets) = (15,720 / 29,935) = 52.6%

Times interest earned = (EBIT / Interest) = (12,715 / 1,560) = 8.14

B) Based on the above industry averages:

profitability: the company's profit margin ratio of 22.9% is lower than the industry average of 40%, which suggests that the company's profitability is lower than the industry average.

liquidity: the company's current ratio of 2.23:1 is lower than the industry average of 2.5:1, which suggests that the company's liquidity is lower than the industry average.

use of financial gearing: the company's debt ratio of 52.6% is higher than the industry average of 6%, which suggests that the company is more heavily leveraged than the industry average.

In summary, the company profitability is lower than the industry average, liquidity is lower than the industry average, and the company is more heavily leveraged than the industry average.

A company's profitability refers to its ability to generate a profit and return on investment. It is a measure of how well a company is able to generate revenue, control costs, and manage its assets and liabilities. Profitability ratios are used to evaluate a company's financial performance and to compare it to other companies in the same industry. Some of the most common profitability ratios include:

Gross profit margin: measures the percentage of revenue that remains after accounting for the cost of goods sold. It's calculated by dividing gross profit by revenue.

Operating profit margin: measures the percentage of revenue that remains after accounting for all operating expenses. It's calculated by dividing operating profit by revenue.

Net profit margin: measures the percentage of revenue that remains after accounting for all expenses, including taxes and interest. It's calculated by dividing net profit by revenue.

Return on assets (ROA): measures how efficiently a company is using its assets to generate a profit. It's calculated by dividing net income by total assets.

Return on equity (ROE): measures how efficiently a company is using shareholder's equity to generate a profit. It's calculated by dividing net income by shareholder's equity.

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Work Shown:

[tex]\left(3\text{x}^2\text{y}^5\right)^3\\\\\left(3\right)^3\left(\text{x}^2\right)^3\left(\text{y}^5\right)^3\\\\27\text{x}^{2*3}\text{y}^{5*3}\\\\27\text{x}^{6}\text{y}^{15}\\\\[/tex]

Explanation:

The outer exponent 3 is "distributed", so to speak, to each term inside the parenthesis. This isn't the actual distribution rule. But we can think of it as such. This is what's happening in the second step.

So we'll cube the coefficient 3 to get 3^3 = 27, and we'll cube x^2 to get x^6, and finally cube y^5 to get y^15.

I used the rule [tex](a^b)^c = a^{b*c}[/tex] for the third step.

Answer:

11/10

Step-by-step explanation:

33/10 - 22/10

Answer:

The answer is zero

Step-by-step explanation:

Hope it helps

Answer:

I hope this helps. Let me know if you have any doubts. Have a nice day!!

Answer:

Step-by-step explanation:

You want to find a sequence of transformations that will map ∆PZY to ∆RST as shown in the figure.

First of all, we notice the triangles are not the same size. We can find the required dilation factor by finding the ratio of corresponding side lengths.

The first two letters in the triangle designators in the similarity statement are PZ and RS. Since RS is the target size, the dilation factor needs to be ...

  k = RS/PZ

Counting grid squares in the figure, we see this ratio is ...

  k = 2/4 = 1/2

Dilation by a factor of 1/2 will make triangle PZY the same size as ∆RST.

Using the origin as the center of the dilation, all of the points of ∆PZY move to a position that is half their original distance from the origin. The dilated triangle is purple triangle P'Z'Y' in the attached figure.

When we name the vertices of ∆PZY or ∆P'Z'Y', we are naming them in counterclockwise order. The vertices of ∆RST are being named in clockwise order. This reversal of the sequence of vertices is caused by a reflection over a line.

The line of reflection will be halfway between a vertex and its reflected image. For example, reflecting ∆P'Z'Y' across the y-axis give ∆P"Z"Y", as shown in the attached figure. This reflection requires an additional transformation to map P"Z"Y" to RST.

We want to map P' to R, Z' to S, and Y' to T. As it happens the line halfway between these pairs of points is the line y=-x, the dashed line shown in the attachment.

Reflection across the line y = -x will map ∆P'Z'Y' to ∆RST.

This transformation, together with the dilation above, will map the ∆PZY to ∆RST as required.

__

If we use the reflection over the y-axis described above, we are faced with mapping ∆P"Z"Y" to ∆RST. We notice that segment P"Z" points "east" (in the +x direction). We want to map this segment to RS, which points "north" (in the +y direction). That can be accomplished by rotating ∆P"Z"Y" 90° counterclockwise about the origin.

So, another sequence of transformation that will make the required mapping is ...

The order of reflection and rotation is important. The dilation can occur anywhere in the sequence.

Perhaps you realize that we could reflect the figure across the x-axis instead of the y-axis. In that case, the rotation needs to be 90° CW to complete the mapping. That is, yet another sequence could be ...

If you decide you want to do the rotation before the reflection, then the direction of rotation is reversed.

