What are the 5 steps in solving equations by substitution?.

A perimeter is the length of a two-dimensional shape's boundary. It is sometimes described as the total length of the object's sides. The perimeter of that shape is equal to the algebraic sum of the lengths of its sides.

The term "two-dimensional shape" refers to any shape that is flat and has only two dimensions, i.e. length and breadth. Each polygon is a flat, 2-D figure that rests on a plane. Polygons, such as triangles, rectangles, and squares, are closed figures that are enclosed by a series of lines. The length or linear measure of these confined line segments is known as the polygon's perimeter (peri: around; metre: measure). Or to put it another way, it is the length of its borders. The centimetre (cm) or metre is its unit (m).

The whole distance that a rectangle's boundaries, or its sides, cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the sum of its four sides. Since a rectangle's perimeter is a linear measurement, the unit will be in metres, centimetres, inches, feet, etc.

Perimeter of a rectangle = sum of four sides

= AB     +     BC        + CD       +   AD

= length + breadth + length + breadth

= 2 length + 2 breadth

Perimeter of a rectangle =   2 × (length + breadth)

The radius of the circle serves as one of the three variables in the perimeter of a circle formula, along with two constants. The formula for calculating a circle's circumference or perimeter is as follows:

Circumference of a circle is equal to 2πr.

where,

r = radius of the circle

D = diameter of the circle

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There is a loss of $14500 and 30 units are required to be made to break- even. The solution has been obtained using profit function.

What is profit function?

A relationship that depicts the difference created by subtracting the cost function from the revenue function is called a profit function. The ideal pairing of revenues and expenses to generate the greatest possible profit can be seen on the graph of a profit function.

a. The fixed cost of the factory is $5000 + $10000 = $15000

The variable cost of the factory is $700 + $800 = $1500

The revenue of the factory is $2000x.

We need to find profit after 1 unit is made i.e. x = 1

So, TC= FC + VC(x)

⇒ TC = $15000 + $1500(1)

⇒ TC = $16500

Therefore, the profit will be

⇒Profit = R(x) - TC

⇒Profit = $2000(1) - $16500

⇒Profit = -$14500

Hence, there is a loss of $14500.

b. For break even, the total cost must be equal to the revenue

So, TC = R(x)

⇒ FC + VC(x) = R(x)

⇒ $15000 + $1500(x) = $2000(x)

⇒ $15000 = $500(x)

⇒ x=30

Hence, 30 units are required to be made to break- even.

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The graph of F(x), shown below, resembles the graph of G(x) = x2, but it has been changed.

[tex]y=a(x-hx)^{2} + k[/tex]  the answer is F(x) = [tex]4x^{2} -1[/tex]

What is meant by graph?

We are given a function:

G(x)=[tex]x^{2}[/tex]

The graph of G([tex]x[/tex]) is also shown in the given question figure.

It is a parabola with vertex at (0,0).

Sign of [tex]x^{2}[/tex] is positive, that is why the parabola opens up.

General equation of parabola is given as:

[tex]y=a(x-hx)^{2} + k[/tex]

Here, in G(x), a = 1

Vertex (h,k) is (0,0).

As seen from the question figure,

The graph of F(x) opens down that is why it will have:

Sign of [tex]x^{2}[/tex] as negative. i.e. a = -1

And vertex is at (0,-5)

Putting the values of a and vertex coordinates,

[tex]y= -1 (x-0x)^{2} + (-5)[/tex]

Hence, the equation of parabola will become:

[tex]y=-x^{2} -5x[/tex]

The correct answer is:

F(x) =[tex]y=4x^{2} -1[/tex]

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Equation for m< 1 (x - 9)° and m <2 =(8x)° is <1 = 168 <2 = 12

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

When one side of an equation equals the other, it is said to be an equation. For instance, in this case, we know that 4 + 4 = 8 and 10 - 2 = 8, which means that this equation is correct.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10.

To start, you must find x.

8x + x -9 = 180

9x -9 = 180

9x = 189

x = 21

Now, change both angles' x values to 21.

8(21) = 168

(21) - 9 = 12

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Divide the population standard deviation () by the square root of the sample size (n) to obtain the standard deviation of the sample mean (X).

The sample mean is normally distributed, with mean X= and standard deviation X=/n, where n is the sample size, for samples of any size taken from a population that is normally distributed.

The standard deviation of the population divided by the square root of the sample size is equal to the standard deviation of the sampling distribution of means.

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The substitution method is a powerful tool used to solve systems of linear equations with three variables. Beginning with one of the equations for one of the variables, utilise the substitution method.

This will give you an expression for that variable in terms of the other two. Then, substitute this expression into the other equations and solve for the remaining variables.

