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The lens formula is used in optics to calculate the position and size of the image formed by a lens.

A lens is a piece of glass or other transparent material that bends light to form an image. The lens formula relates the distance of the object from the lens, the distance of the image from the lens, and the focal length of the lens.

The lens formula is used to determine the position and size of the image formed by a lens in order to design and analyze optical systems. It is used in the design of camera lenses, telescopes, microscopes, and other optical devices.

It also allows us to determine the size and position of the image formed by a lens in a given situation, which is essential for the analysis and correction of optical aberrations.

The lens formula also allows us to determine the type of image formed by a lens, whether it is real or virtual, inverted or erect, and the size of the image compared to the object.

In conclusion, the lens formula is used in optics to calculate the position and size of the image formed by a lens. It is used in the design and analysis of optical systems such as camera lenses, telescopes, microscopes and other optical devices. It also allows us to determine the type of image formed by a lens and the size of the image compared to the object.

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The shorter side of the triangle will be opposite to 30° angle and larger side will be opposite to 90° angle .

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

The side opposite the smallest angle is the one that is the shortest. The shortest side is opposite the angle that you already know to be the shortest.

The side opposite the right angle is always the hypotenuse of a right triangle. In a right triangle, it is the longest side.

So the shorter side will be opposite to 30° angle and larger side will be opposite to 90° angle .

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Yes, the square of any number like X² is always positive.

Example:

If we calculate the square of a negative number, let's say -x, where x > 0, then (-x) (-x) = x².

Here, x² > 0.

Hence, the square of any number like X² is always positive.

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A polygon having seven sides and seven angles is called a heptagon. Seven straight sides and seven corners, or vertices, make up a heptagon. It's also referred to as a "septagon" at times.

A seven-sided polygon is called a heptagon. A closed figure with seven vertices, it is. Another name for a heptagon is a septagon.

There are various sorts of hexagons, depending on the angles and diagonals.

Regular and Irregular Heptagons

Concave and Convex Heptagon

The following are some heptagon's characteristics:

(1) The inner angles of a heptagon add up to 900 degrees.

(2) A heptagon's outside angles add up to 360 degrees.

(3) The internal angle of a normal heptagon measures approximately 128.57 degrees.

(4) The size of a typical heptagon's central angle is roughly 51.43 degrees.

(5) There are fourteen diagonals in a heptagon.

(6) Convex heptagons are another name for regular heptagons.

(7) A heptagon has a total of five triangles.

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Triangle MNO with sides m = 20, n = 14 and angle m ∠ M = 51° can have two possible configurations.

In this problem we have the knowledge of two sides and an angle of triangle MNO, where angle M is opposite to side m. First, determine the possible values for angle N by law of sine:

n / sin (m ∠ N) = m / sin (m ∠ M)

14 / sin (m ∠ N) = 20 / sin 51°

sin (m ∠ N) = (14 / 20) · sin 51°

sin (m ∠ N) = 0.544

There are two possible values for angle N: m ∠ N₁ ≈ 32.957°, m ∠ N₂ ≈ 147.043°. The existence of two different angles indicates that two distinct triangles can be formed.

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Translation type of transformation can be defined as moving a figure to a new location with no change to the size or shape of the figure.

Now, According to the question:

Type of Transformation:

There are four types of transformation in geometry, namely translation, reflection, rotation, and dilation. In translation, it slides the figure in any direction while in reflection, it flips the figure over a point or a line. Also, in rotation the figure turns, while in dilation the figure is either enlarged or reduced.

The type of transformation can be defined as moving a figure to a new location, without any change in the figure's size or shape being called translation. In translation, the figure merely slides or moves in the same direction and distance.

Therefore, the answer is Translation.

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The Order of the ordered pair is defined as the specific way in which the ordered pair is written having a composition of the x coordinate and the y coordinate .

What is Ordered Pair ?

The Ordered Pair is defined as the pair of numbers in a specific order.

For Example :  (x,y) , here for the given ordered pair , the element x is called as the abscissa and the element y is called as the ordinate .

The Order of the Ordered Pair (x,y) is the first element always represents the abscissa that means the x coordinate and the second element should always represent ordinate that means the y coordinate .

For Example : for the ordered pair (2,4) , the x coordinate of the point is 2 and the y coordinate of the point is 4 .

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The pattern of the sequence 1 1 2 3 5 8 13 is that each term is obtained by adding the previous term and the term before that.

The sequence 1 1 2 3 5 8 13 is also a famous example of the Fibonacci sequence. The Fibonacci sequence is a sequence of numbers in which each term is the sum of the two preceding terms. In this case, the first two terms of the sequence are 1 and 1, and the rest of the terms are obtained by adding the previous two terms.

It's also possible to express the pattern of the Fibonacci sequence by using the formula, F(n) = F(n-1) + F(n-2) where F(n) is the nth term of the sequence.