__

Additional comment

Figuring the answer to these mapping problems requires a certain amount of spatial sense. It can help to cut a figure from paper or cardboard and label the vertices. Then you can translate it, rotate it, flip it over, to see what works to get it to the right position. If you have a little trouble with the rotation, you can stick a pin through the center of rotation so your figure keeps its appropriate distance and orientation relative to that center.

Tracing paper and/or transparencies can be helpful for these exercises.

A system of linear equations with an infinite number of solutions is a(n) equivalent equations system.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

here,
When a system of linear equations consists of an infinite number of solutions then this equation should be dependent and consistent as well, and this system is said to be a system of equivalent equations.

Thus, A system of linear equations with an infinite number of solutions is a(n) equivalent equations system.

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For the given line whose equation is [tex]y=x+3[/tex] :

x   y    (x,y)

0 3     (0,3)

1 4     (1,4)

2 5     (2,5)

3      6      (3,6)

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

A line in slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept .

Given the equation y = x + 3, the slope (m) is 1 and the y-intercept (b) is 3.

So, we can fill the table like this:

For the given line whose equation is [tex]y=x+3[/tex] :

x   y    (x,y)

0 3     (0,3)

1 4     (1,4)

2 5     (2,5)

3      6     (3,6)

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Answer:

The graph of the equation "y - 1 = (x - 3)" is a straight line.

To graph this equation, we can start by rearranging the equation to get "y = x - 3 + 1". This simplifies to "y = x - 2".

This equation is in slope-intercept form, which means that the slope of the line is given by the coefficient of the x term, and the y-intercept (the point where the line crosses the y-axis) is given by the constant term. In this case, the slope is 1 and the y-intercept is (-2, 0).

To graph the line, we can start by plotting the y-intercept at the point (0, -2). Then, we can use the slope of 1 to find a second point on the line and draw a straight line through these two points. The graph of the equation "y = x - 2" is shown below:

[asy]

unitsize(1.5cm);

draw((-1.5,0)--(1.5,0));

draw((0,-2.5)--(0,2.5));

draw((-1.5,-2)--(1.5,2),dashed);

label("$x$", (1.5,0), E);

label("$y$", (0,2.5), N);

[/asy]

The graph of the equation "y - 1 = (x - 3)" is the same as the graph of the equation "y = x - 2", except that all the y-values on the graph are increased by 1. This means that the graph of the equation "y - 1 = (x - 3)" is obtained by shifting the graph of "y = x - 2" upward by 1 unit. The graph of the equation "y - 1 = (x - 3)" is shown below:

[asy]

unitsize(1.5cm);

draw((-1.5,0)--(1.5,0));

draw((0,-2.5)--(0,2.5));

draw((-1.5,-1)--(1.5,3),dashed);

label("$x$", (1.5,0), E);

label("$y$", (0,2.5), N);

[/asy]

The answer choices given in the question do not match the description of the graph of the equation "y - 1 = (x - 3)". "O" does not match the description of the graph, as it is not a graph of a straight line. "(-31)" and "10" do not match the description of the graph, as they are not graphs at all. "CO" does not match the description of the graph, as it is the graph of a circle, not a straight line. "8" does not match the description of the graph, as it is the graph of an exponential function, not a straight line. "fi" does not match the description of the graph, as it is not a graph of a function. "Q" does not match the description of the graph, as it is not a graph at all. "4." does not match the description of the graph, as it is not a graph of a function. "y" does not match the description of the graph, as it is not a graph at all.

Therefore , the solution to the given problem of trigonometry comes out to be  Additionally, the symmetry of these basketball courts, tennis courts, and soccer fields is mirror imaged.

Trigonometry is the discipline of mathematics that studies correlations between angles and sides of triangles. Trigonometry is present in all of geometry because every straight-sided form may be reduced to a set of triangles. Amazingly intricate connections exist between trigonometry and other areas of mathematics, particularly calculus, real or complex, infinite series, logarithms, and infinite series.

Here,

Geometry has a wide variety of shapes depending on the size. The 2-d shapes include a variety of polygonal forms and the following: circle, triangle, square, rectangle, kite, trapezium, parallelogram, and rhombus.

The fundamental shapes in three dimensions are cube, cuboid, sphere, cone, and cylinder.

Many sports use geometric forms to help delineate the precise areas of play.

View the soccer field below to see how it is composed of quadrilaterals, rectangles, 90-degree angles, and circles.

Additionally, the symmetry of these basketball courts, tennis courts, and soccer fields is mirror imaged.

Therefore , the solution to the given problem of trigonometry comes out to be  Additionally, the symmetry of these basketball courts, tennis courts, and soccer fields is mirror imaged.

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Answer:

3 stacks of paper can be purchased.

Step-by-step explanation:

Start by setting up the inequality:

15 = 3.79x

Now that you have set up the inequality, go to solve the inequality.

