What is the formula of image of a point?

The formula for a lens is the lens maker's equation, which states that the focal length of a lens is equal to the inverse of the sum of the inverse of the object distance and the inverse of the image distance.

The formula is an equation or expression that describes the relationship between different variables. It is typically represented by an algebraic expression with symbols representing different constants, variables, and operations. It is used to calculate the unknown values of the variables from the known values of other variables.

This equation can be written as 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. This equation shows that the focal length of a lens is directly proportional to the sum of the inverse of object and image distances.

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The table represents a function. X y 0 6 2 8 4 10 6 12 complete the statement by selecting from the drop-down menu. The rate of change in the function y = x + 4 is  equal to the rate of change of the function represented in the table.

Consider the function shown in the table.

The table's coordinates are as follows:

(0,6) (2,8) (4,10) and (6,12) (6,12)

Take into account the first two coordinates (0, 6) and (2,8)

x₁=0, y₁=6, x₂=2, y₂=8

Linear equation is provided by (y-y₁) =m(x-x₁)

Where 'm' is the slope (rate of change), the following formula is used:

m = y₂ - y₁

      x₂ - x₁

So,

m = 8 - 6 = 1

      2 - 0

So, the line's equation is:

(y-6)= 1 (x-0) (x-0)

y-6=x

y=x+6

Putting it up against the common equation of the line y=mx+c with slope "m."

Thus, m(Rate of Change)=1 is obtained.

Now,

We will calculate the slope for the function y=x+4

Putting it up against the common equation of the line y=mx+c with slope "m."

Thus, m(Rate of Change)=1 is obtained.

The rate of change in the function y=x+4 is therefore equal to the rate of change of the function shown in the table.

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The function that could represent Laura's charges is given by -

y = 5x + 12

Given is that bryan is starting a tutoring company that charges $10 as an initial fee and 7.50 dollars per hour of tutoring. Laura is starting her own company and she wants to charge less for the initial fee, but more per hour.

The function representing the amount charged by Brayan is -

{B} = 10 + 7.5x

Amount charged by Bryan per hour is -

$7.5

Amount charged by Bryan as an initial fee -

$10

The function which charge less for the initial fee, but more per hour is -

y = 5x + 12

Therefore, the function that could represent the amount charged by Laura is given by -

y = 5x + 12

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Answer:

x=18/5, y=40. (18/5, 40).

Step-by-step explanation:

y=5x+22

y-4=10x

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

y=10x+4

10x+4=5x+22

10x-5x=22-4

5x=18

x=18/5

y-4=10(18/5)

y-4=36

y=36+4

y=40

If in 1990 the cost of tuition at a state university was 4300 during the next eight years that tuition rose 4% each year.  the equation is A = $4300 (1+0.04)^t and the tuition is $5,231.61.

Using this formula to find the tuition

A = P (1+ r)^t

The equation is:

A = $4300 (1+0.04)^t

Where:

A =Amount = ?

P = Principal = $4300

r = rate = 4%

t = time =?

Now let find the tuition in 1995

A = P (1+ r)^t

A =Amount = ?

P = Principal = $4300

r = rate = 4%

t = time =  (1995 - 1990) = 5 years

Let plug in the formula

A = $4300 (1+0.04)^5

A = $4300 (1.04)^5

A = $5,231.61

Therefore the equation is A = $4300 (1+0.04)^t and the tuition is $5,231.61.

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The complete question is:

In 1990 the cost of tuition at a state university was 4300 during the next eight years that tuition rose 4% each year.  Write an equation to model the amount of  tuition  (in dollars) for t years after 1990. Then find the tuition in 1995

The Fundamental Theorem of Algebra asserts that this 2 n d degree polynomial must have precisely two roots.

According to the Fundamental Theorem of Algebra, this 2 n d degree polynomial must have precisely two roots. Algebra is the branch of mathematics that aids in the representation of problems or situations using mathematical expressions. In algebra, we utilize integers with definite or fixed values such as 2, 7, 0.068, and so on. In algebra, we employ variables such as x, y, and z in addition to integers. Elementary algebra, advanced algebra, abstract algebra, linear algebra, and commutative algebra are all sub-branches of algebra. In algebra, an algebraic expression is composed of integer constants, variables, and the basic arithmetic operations of addition(+), subtraction(-), multiplication(), and division(/). 5x + 6 is an example of an algebraic expression.

Here,

According to the Fundamental Theorem of Algebra, this 2 n d degree polynomial must have precisely two roots.

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The number of students in Erwin Middle School is 1195.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, Erwin Middle School has 478 boys.

If 60% of the students are girls, then 40% of the students are boys 40%.

Let the number of students be x.

Now, 40% of x=478

40/100 ×x=478

0.4x=478

x=478/0.4

x=1195

Therefore, the number of students in Erwin Middle School is 1195.

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Answer:

6/98

Step-by-step explanation:

Answer:

The slope-intercept form of a linear equation is y = mx + b, where m is the slope (rate of change) and b is the y-intercept (where the line crosses the y-axis).

