What is equality for Class 7?

The horizontal line test is a method used to determine if a given function is one-to-one, which means that for every unique x-value, there is a unique y-value. A function that is one-to-one can be inverted, meaning that it has an inverse function.

The inverse function of a one-to-one function is a function that undoes the original function.

The horizontal line test is used to determine if a given function is one-to-one by drawing a horizontal line through the graph of the function and seeing if the line intersects the graph at most once.

If the function is one-to-one, it has an inverse function and it can be found by switching the x and y values and solving for y.

For example, if the original function is f(x) = 2x + 1, its inverse function is f^-1(x) = (x-1)/2. This inverse function undoes the original function and it can be used to solve equations, find derivatives, and study geometric transformations.

It's important to note that the horizontal line test is only a sufficient condition, meaning that a function that passes the horizontal line test is one-to-one, but not all one-to-one function pass the horizontal line test.

In conclusion, the horizontal line test is a method used to determine if a given function is one-to-one, which is important because one-to-one functions can be inverted.

The inverse function undoes the original function, and it can be found by switching the x and y values and solving for y. The test is simple and easy to apply, but only a sufficient condition.

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Customer questions had no impact on changes in discounts or customer behavior, according to those two variables.

A non-binding request for a quote or sales information from a customer to a business. The request may mention particular goods or services, terms, and, if required, delivery deadlines.

For the stated question-

Since, customer inquiries did not alter in response to changes in discount, we can conclude that discounts had no influence on them.

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The correct question is attached.

Answer:

2x+3=5

Step-by-step explanation:

2x+3=5 us the only one with an equals to sign

an equation always have an equals to

Answer: The value of x = 7

Step-by-step explanation:

In the figure consider the parallelogram is a ABCD parallelogram

A parallelogram is a two-dimensional shape.

It has four sides, in which two pairs of sides are parallel.

Also, the parallel sides are equal in length.

If the length of the parallel sides is not equal in measurement, then the shape is not a parallelogram.

Similarly, the opposite interior angles of a parallelogram should always be equal. Otherwise, it is not a parallelogram.

AB = 3x+5

CD = 5x-9

where AB || CD and AD || BC

Also, AB = CD and AD = BC

then 3x+5 =  5x-9

when simplify the equation,

5x = 3x+5+9

5x = 3x+14

then

     5x-3x = 14

     2x = 14

     x  = 14÷2

     x = 7

then the value of x = 7

when substituting value of x in equations

AB = 3x+5 = 21+5 = 26

CD = 5x-9 = 35-9 = 26

AB = CD

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The coordinates of B is (-2, -6)

The formula to determine the midpoint of a straight line using the coordinates of its endpoints is known as the midpoint formula in coordinate geometry.

The formula is of the form

X= (x₂ + x₁)/2

Y = (y₂ + y₁)/2

From the formula the coordinates of B is solved knowing that midpoint is

M (3,-1) and A is (8,4) and say B (x₁, y₁)

3 = (8 + x₁)/2

6 = 8 + x₁

x₁ = -2

-1 = (4 + y₁)/2

-2 = 4 + y₁

y₁ = -6

hence B is (-2, -6)

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By evaluating the formula for the sequence, we will get the terms:

Here we want to find the second, fourth, and eleventh terms in the sequence:

A(n) = -9 + (n - 1)*3

n defines the "number" of the term in the sequence.

So to get the second term, we need to use n = 2, we will get.

A(2) = -9 + (2 - 1)*3

A(2) = -9 + 3 = -6

The fourth term is what we get if we evaluate in n = 4, then:

A(4) = -9 + (4 - 1)*3

A(4) = -9 + 9 = 0

And the eleventh term is what we get when we use n = 11, we will get:

A(11) = -9 + (11 - 1)*3

A(11) = -9 + 30 = 21

These are the 3 terms of the sequence that we wanted to find.

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The value of b is 2. Therefore (2, 1) is the midpoint of the line segment with endpoints (-4, 2) and (8, 0)

An equation is an expression that shows the relationship between numbers and variables.