Consider, for example, a set of linear equations involving the variables x, y, and z:

x + y + z = 13

2x + 4y - z = 6

3x - 2y + 3z = 11

Start by solving the first equation for x in order to apply the substitution method here:

x = 13 - y - z

Now solve for y and z by substituting this expression into the previous two equations:

2(13 - y - z) + 4y - z = 6

39 - 2y + 3z = 6

3(13 - y - z) - 2y + 3z = 11

39 - 5y + 6z = 11

Subtract 39 from both sides of each equation, then solve for y and z using elimination or another method. Once you have found values for both variables, plug them into the original expression for x to find its value.

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A BAR graph would be most suitable for displaying the given data.

The visual representation of numerical data is a graph. Graphs offer a visual means of presenting complicated data and demonstrating the link between various variables or data sets. Graphs are a fantastic tool for highlighting patterns and connections in data.

Given data, The number of pets in each student's household.

Stem-and-leaf plot:

A stem and leaf plot, often known as a stem plot, is a method for categorizing discrete or continuous data. As data are gathered, they are organised using a stem and leaf plot. A stem and leaf plot resembles a bar graph in appearance. The term stems from the fact that each number in the data is divided into a stem and a leaf.

Thus it is not suitable for given data.

Line graph:

An individual data point is connected by a line in a line graph, sometimes referred to as a line plot or a line chart. A line graph shows numerical values over a predetermined period of time. Line graphs are frequently used in finance to show the historical price movement of an asset or instrument.

Since, we have similar but Discrete with three variables in our data thus this graph is also not suitable.

Bar graph:

A bar graph (also known as a bar chart or bar diagram) is a visual tool that uses bars to compare data among categories. A bar graph may run horizontally or vertically.

Since we need to compare the data thus, bar graph is most suitable for the giving condition.

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Answer:

C

Step-by-step explanation:

multipled is 12/56 but simplified is 3/14

The point (-4, 2) be located in second quadrant. Due to the fact that x is negative and y is positive.

The coordinate system's two axes, the x-axis and the y-axis, define a region is called a quadrant. The quadrants are generated when the two axes, the x-axis and the y-axis, cross at a 90-degree angle.

These areas include coordinates, or positive and negative values of the x- and y-axes. The position of a point in a quadrant is indicated by the coordinates.

The first quadrant is located in the graph's upper right-hand corner. Both the x and y values in this quadrant are positive.

The second quadrant is located in the graph's upper left corner. The value of y is positive in this quadrant while the value of x is negative.

The third quadrant is located in the graph's lower left-hand corner. It includes both the negative values of x and y.

Fourth Quadrant, the final quadrant has a positive x value and a negative y value, and it is located in the lower right corner.

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The complete question is:

What quadrant will the point (-4, 2) be located in?

The correct option is 'The domain of both functions is all real numbers'.Option A

Generally, functions are f(x) = 5x and g(x) =5x

Since the domain of f(x) is, D= { x : x belongs to all real numbers.}

Therefore, the set of all real numbers constitutes the domain of f(x).

Due to the fact that f(x) and g(x) both return the same result,

Therefore, the set of real numbers is likewise included in the domain of g(x).

Now, the range of f(x) is , R=  { 5x : x belongs to all real numbers.}

As a result, the set of possible values for f(x) includes only real numbers.

In addition, the range of g(x) includes all real values.

Given what has been said so far, it is clear that only choice (1) should be considered accurate.

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CQ

Keshawn is asked to compare and contrast the domain and range for the two functions.

f(x) = 5x

g(x) = 5x

Which statements could he include in his explanation? Check all that apply.

1. The domain of both functions is all real numbers.

2. The domain of f(x) is x > 5.

3. The domain of g(x) is x > 5.

4. The range of both functions is y > 5.

5. The range of f(x) is y > 0.

6. The range of g(x) is y > 0.

The slope is 2 when expressed in the slope-intercept form. Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5.

When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). The y value of the y intercept point is represented by b in the equation.

Writing an equation for a line in the form y = mx + b is known as slope intercept form in mathematics. The m indicates the line's slope, while the b indicates the y-intercept. When attempting to locate a point on a line or determine y given x, the slope intercept form is utilized.

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Answer:

answer is 114 I have confirmed it

The cost of plan A is represented by the equation:

Cost A = 40 + 0.02x

where x is the number of minutes of calls.

The cost of plan B is represented by the equation:

Cost B = 0.18x

To find the point where the two plans cost the same, we can set the two equations equal to each other and solve for x:

40 + 0.02x = 0.18x

40 = 0.16x

x = 250

So when the customer makes 250 minutes of calls, the cost of the two plans will be the same.

The cost of plan A will be 40 + 0.02250 = $50 and the cost of plan B will be 0.18250 = $45

So when the customer makes 250 minutes of calls, Plan A and Plan B cost the same amount of money.

