A function of x is shown on the coordinate plane. Over which intervals is the function increasing ??

Quickest gets brainlest

Therefore the solution to the difference of fraction comes out to be

12/95

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, and three-quarters, denotes the number of components of a specific size when used in conversational English.

Here,

the given fractions are 3/5 and 9/19

and to find the difference

we take lcm of both denominators

=>  3/5-9/19

=>  (3*19-9*5)/5*19

=>  (57-45)/95

=> 12/95

Therefore the solution to the difference of fraction comes out to be

12/95

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Answer:

[tex] \displaystyle{ y' = \dfrac{2}{1 - {x}^{2} }}[/tex]

Step-by-step explanation:

Apply natural logarithm chain rule:

[tex] \displaystyle{y = \ln(u) \to y' = \dfrac{u'}{u}}[/tex]

Where u is a function. The ' symbol indicates that the function to be derived. From this formula, we will have:

[tex] \displaystyle{y' = \dfrac{ \left (\dfrac{1 + x}{1 - x} \right)'}{ \dfrac{1 + x}{1 - x}}}[/tex]

Now we have to derive quotient functions, we can use quotient rule for this:

[tex] \displaystyle{y = \dfrac{u}{v} \to y' = \dfrac{u'v - uv'}{ {v}^{2} }}[/tex]

Where u and v are functions. Therefore, from numerator:

[tex] \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{(1 + x)'(1 - x) - (1 + x)(1 - x)'}{ {(1 - x)}^{2} }}[/tex]

Derive using power rule and constant rule where:

[tex] \displaystyle{y = {x}^{n} \to y' = n {x}^{n - 1} } \\ \\ \displaystyle{y = c \to y' = 0 \: \: \: \: ( c \in \mathbb{R})}[/tex]

Thus:

[tex] \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{1(1 - x) - (1 + x)( - 1)}{ {(1 - x)}^{2} }} \\ \\ \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{1 - x- ( - 1 - x)}{ {(1 - x)}^{2} }} \\ \\ \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{1 - x + 1 + x}{ {(1 - x)}^{2} }} \\ \\ \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{2}{ {(1 - x)}^{2} }}[/tex]

Therefore, we will now have:

[tex] \displaystyle{y' = \dfrac{ \dfrac{2}{ {(1 - x)}^{2} }}{ \dfrac{1 + x}{1 - x}}}[/tex]

Simplify expressions:

[tex] \displaystyle{ \dfrac{ \dfrac{2}{ {(1 - x)}^{2} }}{ \dfrac{1 + x}{1 - x}} = \dfrac{2}{ {(1 - x)}^{2}} \times \dfrac{1 - x}{1 + x} } \\ \\ \displaystyle{ \dfrac{ \dfrac{2}{ {(1 - x)}^{2} }}{ \dfrac{1 + x}{1 - x}} = \dfrac{2}{ 1 - x} \times \dfrac{1 }{1 + x} } \\ \\ \displaystyle{ \dfrac{ \dfrac{2}{ {(1 - x)}^{2} }}{ \dfrac{1 + x}{1 - x}} = \dfrac{2}{ (1 - x)(1 + x)}}[/tex]

Therefore, the derived function is:

[tex] \displaystyle{ y' = \dfrac{2}{1 - {x}^{2} }}[/tex]

The value of z if a 5-sided regular polygon with one angle labeled a, If m ∠ a = (2z + 54)° is 27.

A polygon can be defined as a flat or plane, two-dimensional closed object circumscribed with straight sides. Its sides are not curled. A polygon's edges are another name for its sides. The vertices (or corners) of a polygon are the places where two sides converge.

Given:

m ∠ a = (2z + 54)°

The number of sides = 5,

Calculate the value of the sum of the interior angle by the formula given below,

[tex]S = 180(n - 2)[/tex]

S = 180 (5-2)

S = 180 × 3

S = 540°

Calculate the value of a as shown below,

[tex]a = S/5[/tex]

a  = 540 / 5

a = 108

108 = 2z + 54

2z = 108 - 54

z = 54 / 2 = 27

Therefore, the value of z if a 5-sided regular polygon with one angle labeled a, If m ∠ a = (2z + 54)° is 27.

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( g - 14)² is factor of equation .

What is factor ?

A number that divides another number by itself with no residual is known as a factor.The factors of 8 are the numbers that divide 8 exactly without leaving any remainder. There are four factors of 8, they are 1, 2, 4, and 8.

             In other words, if multiplying two whole numbers results in a product, the numbers we are multiplying are factors of the product since the product is divisible by them. Since the numbers we are multiplying are divisible by the product, they are factors of the product.

g2 − 28g + 196

= g² - 14g - 14g + 196

= g( g- 14 ) - 14( g - 14 )

= ( g - 14) ( g - 14)

= ( g - 14)²

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The complete question is -

One of the factors of g2 -28g + 196 is a. g-7 b. g-14 c. g+14 d. g+7

The movie claims that 40% of your brain is used for visual decoding.

Williams, the William G. Allyn Professor of Medical Optics, notes that processing visual information takes up more than 40% of the cortex, the surface of the brain.

Light and dark pixels in the eye are where our visual experience begins. These signals are sent to the V1 region in the rear of the brain, where they are changed to match to the borders of visual scenes.