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Answer:

x = 0.25y + 7/12

Step-by-step explanation:

12x - 3y = 7

12x = 3y + 7

x = 0.25y + 7/12

The Factor Theorem states that if a polynomial is divided by (x-a) then the remainder is equal to zero if and only if (x-a) is a factor of the polynomial.

To solve the Factor Theorem, first you need to determine the polynomial and the value of (x-a).

Then you divide the polynomial by (x-a). To do this, use synthetic division. Synthetic division is a shorthand way of dividing a polynomial by a linear factor.

If the remainder is 0, then the polynomial is divisible by (x-a). If the remainder is not 0, then (x-a) is not a factor of the polynomial.

To summarize, the Factor Theorem states that if the remainder is 0 after dividing a polynomial by (x-a), then (x-a) is a factor of the polynomial.  The Factor Theorem can be solved by using synthetic division.

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Answer:

C(x) = 25 + 1.5x

Step-by-step explanation:

A function is a mathematical equation that describes how two variables are related. To write a function that models the cost of having a carpet installed, we can use the information provided in the problem.

The cost of having a carpet installed is:

C(x) = 25 + 1.5x

Where C(x) represents the total cost of the carpet installation and x represents the number of square yards of carpet.

25 is a fixed cost for delivery , and $1.5 is cost per sq yard.

So, C(x) = 25 + 1.5x this function is representing the cost of having a carpet installed in x sq yard.

The additive inverse of the expression is 4x + 8

From the question, the expression is given as

negative 4X -8

Express properly

So, we have the following representation

-4x -8

For an expression y, the additive inverse is -y

Using the above as a guide, we have the following:

Additive inverse of -4x -8 = -(-4x -8)

Open the bracket

Additive inverse of -4x -8 = 4x + 8

Hence, the additive inverse is 4x + 8

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Answer:

[tex]y= \frac{x}{2x−1}[/tex]

Step-by-step explanation:

To find the inverse function, swap x and y, and solve the resulting equation for x.

If the initial function is not one-to-one, then there will be more than one inverse.

So, swap the variables: y=x/2x−1 becomes x=y/2y−1.

Now, solve the equation x=y/2y−1 for y.

y=x/2x−1

An ordered pair is a pair of numbers that are usually represented in the form of (x, y) and it is used to indicate the position of a point in a coordinate system or a Cartesian plane.

Another example is an ordered pair (-2, 1) representing a point in the coordinate system located 2 units to the left of the y-axis and 1 unit above the x-axis.

In this way, any point in a coordinate system can be represented by an ordered pair.

In summary, the ordered pair is a way to represent a point in a coordinate system and it is made up of two numbers (x, y), where x represents the horizontal position and y represents the vertical position of the point in the coordinate system.

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The maximum number of drinks Liam can buy is 4 without over exceeding his price.

Unitary method:

The unit method is a method of obtaining a single-unit value from a multiple-unit value and obtaining a multiple-unit value from a single-unit value. This is the method used for most calculations in mathematics. This method is useful when solving problems involving proportions and proportions, algebra, geometry, and more.

The unit method allows us to find missing values. For example, if a pack of juice costs $5. Then you can easily see that the cost is 5 packages, or $25.

According to the Question:

If Liam has $30 to spend and he must buy at least 9 drinks and tacos altogether, it means that,

$3.50 for 5 tacos

⇒ 3.50 x 5 =  $17.50

Now,

9 - 5 tacos = 4 drinks

Cost of 4 drinks x $2 = $8

The total price :

$17.50 + $8 = $25.50 out of $30 price limit

Thus, the number of drinks that she could buy is 4.

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Answer:

B.  x + 10 ≥ 70;  x ≥ $60

Step-by-step explanation:

Given:

The equation that models the given parameters is:

To solve for x, subtract 10 from both sides of the equation:

[tex]\implies x+10-10 \geq 70-10[/tex]

[tex]\implies x \geq 60[/tex]

Therefore, Kelvin needs to withdraw at least $60 from the bank.

Equivalent expressio

When two expressions can be reduced to a single third expression or when one of the expressions can be written in the same way as the other, they are said to be equivalent. When values are replaced for the variable and both expressions yield the same result, you may also tell if two expressions are equal.

Because both expressions have the same value for any value of x, 3(x + 2) and 3x + 6 are identical expressions. 3x + 6 = 3 × 4 + 6 = 18. Algebraic equations with equivalent solutions or roots are called equivalent equations.

An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation. Expressions that are equivalent do the same thing even when they have distinct appearances. In the event when two algebraic expressions.

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The slope of the equation of the line 3f - s = 24 is 3.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, let's model the equation of the line y = mx + b to 3f - s = 24. Then, we can locate the slope in the equation.