Answer:

Step-by-step explanation:

p

By using exponential growth formula we get 5531 fish in the pond after 6 months.

To find the number of fish in the pond after 6 months, we can use the formula for exponential growth:

N(t) = N0 * [tex](1 + r)^{t}[/tex]

where N(t) is the number of fish at time t (in this case, after 6 months), N0 is the initial number of fish (7), and r is the growth rate (2.9 fish per month).

We can substitute these values into the formula and solve for N(6):

N(6) = 7 * [tex](1 + 2.9)^{6}[/tex]

N(6) = 7 * [tex](3.9)^{6}[/tex]

Using the calculator, we get N(6) = 7 * 791.64 = 5530.5

Rounding up to the nearest whole fish, we get 5531 fish in the pond after 6 months.

Note: The exponential model assumes that the growth rate is constant over time and that the pond has unlimited resources to sustain the fish population.

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Slope of the line that contains the points (13, -2) and (3,-2) is 0.

What is Slope of line?

The increase divided by the run is the slope. By examining the rise and run, you can infer the slope of a line from its graph. A line has the property that its slope remains constant throughout. Therefore, you may determine the slope by selecting any two points along the line's graph.

By definition, the slope or gradient of a line describes its steepness, incline, or grade.

m = y2 - y1/x2 - x1

Given ;

x1 =13, x2 = 3, y1 = -2, y2 = -2

ΔX = x2-x1

ΔX = 3 - 13

ΔX = -10

Now, calculating ΔY ;

ΔY = y2 - y1

ΔY =-2 - (-2)

ΔY = 0

Hence, Slope of the line is ;

Slope(m) = ΔY/ΔX

Slope(m)= 0/-10

Slope (m) = 0

Therefore , Slope of the line that contains the points (13, -2) and (3,-2) is 0.

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Its slope is 0, which indicates that it is a horizontal line, and its

y-intercept is −3.

When an equation of a line has only one variable, the resulting graph is a horizontal or a vertical line.

The graph of the line  x=a

, where  a is a constant, is a vertical line that passes through the point  (a,0) . Every point on this line has the x-coordinate equal to a, regardless of the y-coordinate.

The graph of the line  y=b , where  b  is a constant, is a horizontal line that passes through the point  (0,b) . Every point on this line has the y-coordinate equal to b, regardless of the x-coordinate.

We can write

y=−3

as

y=0x−3

So, its slope is 0, which indicates that it is a horizontal line, and its

y-intercept is −3. Hence, its graph looks like

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One binomial's terms are multiplied by the other binomial's terms. The algebraic total of these products is then calculated after this step. We employ a technique called the FOIL method to multiply binomials.

Therefore, the order in which the terms are multiplied in this order is FOIL (First Outer Inner Last).

An algebraic expression with two terms joined by a plus or minus sign is known as a binomial. Binomial multiplication is comparable to multiplying two whole numbers or fractions. Utilising the distributive property of multiplication twice is one way to multiply binomials.

The letters in the acronym FOIL stand for First, Outer, Inner, and Last. Since only binomials may be multiplied using this approach, it cannot be used to multiply all polynomials. The FOIL formula has the following general form: (a + b) (c + d) = ac + ad + bc + bd.

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0.5 is equivalent to the fraction 1/2.

What is a fraction?

In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

We are given 0.5 which is to be converted into a fraction.

So, for this we will take 0.5 as the numerator and 1 as the denominator because anything divided by 1 is the number itself.

Thus, we get

⇒0.5/1

Now, we will multiply both numerator and denominator by 10.

From this, we get

⇒(0.5*10)/(1*10)

⇒5/10

Now, we will reduce the fraction to the lowest form by dividing both numerator and denominator by 5.

From this, we get the fraction as 1/2.

Hence, 0.5 is equivalent to the fraction 1/2.

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Answer:

15 boys

Step-by-step explanation:

We know

A group has 20 children

25% girls

25% = 0.25

20 times 0.25 = 5 girls

20 - 5 = 15 boys

So, there are 15 boys

To find the number of solutions to given equation by comparing the coefficients of the variables of the equations.

We know that a solution of an equation is a value that satisfies given equation.

We can find the number of solutions to given equation by comparing the coefficients of the variables of the equations.

There are three types of solutions to the set of linear equations:    Unique Solution: The linear equation in one variable (equation of the form ax + b = 0) always has a unique solution.    

No Solution: When the graphs of the linear equations represents parallel lines, then the system of linear equations has no solution.

Infinitely Many Solution: if the system of equations represent coincident lines, and they have the same y-intercept, then the system of equations has infinitely many solutions.

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The size of the angle marked y correct to three significant figures is 26.6°.