If a point O(x, y) divides line segment AB with endpoints A(x₁, y₁) and B(x₂, y₂) in the ratio of 1:1 (midpoint). The coordinates of O is:

x = (x₁ + x₂)/2

y = (y₁ + y₂)/2

Given that (2, 1) is the midpoint of the line segment (-4, b) and (8, 0). Therefore:

1 = (0 + b)/2

b/2 = 1

b = 2

The value of b is 2.

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R's positive value is [tex]\sqrt{\frac{v}{\pi h} }[/tex]  V =r²h in terms of h is the formula used to calculate the volume of a cylinder.

The object's capacity is another name for it. The basic formula for volume is length, width, and height, as opposed to the basic formula for the area of a rectangular shape, which is length, breadth, and height. No matter how you refer to the various dimensions, the calculation remains the same. For instance, you can use "depth" instead of "height." The capacity of an object is expressed in terms of volume. A cup's capacity is said to be 100 ml, for instance, if it can hold 100 ml of water in its brim. The quantity of space a three-dimensional item takes up can also be referred to as volume.

given

Cylinder(volume )'s is equal to  = [tex]\pi r^{2}h[/tex]

where r = radius, h = height, and v = volume of the cylinder

⇒  [tex]r^{2} = \frac{v}{\pi h}[/tex]

⇒ ±r  = [tex]\sqrt{\frac{v}{\pi h} }[/tex]

The problem states that only the positive value of r is necessary.

So, r =  [tex]\sqrt{\frac{v}{\pi h} }[/tex]

R's positive value is [tex]\sqrt{\frac{v}{\pi h} }[/tex]  V =r²h in terms of h is the formula used to calculate the volume of a cylinder.

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Yes, it is possible to draw a triangle the length of whose sides are 2.5 cm 4.2 cm 8 cm.

The possibility to draw a triangle from mentioned three sides can be checked through SSS or side-side-side rule of triangle. It states that sum of any two sides should be greater than third side of the triangle. Assuming 2.5 cm to be side a, 4.2 and 8 cm to be side b and c respectively.

Side a + side b > side c

2.5 + 4.2 > 8

Add the values

6.7 not greater than 8

Side b + side c > side a

4.2 + 8 > 2

Add the values

12.2 > 2.5

side c + side a > side b

8 + 2.5 > 4.2

Add the values

10.5 > 4.2

As we see, that two cases show sum to be greater than third side. Thus, triangle can be drawn.

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The equation which gives solutions, x=0 and y=-6.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

y=-x-6............................(1)

x+3y=-18.........................(2)

now, solving both equation we get

x+3y=-18

x + 3(-x-6) = -18

x - 3x - 18 = -18

-2x = 0

x= 0

and, y= -0 -6 = -6

Hence, the solution is x=0 and y=-6.

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Therefore , the solution of the given problem of triangle comes out to be √3 ,√4,√5  advance to acute triangle category as they have small angle less than 90 degree.

Given that it has three sides and three vertices, a triangle qualifies as a polygon. It is a fundamental geometric figure. Triangle ABC is the term used to refer to a triangle containing the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.

Here:

Given :

=> 4 ,4√3,8

=> 0.5 , 1.3 , 1.2

=> 1.8 ,√6 ,0.8

=> √3 ,√4,√5

These can be advance to acute triangle category as they have small angle less than 90 degree.

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Calculating the pixel ratio of a website involves measuring the width and height of each element on the page and then dividing the width by the height.

Ratio is a comparison of two numbers or values expressed as a fraction or proportion. Ratios are used to compare different measures, such as costs, efficiency, productivity, or profitability, and to evaluate the relative importance of different elements. Ratios are also used to compare different items to each other, such as the ratio of sales to expenses. Ratios can be used to compare different time periods, and to assess the performance of a company over time.

The result is the pixel ratio, which can be used to determine how much of an element is visible on the page and how much is hidden. To calculate the pixel ratio, you can use a variety of tools, such as online tools, browser extensions, or specialized software. It is also important to note that the pixel ratio will vary depending on the device used to view the website, so it is important to test the website on multiple devices. Once the pixel ratio is calculated, it can be used to optimize the website for different devices.

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The constraint to make the statement true is -A< -B: Option C

A Constraint is a situation when an individual is limited or restricted to carry out an activity. It can also be seen as strictness or inhibition in relation to a variable

In most organizations, project managers are faced with constraints when they want to carry out an activity. Most of these constraints are external and out of the project manager's control.

