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The magnification of the system with an object distance of 5 cm and an image distance of 15 cm is 0.33.

A lens is a transmissive optical tool that employs refraction to focus or disperse a light beam.

In optics, magnification refers to the image's size in relation to the item that produced it. The ratio of the image length to the object length, as measured in planes perpendicular to the optical axis, is referred to as linear magnification, also known as lateral or transverse magnification.

The size of an object is u = 5 cm

The size of the image formed by the lens is v = 15 cm

Then the magnification M will be:

Magnification = Image distance/ Object distance

M = v/u

M = 5/15

M = 1/3

M = 0.33

Hence, the magnification of the system is 0.33.

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Answer:

Explanation:

For the matrix equation

We first subtract A from both sides to get

Now,

Hence, we have

Dividing both sides by 2 gives

which is our answer!

George is putting trim around the rectangular deck, this means that he is surrounding the deck's perimeter with trim.

You know that he needs 50ft of trim to do the entire deck, this value represents the perimeter of the rectangular deck, and the length of the deck is 15ft.

Knowing the perimeter (P) and the length (l) of the rectangular deck, you can calculate the width (w) of the deck.

The formula for the perimeter of the rectangle is:

Write the formula for w:

Use P=50ft and l=15ft to calculate the width:

The width of the deck is 10ft (option C)

The function g(x) that results when translating the function f(x)=x to the left 12 units and reflecting it over the x-axis is g(x) = -|x + 12|

Translating to left ≡ f(x + 12)

Translation up 12 units means g(x)=f(x)+5g(x)=f(x)+5. Reflecting this across the x-axis means g(x)=-(f(x)+12)g(x)=−(f(x)+12)

-(x+12)=-x-12

f(x + 12) = |x + 12|

Reflection of a function f(x) about the x - axis is keeping the x value same but negating the y values

Reflected f'(x) = -y = -f(x)

Taken together

g(x) = -(|x + 12|)

The function g(x) that results when translating the function f(x)=x to the left 12 units and reflecting it over the x-axis is g(x) = -|x + 12|

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Answer:

what red and blue dots?

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

x + 3 + 7 = 2x + 10 - x ( simplify both sides )

x + 10 = x - 10 ( subtract 10 from both sides )

x = x - 20 ( subtract x from both sides )

0 = - 20 ← not possible

this indicates the equation has no solution

The domain is (2,4,6,8,10,12,14) and range is (8,6,4,2,0,2,4).

The domain of a function refers to the set of values that we are allowed to enter into our function.

The set of values that a function can accept as input is known as its range. Once we enter an x value, the function returns this list of values , the y values are these.

The range and domain must be understood to be all the values that the variable y can represent, respectively, and the x values.

Since the ordered pairs have the form (x,y), we can determine the values of x and y.

The x and y values of function are:

F(x,y) = (2,8), (4,6), (6,4), (8,2), (10,0), (12,2), (14,4)

Domain (x) = (2,4,6,8,10,12,14)

Range (y) = (8,6,4,2,0,2,4)

.

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On solving the system of equation using elimination method , the value of x is 1 and value of y is 3 .

in the question ,

the two equations are given as

3x+y=6   ...(i)

and

-8x+2y= -2     ...(ii)

In elimination method, the equation is multiplied by some constant and then add/subtract the equations to eliminate any variable x or y.

multiplying equation(i) by 2 we get

6x+2y=12      ....(iii)

subtracting , the equation (ii) from equation (iii) , we get

(6x+2y) - (-8x+2y) = 12-(-2)

6x+2y+8x-2y = 12+2

14x = 14

x = 1

We eliminate 'x' from equation (ii) by replacing the value of 'x' with 1 ,

we get

-8x+2y= -2  

-8(1)+2y= -2

-8 + 2y = -2

2y = -2 + 8

2y = 6

y = 3

Therefore , On solving the system of equation using elimination method , the value of x is 1 and value of y is 3 .

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HF, JN

1) Examining this question, we can state that a tangent line is the one that "touches" the circle in one single point.

So, in this diagram we can state that the tangent line is HF

2) On the other hand, a secant line crosses the circle in two points at least. So the one that fits in this definition is the line defined by points JN

3) In Euclidian Geometry, a chord is a line segment that connects two points in a circle or curve. Examning the diagram again, we can state that KM is a chord.

Answer:

Step-by-step explanation:

40x+20y x is for the amount of hours he spends on web design and y for 20 obviously

Ok, so

We want to find the area of the following triangle:

Remember that the area of a trangle is given by the following equation:

Where b is the base of the triangle and h is its height.

If we replace our values:

Therefore, the area is equal to 11 square units.