In this case, the number of times the insect beats its wings is the dependent variable (y) and the flying time in seconds is the independent variable (x). We know that the insect beats its wings 240 times per second, so the slope of the equation is 240.

To find the y-intercept, we need to know the number of times the insect beats its wings when it has flown for 0 seconds. Since the insect starts beating its wings immediately, the y-intercept is 0.

So the equation in slope-intercept form is:

y = 240x + 0

This equation represents the relationship between flying time in seconds (x) and the number of times the insect beats its wings (y).

Also, it is important to note that, the slope (240) is the rate of change of the number of times the insect beats its wings per second.

Step-by-step explanation:

Answer: 0.2 cm/yr

Step-by-step explanation:

simply divide centimeters by years

25.0 cm ÷ 125 yr

0.2 cm/yr ... answer



The rate of uplift is 0.2 cm/yr

hope that helps...

Therefore, the volume of the cone to the nearest whole number is 94 m^3.

The measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units. Volume and the notion of length are connected.

The units that may be produced in terms of basic units to measure quantities other than those measured in those units are known as derived units. Examples of derived units are the meter per second (distance), mole per cubic meter (material concentration), and specific volume (cubic meter per kilogram).

We are given, the radius of the cone as 3m and a height is 10m

Using formula,

V = (1/3) * pi * r^2 * h

V = (1/3) * 3.14 * 9 * 10

V = 94 m^3

So, The correct answer is B. 94 m^3

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On solving the provided question, we can say that in right angled triangle the value of x = 5√3 and value of y = 10.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

Using the table of trig values, we find that

sin30°=1/2

So, this gives us:

1/2 = sin 30° = 5/y

1/2 = 5/y

(1xy)/2 = 5

y= 2×5 =10

Next, using the Pythagorean Theorem, we find that

5²+x²=10²

x²=100−25=75

Solve for x:

x=√75=√3×25=5√3

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Yes, the given function y = g(x) in the attached graph is invertible as each input value of x has unique output y.

As given in the question,

Graph of the function y = g(x) is attached.

Invertible function are defined as when each input value of the function has unique output or for each input there is only one and only one output.

In the given graph of the function y = g(x)

Each input value of x there is only one and only one output.

Given graph y = g(x) is representing the straight line.

Therefore, the given graph of the function y = g(x) represent it is an invertible function as each input as one and only one output.

The above question is incomplete, the complete question is :

Does function g appear to be invertible? Use complete sentence to explain you reasoning?

Graph of the function g(x) is attached.

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The system of equations 2x + y = 40 and x - 2y = -20 has a solution of x = 12 and y = 16. We can solve this system by using the method of substitution or elimination.

One way to solve the system is to use the method of substitution. We can first solve one of the equations for one of the variables and substitute that expression into the other equation.

For example, we can solve the first equation for y by isolating y on one side: y = 40 - 2x. Then we can substitute that expression into the second equation and solve for x:

x - 2(40 - 2x) = -20

x - 80 + 4x = -20

5x = 60

x = 12

Then we can substitute x = 12 into the first equation, or either equation to find the value of y:

2(12) + y = 40

y = 16

So the solution to the system of equations is x = 12 and y = 16.

Another way to solve the system of equations is to use the method of elimination. This involves adding or subtracting the equations to eliminate one of the variables. For example, we can add the equations and get:

3x - y = 20

Then we can solve for x or y and substitute it back into either of the equation to find the other variable.

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The complete question is:

What is the solution to this system of equations 2x + y = 40 and x - 2y = -20?

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Answer:

p = 0.531

Step-by-step explanation:

26 + 9p = 58p

subtract 9p from both sides:

26 + 9p - 9p = 58p - 9p

26 = 49p

divide both sides by 49:

26/49 = 49p/49

0.530612 = p

rounded to the nearest hundred

p = 0.531

Answer:0.125% on all ingredients or go to the store and buy more

Step-by-step explanation:

what persent is 3 1/2 out of 4 is 87.5%

87.5% - 100% = 0.125%

The scatter plot shows the results of the survey and yes, there is an outlier in the data set which is the lowest time value of grade 11 and it is an outlier because it is an extremely low data point relative to the nearest data point.

This is referred to as an extremely high or extremely low data point relative to the nearest data point and the rest of the neighboring co-existing values in a data graph.

The outlier is at the lowest time value if grade 11 and it falls under such category because it is an extremely low data point relative to the nearest data point in the given graph.

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In this quadrilateral, Dilation A will have largest scale factor.  Dilation B is smallest and will have smallest scale factor. Now for the given scale factors: 3/4 > 1/2 > 1/4

A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

here,

in this quadrilateral

Dilation A will have largest scale factor.

Dilation B is smallest and will have smallest scale factor.

Now for the given scale factors:

3/4 > 1/2 > 1/4

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Answer:

19.5 miles

Step-by-step explanation:

6.5 x 3 = 19.5

Answer:

35feet

Step-by-step explanation:

Since it's a scale, we can take the backsides of both buses. They read 2in and 10ft

12 inches are in one foot, so 120 inches are in 10ft

Next we'll divide 120/2 and we get 60.