Based on that if A<B, then - A < -B and this makes the constraint true.

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The formula for finding the hypotenuse of an isosceles right triangle when given the area is A = (1/2)bh, where A is the area, b is the base, and h is the height.

To calculate the hypotenuse, first solve for h, which is h = 2A/b. Then, use Pythagorean theorem to solve for the hypotenuse c, which is c = sqrt((b^2)+(2A/b)^2). To illustrate the formula, consider a triangle with an area of 20 and a base of 10. First, solve for h, which is h = 2(20)/(10) = 4. Then, solve for c, which is c = sqrt((10^2)+(4^2)) = sqrt(196) = 14. Therefore, the hypotenuse of the isosceles right triangle with an area of 20 and a base of 10 is 14.

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The value of q, based on the equation given, can be found to be - 1 / 6

To find q, you need to collect like terms on the correct side of the equation to be able to solve for q.

When given the equation,

1 / 2 = q + 2 / 3

You collect like terms to be:

q = 1 / 2 - 2 / 3

q = ( 3 - 4 ) / 6

q = - 1 / 6

In conclusion, the value of q is - 1 / 6.

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The function that represents the data in the table is 3x²+2. The correct answer is B.

The quadratic function is shown in the data table.

We must ascertain the function's equation.

The quadratic equation's generic form is

Let's replace the general form with the three coordinates (1,5, (2,14), and (3,29).

We therefore have;

a+b+c =5——— (1)

4a+2b+c= 14——— (2)

9a+3b+C =29------(3)

When (2) is subtracted from (1), we have;

9= 3a+b(4)

Subtracting (3) from (2) gives us;

15= 5a +b(5)

Subtracting (5) from (4) gives us;

6= 2a

3= a

As a result, the value of an is 3. When we replace this value in equation (4), we obtain;

3(3)+b= 9

b= 0

When a = 3 and b = 0 are substituted in equation (1), we obtain;

a+b+c =5

3+0+c=5

c=2

As a result, c has a value of 2.

As a result, when we substitute a = 3, b = 0, and c = 2 in the quadratic equation's general form y =ax²+bx+c, we obtain;

3x²+2

Consequently, the function that symbolizes the information in the table is 3x²+2

As a result, Option B is the right response.

Your question is incomplete but maybe your full question attached below

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The pole was at a depth of 2 feet  = - 2

What is height and distance ?

height can be defined as the the measurement in vertical direction where as the distance can be defined as the measurement in horizontal direction.

Given :

Casey was at the surface of a swimming pool and recorded the following two measurements,

in feet, on a number line: −8, which represents the depth of water in the swimming pool +7,

which represents the height of the slide at the pool  

To Find, What does 0 represent in this situation?  

Describe the height of the slide in relation to 0 in the situation

Casey held a pole in the swimming pool. The bottom of the pole was at a depth of 2 feet. How should Casey mark the level of the bottom of the pole on the number line

0 represent in this situation  - Top surface of Swimming pool  - Surface matching with ground

height of the slide in relation to 0 in the situation  = 7 feet

pole was at a depth of 2 feet = - 2

Hence, The pole was at a depth of 2 feet  = - 2

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Answer: There is only 5 rules in algebra.

Step-by-step explanation:

the unit price of the cheddar cheese is $0.15.

Division is the process of splitting a number or an amount into equal parts.

here, we have,

Hector paid $2.70 for a package of cheddar cheese slices.

There are 18 slices in the package.

i.e. the unit price of the cheddar cheese = $2.70/18

                                                                    =$0.15

hence, the unit price of the cheddar cheese is $0.15.

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If the sidewalk A , B ,C are horizontal to each other and D is connecting them, then we can say that the the sidewalk D is perpendicular to them .

We say that two lines are perpendicular if they form the angle of 90 degree between them. Thus , we can say that the sidewalk D are having a perpendicular relationship whit the other 3 sidewalks.

Horizontal means something which has a parallel relationship with the horizon . The opposite of horizontal is vertical which is also known as the portrait mode. A horizontal line is any line normal to a vertical line. Horizontal lines do not cross each other similarly the vertical lines do not cross each other.