Hence,

3f - s = 24.

add s to both sides of the equation

3f - s + s = 24 + s

3f = 24 + s

subtract 24 from both sides of the equation

3f = 24 + s

3f - 24 = 24 - 24 + s

s = 3f - 24

Therefore, the slope is 3.

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The value of x for the given expression is,

⇒ x = 5/44

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

'' 4 times x plus one third equals one third times x plus 4''.

Now, The mathematical expression is,

⇒ 4x + 1/3 = 1/3 (x + 4)

Solve for x as;

⇒ 4x + 1/3 = 1/3x + 3/4

⇒ 4x - 1/3x = 3/4 - 1/3

⇒ 11/3x = 5/12

⇒ x = 5 × 3 / 12×11

⇒ x = 15/ 132

⇒ x = 5/44

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I got a similar one too. It was 6(4.5x+1.5) ..

Step-by-step explanation:

The answer is the point (5, -27) and no other solution.

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here: The equation y=-6x+23

Checking for  (5, -27) we get -27=-6×5+23

                                                      =-27

Hence, The answer is the point (5, -27)

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Answer:

The total number count we are looking at from the numbers 30 to 65 is 36. So that is a total of 72 digits making up this numbers from 30 to 65. Also, we can see that the whole range of numbers 0 to 9 is being used for this range

The first step in solving an inequality is to isolate the variable on one side of the inequality sign. This is also known as "clearing the inequality" of the variable. This can be done by using inverse operations such as addition, subtraction, multiplication, and division.

For example, if the inequality is 3x + 2 > 7, the first step is to isolate the variable x by subtracting 2 from both sides:

3x + 2 > 7

3x > 5

Then, divide both sides by 3 to get x > 5/3

This is the first step in solving an inequality, as now the variable x is isolated on one side of the inequality sign, and it's clear what the inequality is asking for.

It's important to note that when solving inequalities, it's crucial to keep the direction of the inequality sign the same, meaning if you multiply or divide by a negative number, you need to switch the direction of the inequality sign as well.

Also, it's important to check if the inequality is not valid, if the operation you are doing creates a division by zero, it will be an invalid inequality.

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The price of the adult ticket is $9

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Set up equations to represent the problem.

Let the A and S represent the prices of adult and student ticket respectively. So we can write:

4A + 10S = 106 --- (1)

4A + 9S = 99  --- (2)

Subtracting (2) from (1) will give:

S = 7

Put S = 7 into (1):

4A + 10S = 106

4A + 10(7) = 106

4A + 70 = 106

4A = 106 - 70

4A = 36

A = 36/4

A = 9

Thus, the price of the adult ticket is $9

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Answer:

5.6 or 28/5

Step-by-step explanation:

We know that A = 8 and B = 4

The expression is A/5 + B

8/5 + 4

The answer in decimal is 5.6

The answer in fraction is 28/5

Therefore , the solution of the given problem of factor comes out to be

Ax²+Bx+C= (x-a)(x-b) is the formula for factor form.

It appears that a factor is a parameter that is combined by another to achieve an outcome. A product is the solution to a multiplication puzzle. Think of mixing the factors in an arithmetic problem to get the product. 8 has the elements 2 and 4, for instance: There could be just two parts to a number or many more.

Here,

Take a look at the generic form:

=>Ax²+Bx+C= (x-a)(x-b),

where a & b are the polynomial's roots.

Here, b=2 and a=1

(x+1)(x2) (x + 1)(x 2) is the factored form.

Therefore , the solution of the given problem of factor comes out to be

Ax²+Bx+C= (x-a)(x-b) is the formula for factor form.

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The (2,1) is a solution of the system of equations is shown. A formula that expresses the connection between two expressions on either side of a sign. Typically, it has a single variable and an equal sign.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

2 + 3·1 = 5

5 = 5

1 = -2 +3

1 = 1

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A polynomial is factored when it is broken down into the sum of two or more other polynomials. For instance, f (x) = x 2 + 5 x + 6 can be broken down into f(x) = (x+3)(x+2) and f(x) = x2 + 5 x + 6.

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.

A polynomial is factored when it is broken down into the sum of two or more other polynomials. For instance, f (x) = x 2 + 5 x + 6 can be broken down into f(x) = (x+3)(x+2) and f(x) = x2 + 5 x + 6.

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The student whose measurement had the greatest percentage error is Tenicia with a measurement of 23mm.

Percentage error refers to the difference between the estimated value and the actual value which is then expressed as a percentage. In the question given, the students and their values are; Layne, 26 mm, Tenicia, 23 mm, and Juan 25 mm.

Juan was the only student who had no error in the value obtained because she got the exact figure of 25 mm. Tenicia recorded the greatest value because the difference between the actual and estimated value was apart with so much difference. Her error was an 8% error.

25 -23/25 × 100

= 8%

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