That's means we can multiply 7 * 60, getting 420inches

To get it back to feet, we divide by 12

420/12 = 35 feet

−5.25  > −6.

There are two of them.

These two numbers need to be compared.

A number's square root is never greater than the number itself.

According to the question, we have -

A = −5.25

B =  −6.

Clearly, A > B

Hence,−5.25  > −6.

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The coordinates of  the intersection of the diagonals of STUV with vertices S(-2, 3), T(1, 5), U(6, 3), and V(3, 1) is solved to be (2, 3)

In a coordinate graph, the position of a point is represented by an ordered pair (x, y), where x is the number on the x-axis and y is the number on the y-axis.

Coordinates refer to the two numbers in the ordered pair (x, y) of x and y.

The quadrialteral was plotted on a graph and the point o fht intersection was read from the coordinate graph. The value of the point of the intersection from the graph is (2, 3)

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Maryellen will have in her account at the end of 3 year? (Round to the nearet cent. ) is 1578.93 dollar of 5% interest

Why is it called compound interest?

Compound interest is the interest on a deposit calculated based on both the initial principal and the accumulated interest from previous periods. Or, more simply put, compound interest is interest you earn on interest

What are simultaneous equations?

When two or more algebraic equations are solved concurrently, we call them simultaneous equations.

We can solve simultaneous equations by graphing, elimination, or substitution methods.

deposit = 1500

interest = 5%

after one year = 1500+75= 1575

second year = 78.75+1500 = 1578.75

third year = 78.93+1500= 1578.93

Maryellen will have in her account at the end of 3 year? (Round to the nearet cent. ) is 1578.93 dollar of 5% interest

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Answer: -12ab^3

Step-by-step explanation: (-3ab^3) 4 -12ab^3

[tex]\dfrac{2}{3} (n-6)=5n-43[/tex]

Distribute:

[tex](\dfrac{2}{3} )(n)+(\dfrac{2}{3} )(-6)=5n-43[/tex]

[tex]\dfrac{2}{3} n-4=5n-43[/tex]

Subtract 5n from both sides:

[tex]\dfrac{2}{3} n-4-5n=5n-43-5n[/tex]

[tex]-\dfrac{13}{3} n-4=-43[/tex]

Add 4 to both sides:

[tex]-\dfrac{13}{3} n-4+4=-43+4[/tex]

[tex]-\dfrac{13}{3} n=-39[/tex]

Multiply both sides by -3/13:

[tex]-\dfrac{3}{13} \times(-\dfrac{13}{3} n)=-\dfrac{3}{13} \times(-39)[/tex]

[tex]\fbox{n = 9}[/tex]

The correct option is C. 2n which is the expression for the number of strawberries, if bananas and strawberries are bought in the ratio of 1 : 2.

A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. It can be used to express one quantity as a fraction of the other ones.

The ratio 1 : 2 expressed as fraction is 1/2

when n bananas is bought, then we derive the expression for the number of strawberries as follows:

1/2 = n/number of strawberries

number of strawberries = (2×n)/1 (cross multiplication)

number of strawberries = 2n

In conclusion, with the ratio of 1 : 2 , the number of strawberries bought when n bananas is bought is equal to the expression 2n.

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The prove that segment MP is congruent to segment NO (MP ≅ NO) can be presented as follows;

Statement [tex]{}[/tex]                             Reasons

1. ∠LMN ≅ ∠LNM [tex]{}[/tex]                 1. Given

∠MPN ≅ ∠NOM

2. MN ≅ MN  [tex]{}[/tex]                        2. Reflexive property

3. ΔMNP ≅ ΔNMO [tex]{}[/tex]               3. SAA congruency postulate

4. MP ≅ NO  [tex]{}[/tex]                         4. CPCTC

Two segments are congruent if they have the same length

The known relationships between the measures of the angles are;

∠LMN ≅ ∠LNM

∠MPN ≅ ∠NOM

Required to prove that MP ≅ NO

The two column method can be used to prove the congruency of the sides MP and NO as follows;

Statement     [tex]{}[/tex]                                 Reasons

1. ∠LMN ≅ ∠LNM         [tex]{}[/tex]                1. Given            

∠MPN ≅ ∠NOM

2. MN ≅ MN     [tex]{}[/tex]                            2. Reflexive property of congruency

3. ΔMNP ≅ ΔNMO     [tex]{}[/tex]                  3. SAA congruency rule

4. MP ≅ NO     [tex]{}[/tex]                             4. CPCTC

Details of the above postulates and rules used to prove the congruency of the segments MP and NO are as follows;

SAA congruency postulate

The SAA (SAA is an acronym for Side-Angle-Angle) congruency postulate states that if two angles and a non included side of one triangle are congruent to two angles and a non included side of another triangle, then the two triangles are congruent.

CPCTC

CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent. It indicates that if two triangles are congruent, then, their corresponding sides are also congruent.

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Answer:

0.36

0.0068

0.043

0.00048

Step-by-step explanation:

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