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Answer:

Step-by-step explanation:

y = kx

proportionality constant = k = y/x

A.  k = y/x = 7/2 = 3.5   (you can plug in any x,y pair from the table and will get the same answer, 3.5)

B. k = y/x = 12/3 = 4   (you can choose any point on the line)

C.  k = y/x = 2.75   (same as the slope of the line)

D.  k = y/x = earnings/games = 65/5 = 13

E.  k = y/x = 12/3 = 4   (you can plug in any x,y pair from the table and will get the same answer, 4)

Knowing a circle's circumference can be used to calculate its radius, which is given by the formula r = c / (2 * π ). If you know the diameter, D, you may calculate the radius, R, which is equal to D divided by 2.

For Example

Circumference c = 26.8in

Area A = 57.156

Diameter = 8.5307

Radius of the circle Radius r = 4.26535.

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Answer:

A. The domain should be all reals.

B. The range is y≤1 if the function is |x-2|+1.

C. It's a function.

If you get this wrong then my bad

The angle of refraction is 32 degrees. The result is obtained by using the formula from the Snell's Law.

The Snell's Law is a formula to describe the relationship between the angles of incidence and refraction when a light passes through two medias. It can be expressed as

n₁ / n₂ = sin θ₂ / sin θ₁

Where

We have:

Find the angle of refraction!

Using the formula of Snell's Law, we'll get the refracted angle.

n₁ / n₂ = sin θ₂ / sin θ₁

1.5 / 2.0 = sin θ₂ / sin 45°

3 / 4 = sin θ₂ / (½√2)

sin θ₂ = 3(½√2)/4

sin θ₂ = 3/8 √2

sin θ₂ = 0.53

θ₂ = arc sin 0.53

θ₂ = 32°

Hence, the refracted angle is 32 degrees.

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So on solving the provided question we can say  that  the importance of roots of polynomial equation because as the roots are the core of it. it helps in forming of that polynomial

A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.

here,

the importance of roots of polynomial equation because as the roots are the core of it. it helps in forming of that polynomial

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Answer:

144%

Step-by-step explanation:

I hope this helps you

1. MO = NP (Given)

2. MO = MN + NO (Segment Add)

  NP = NO + OP (Segment Add)

3. MN + NO = NO + OP (Transitive / Substitution)

4. MN = OP (Subtraction POE)

Answer: sinθ=-12/13

Step-by-step explanation:

[tex]\displaystyle\\Given:\ cot\theta=\frac{5}{12} \ \ \ \ \pi < \theta < \frac{3\pi }{2} \ \ \ \ Find:\ sin\theta\\\\\frac{cos\theta}{sin\theta} =\frac{5}{12}[/tex]

 Multiply both parts of the equation by 12sinθ:

[tex]12cos\theta=5sin\theta[/tex]

Squared both parts of the equation:

[tex](12cos\theta)^2=(5sin\theta)^2\\\\144cos^2\theta=25sin^2\theta\ \ \ \ (1)\\[/tex]

[tex]Find\ sin\theta[/tex]

Add 144sin²θ to both parts of the equation (1):

[tex]144cos^2\theta+144sin^2\theta=25sin^2\theta+144sin^2\theta\\\\144(sin^2\theta+cos^2\theta)=169sin^2\theta\\\\144(1)=169sin^2\theta\\\\144=169sin^2\theta\\\\Thus,\ 169sin^2\theta=144[/tex]

Divide both parts of the equation by 169:

[tex]\displaystyle\\sin^2\theta=\frac{144}{169} \\\\sin\theta=б\sqrt{\frac{144}{169} } \\\\sin\theta=б\sqrt{\frac{12^2}{13^2} } \\\\sin\theta=б\sqrt{(\frac{12}{13})^2 } \\\\sin\theta=б\frac{12}{13}[/tex]

[tex]\displaystyle\\As, \ \pi < \theta < \frac{3\pi }{2} \ \ \ \ \Rightarrow\ \ \ \angle\theta\ is \ in\ the\ 3rd\ quadrant\\\\ So \ sin\theta\ takes \ negative \ values\\\\sin\theta=-\frac{12}{13}[/tex]