Right angled triangle are those triangle for which one of the angle is 90 degrees.

Given is a right angled triangle.

By the definition of trigonometric functions,

Sin y = Opposite side / Hypotenuse

sin y = 31.4 / 70.2

sin y = 0.447

y = 26.57

  = 26.6

Hence the value of y is 26.6.

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Answer:

Randy

Step-by-step explanation:

Randy:  2 runs / 3 innings = 0.67

Felix:  4 runs / 5 innings = 0.80

Johan:  5 runs / 7 innings = 0.71

The simplification of the expression is [tex]\frac{7}{5}[/tex].

What is expression?

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. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here the given expression is

=> 1 + [tex]\frac{1}{1+\frac{1}{1+\frac{1}{2} } }[/tex]

=> 1 + [tex]\frac{1}{1+\frac{1}{\frac{2+1}{2} } }[/tex]

=> 1 + [tex]\frac{1}{1+\frac{1}{\frac{3}{2} } }[/tex]

=> 1 + [tex]\frac{1}{1+\frac{3}{2} }[/tex]

=> 1 + [tex]\frac{1}{\frac{2+3}{2} }[/tex]

=> 1 + [tex]\frac{1}{\frac{5}{2} }[/tex]

=> [tex]1+\frac{2}{5}[/tex]

=> [tex]\frac{5+2}{5}[/tex]

=> [tex]\frac{7}{5}[/tex]

Hence the simplification of the expression is [tex]\frac{7}{5}[/tex].

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The inequality equation for the measurements of the rectangular field must satisfy t<225.

If two real numbers or algebraic expressions are related by the symbols “>”, “<”, “≥”, “≤”, then the relation is called an inequality.

Given that,

The length of the rectangle is 2t meters

the breadth of the rectangle is 50 meters

The perimeter of the rectangle is given by 2×(length+breadth)

Here the perimeter of the rectangle is less than 1km=1000meter

Forming an equation with the given data

2×(2t+50)<1000

2t+50< 1000/2

2t+50<500

2t<500-50

2t<450

t<450/2

t<225

Thus, The inequality equation for the measurements of the rectangular field must satisfy t<225.

Complete question: A rectangular field has these measurements kim walks around the edge of the field. she walks less than 1km. form and solve an equality to find the possible values of t when length of the field is 2t meters and breadth is 50 meters

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In a continuous series, the mean is 5, If efx= p and ef= 10 than the value of p​ = 50

Instead of being presented as a single number in a continuous series, the observations are presented in different class intervals, and the frequency represents the percentage of observations that fall into each class interval.

Continuous series are those in which frequencies are provided along with the variable's value as class intervals. an example: Their respective frequencies are 3, 7, 11, 9, and 6.

step1:

here mean(x)=5

and e f x=10

then as given

p=e f x

step2;

p=10*5=50

p=50

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You get the "Array indices must be positive integers or logical values" error when using the "angle" function because you are trying to use a non-numeric or non-logical value as an index.

The "angle" function in MATLAB is used to find the phase angle of a complex number. When you are trying to use the function, you are probably passing in a variable or expression that is not a numeric or logical value.

In MATLAB, array indices must be positive integers or logical values. When you try to use a non-numeric or non-logical value as an index, you will get the "Array indices must be positive integers or logical values" error.

This means that you need to make sure that the variable or expression you are passing into the "angle" function is a numeric or logical value before using it as an index.

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Complete question:

Why do I get "Array indices must be positive integers or logical values" error when using "angle" function?

Answer:(8,6)

Step-by-step explanation:

The slope of the given graph is m = -1, and the y-intercept is y = 1.

A line's slope reveals its inclination and direction. Without actually using a compass, determining the slope of lines in a coordinate plane can aid in determining whether the lines are parallel, perpendicular, or have no relation at all.

Any two different points on a line may be used to derive the slope of that line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line equation.

Consider each box of the graph as 1 unit.

So, from the graph, at x = 0

y = 1

So, this is the y-intercept of the line.

Consider any two points

(x₁, y₁) = (0, 1)

(x₂, y₂) = (1, 0)

The slope is given by the slope formula as

m = (y₂ - y₁)/(x₂ - x₁)

= (0 - 1)/(1 - 0)

= -1

The slope of the graph is m = -1.

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The total reports during the year is 15.

percentage, a relative value indicating hundredth parts of any quantity.

Given that tanik turns in his third report. his teacher says 20% of his reports for the year are done.

We have to find the number of research reports will Tanik complete during the school year.

Let the number of reports be = x

As mentioned, when Tanik submitted his 3rd report, he had completed 20% of the reports so

20/100×x=3

0.2x=3

Divide both sides by 0.2

x=15

Hence,  the total reports during the year is 15.

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