MULTIPLY EVERY TERM IN THE BRACKETS BY 3

[tex] = 3(x) + 3( - y) \\ = 3x - 3y[/tex]

ATTACHED IS THE SOLUTION

From the table,

Total number of students that failed the test = 2 + 7 = 9

The total number of students that participated = 10 + 3 + 2 + 7 = 22

The possibility that a student chosen randomly from the class failed the test = ​Total number of students that failed the test divided by the total number of students that participated

= 9/22

Hence, the possibility that a student chosen randomly from the class failed the test is 9/22

numbe

Answer:

Step-by-step explanation:

Mean is the average.

It is calculated as:

Find it using the equation above:

Correct choice is C

Answer:

c

Step-by-step explanation:

The coordinates of the vertices after the reflection are V'(-3,2), U'(0,-2), W'(-1,3) and T'(1,2) .

A reflection in mathematics is a mapping from a Cartesian coordinates to itself which is an isometry with such a set of fixed points known as the hyperplane, also known as the axis or plane of reflection.

We know that when a figure is reflected along the line y = -x then the coordinates change their places and they are negated.

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The equation y = 7/4x - 1​ is in slope-intercept form, with a slope of 7/4 and a y-intercept of -1.

To graph it, you need to locate the point (0, -1) - the y-intercept -, and then use the slope to find another point. From (0, -1) you have to move 4 units to the right, and 7 units up, reaching the point (4, 6). Then, you have to draw the line that passes through theses points, as follows:

Answer:

never to leave the unknown shackspeare

Step-by-step explanation:

it never leaves

or never stays

and never comes back

The Slope-Intercept form of the equation of a line is:

Where "m" is the slope of the line and "b" is the y-intercept.

Given the equation of the line "g":

You can identify that:

By definition the slopes of perpendicular lines are opposite reciprocals. Then, the slope of the line "h" is:

Knowing a point on the line "h" and its slope, you can substitute them into the equation

And solve for the y-intercept:

Then, the equation of the line "h" is:

The word for added and subtracted parts of an expression is known as the term.

An expression in math is an arithmetic set of numbers and variables with signs and calculations. For example, 4x - 2x = 2x is an expression. The parts that are connected with addition or subtraction or other signs are called terms.

Terms that have the same base exponent can be joined with addition and subtraction. These are called like terms. For example, 3 x 3 and 5 x 3 are like terms.

Therefore, the term is the term for the added and removed components of an equation.

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Let's begin by identifying key information given to us:

Imaginary solutions

Step 1

Redraw the diagram and use the Pythagoras theorem to find the value of c\x.

Step 2:

Find the value of y from the right-angle triangle of sides: 10, 25 and y using the Pythagoras theorem

Opposite = y

Adjacent = 10

Hypotenuse = 25

Step 3

Next, use the Pythagoras theorem to find x from the triangle with sides

28, x and y

Hypotenuse = 28

Opposite = x

Adjacent = y

Final answer

x = 16.1

18-6=12

8-16=-8 not equal 18-6

14-8=6 not equal 18-6

14-7=7 not equal 18-6

16-8=8 not equal 18-6

Hence none of the options has the same difference as 18-6

Answer:

5x-2

Step-by-step explanation:

the 'x' is "a number"

The set of, S - T = {3, 9}

Define Set Operation.

To obtain a combination of components according to the operation done on them, the set operations are conducted on two or more sets.

In a set theory, there are three major types of operations performed on sets, such as:

1) Union of sets (∪)

2) Intersection of sets (∩)

3) Difference of sets ( – )

We know, S -T = S ∩ T'

Given, universal set is U = {1, 2, 3, ..., 10}

S = {3, 5, 7, 9} and T = {4, 5, 6, 7}

Now, find T' (T's compliment),

The complement of set T is defined as a set that contains the elements present in the universal set but not in set T.

T'  = {1, 2, 3, 8, 9, 10}

given, S = {3, 5, 7, 9}

Find, S ∩ T'

S ∩ T' = {3, 5, 7, 9} ∩ {1, 2, 3, 8, 9, 10}

The intersection of two sets S and T is a subset of the universal set U and contains elements that are present in both sets S and T. It is represented by the symbol "∩".

so, S ∩ T'  = {3, 9}

Hence, S - T = S ∩ T'  = {3, 9}

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Hello there. To solve this question, we have to remember some properties about equations of circles.

Given the following equation:

It is called the equation of a circle with center at

And radius R.

In the question, it gives us two equations that we might describe the shape of the equation, considering its key features (center, foci, asymptotes, semi-major and semi-minor axes, if applicable).

We have that

Is the equation of a circle with center at (-4, 2) and radius equal to

For the other equation

Is also the equation of a circle, with center at (2, 5) and radius equal to