You should get the answer 3.958 (rounded). Since Mr. Valentino can not by a half stack of paper, drop the decimal so we are left with 3.

I would describe the graph as a straight line increasing, with money on y and stacks of paper on the x axis

Therefore , as a result, we may state that the stated trapezoid angles x = 110°, which is the solution to the problem.

A trapezoid is a quadrilateral that has at least one connected pair of sides. It has the name trapezium. By definition, a trapezoid in Euclidean geometry is a convex quadrilateral. The trapezoid's base is made up of its parallel sides. A closed, flat shape having two neighboring sides and four successive sides is called a trapezoid. The parallel walls and base of the trapezoid are commonly referred as as the parallel sides and the legs, respectively.

Here,

Given : 110°

and 90°

To find the value of x ,

Thus,

The value of angle opposite to x :

=> 110° + y =180°

=>y =180°-110°

=>y = 70°

thus, x value is

=> x + 70° =180°

=> x =110°

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The constant term that should be used to complete the square? x2 - 5x + _____ = 7 is 25/4

What is quadratic equation ?

A quadratic equation in the variable x is of the form. ax2 + bx + c = 0, where a, b, c are real numbers and a ≠ 0. • Roots of a quadratic equation : A real number α is said to be a root of the. quadratic equation ax2 + bx + c = 0, if aα2 + bα + c = 0.

Given:

x^2-5x+c=7, the constant term c will be obtained using the formula:

c=(-b/2a)²

The quadratic equation in its generic form is:

ax^2 + bx + c

To complete squares we must add the following term:

(b / 2) ^ 2

The equation is:

ax^ 2 - 5x + k = 7

By completing squares we have:

x ^ 2 - 5x + (-5/2) ^ 2 = 7 + (-5/2) ^ 2

Rewriting:

x ^ 2 - 5x + 6.25 = 7 + 6.25

Hence, A constant term should be used to complete the square is 25/4 or 6.25.

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Answer:

Choose the right container: Select a container that is appropriate for the size and type of plant you want to grow. Make sure the container has drainage holes to allow excess water to drain away.

Use the right soil: Use a well-draining soil mix that is appropriate for the type of plant you are growing. Avoid using soil from your garden, as it may contain pests or diseases that can harm your plant.

Provide proper lighting: Most plants need plenty of sunlight to grow, so choose a location that gets plenty of light. If you are growing plants indoors, you may need to use grow lights to provide adequate lighting.

Water properly: Water your plants regularly, but avoid overwatering, as this can lead to root rot. Check the soil moisture level regularly and water when the top inch of soil is dry.

Fertilize: Use a balanced fertilize to provide your plants with the nutrients they need to grow. Follow the instructions on the fertilize package for the proper amount and frequency of application.

Pest control: Keep an eye out for pests such as aphids, thrips, and mealybugs, and take action if necessary. There are many natural ways to control pests, such as introducing predatory insects or using neem oil.

By following these general tips, you should be able to successful

There are three popular choices when it comes to growing - Hydroponics, Soil and Coco. These methods vary widely according to the source, understanding the source of your media can lead to a grower getting better results.

The number in the replacement set that will make the equation true is (c) 112

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

x ÷ 2 = 56

Rewrite the expression properly

so, we have the following representation

x/2 = 56

Also, we have the replacement set to be

{28, 56, 112}

In the given equation, we have the variable to be

The variable is x

Multiply 2 to both sides of the expression

So, we have the following representation

2  * x/2 = 56 * 2

Evaluate the products on both sides of the equation

x = 112

Hence, the solution is x = 112

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x = 3/4 is the correct solution of the given expression.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,

The expression Lin tried to solve
8(x-3)+7=2x(4-17)

Simplifying the expression,
8x - 24 = 2x(-13)
8x - 24 = -26x
8x+26x = 24
32x = 24
x = 24/32
x = 3/4

Thus, x = 3/4 is the correct solution of the given expression.

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The pound of cement used based on the information will be C. 2 pounds.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

In this case, for each pound of sand, he uses 1 2/3 pounds of gravel and for each pound of gravel, he uses 2/5 pound of cement.

The pound of cement used will be:

Gravel = 1 2/3 × 3

= 5 pounds

Cement used will be:

= 2/5 × 5.

= 2 pounds.

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Elena swaps her cookies for a friend's doughnut is the examples of voluntary exchange. Hence,

A voluntary exchange occurs when two parties freely exchange products or services without the use of coercion or other restrictive measures. Both parties will gain from the deal and both parties want to make the exchanged items. The idea of voluntary exchange is crucial to a free market economy.

Customers also willingly swap money to buy his strawberries. They can choose to buy strawberries somewhere else if they see that some of his strawberries have flaws. This is a voluntary exchange because both sides gain from it.

One of the most crucial principles of economics is voluntary exchange. In a market economy, where producers and consumers freely exchange products and services, this transaction is taking place. In the end, both sides benefit from the process.

Thus, option A is correct.

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