The visual cortex processes information from the sensory periphery in accordance with a highly regulated hierarchy, according to experiments utilizing static stimuli, such as images. The information about visual sceneries is subsequently translated by deeper brain areas into more intricate forms, objects, and ideas.

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The right response is that the two linear equation never intersect , because the graph of these two linear equation will be two parallel lines.

How many types of solution are there for two linear equations ?

There are 2 types of solution :
Consistent :

A consistent system is said to be an independent system if it has a single solution.

A consistent system is said to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide, so the equations represent the same line. Each point on the line represents a pair of coordinates that fits the system. So there are an infinite number of solutions.

Non-consistent :

Another type of system of linear equations is the inconsistent system, in which the equations represent two parallel lines. The lines have the same slope and different y-intercepts. There are no common points for both lines; therefore, there is no solution to the system and if we draw the graph of these equations then the graphs of both equation becomes parallel to each other.

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The two linear equations never intersect.

When a system of two linear equations in two variables has no solution, it means that there is no set of values for the variables that satisfies both equations simultaneously. Geometrically, this corresponds to the two lines represented by the equations being parallel. Since parallel lines never intersect, the statement "The two linear equations never intersect" accurately describes the situation.

If the two linear equations were graphed on a coordinate plane, they would appear as two distinct lines that run parallel to each other without ever crossing or intersecting. This indicates that there is no common point of intersection between the lines, and therefore no solution exists for the system of equations.

It is important to note that this scenario is different from the case where the two linear equations represent the same line. In that case, the equations would be equivalent, and every point on the line would satisfy both equations. However, when there is no solution, it means that the lines do not share any common points and never intersect.

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√13 is the absolute value of |-3 + 2i| .

Complex numbers are the numbers that are expressed in the form of a+ib where, a, b are real numbers and 'i' is an imaginary number.

For a complex number z = x + iy,

The absolute value |z| as being the distance from z to 0 in the complex plane C

Complex numbers are the numbers that are expressed in the form of a+ib

The complex number here is minus three plus two i.

|-3 + 2i|

Absolute value=√(-3)²+(2)²

=√9+4

=√13

Hence, √13 is the absolute value of |-3 + 2i| .

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

Orthocentre (0, - 5 ).

Triangles are polygons with three sides and three vertices. The triangle's angles are created by joining its three sides end to end at a single point. The triangle has three angles, and the sum of them is 180 degrees.

Here,

We need the lengths of the triangle's three sides in order to identify which of the aforementioned cases the triangle fits into.

Make the length calculations using the distance formula.

d = [tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}[/tex]

L(0, 5) and M(3, 1)

LM =d = [tex]\sqrt{(3-0)^{2}+(1-5)^{2}}[/tex]  = 5

L(0, 5) and (N(8, 1)

LN = d = [tex]\sqrt{(8-0)^{2}+(1-5)^{2}}[/tex]   = √80

M(3, 1) and (N(8, 1)

MN = [tex]\sqrt{(8-3)^{2}+(1-1)^{2}}[/tex]  = 5

If a triangle has three sides, a, b, and c, and side c is the longest, then

• Right triangle formed by a2 + b2 = c2

• a2 + b2 c2 - acute triangle

Triangle with angles a2, b2, and c.

A, B, and C are equal to five in this instance.

a² + b² = 5² + 5² = 25 + 25 = 50

c² = (4 )² = 80

A triangle is obtuse and the orthocentre lies outside the triangle because a2 + b2 c2.

The place where the triangle's three altitudes converge is known as the orthocentre.

For the orthocentre's coordinates, we only need to simultaneously solve

the equations for two of the altitudes.

A line drawn at a right angle from a vertex to the other side is known as an altitude.

Altitude from M to LN

Calculate the slope of LN using the slope formula

m =  (y2 - y1 )/ (x2- x1 ) = 1-5/8-0   ⇒  = 2

Equation of altitude

y - 1 = 2(x - 3)

y - 1 = 2x - 6

y = 2x - 5 → (1)

Altitude between M and LN

Utilize the slope formula to determine LN's slope.

m = (y2 - y1)/ (x2- x1) = 1-5/8-0 ⇒ = 2

formula for altitude

y - 1 = 2(x - 3) (x - 3)

y - 1 = 2x - 6

y = 2x - 5 → (1) (1)

Altitude between N and LM

m = (y2 - y1)/ (x2- x1) = 1-5/3-0 ⇒ -3/4

formula for altitude

y - 1 = (x - 8) (x - 8)

y - 1 = x - 6

y = x - 5 → (2) (2)

Adding (1) to (2)

2x - 5 Equals x - 5 ( multiply through by 4 ) ( multiply through by 4 )

8x - 20 = 3x - 20

5x - 20 = - 20 ( add 20 on both sides ) ( add 20 to both sides )

5x = 0 ⇒ x = 0

Place x = 0 in place of (1)

y = 0 - 5 = - 5

It is the orthocentre (0, - 5 )

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a) Natural number: [tex]12[/tex]

b) Integer that is not a natural number:[tex]-8[/tex]

c) Rational number that is not an integer: [tex]\frac{5}{10} or 0.5[/tex]

d) An Irrational number: [tex]\sqrt{3}[/tex]

A natural number is any whole number greater than zero, such as [tex]1,2,3,4,5,6[/tex]  etc. Natural numbers are also known as counting numbers.

An integer is a whole number (not a fraction) that can be positive, negative, or [tex]0[/tex]. Examples of integers are: [tex]-5,0,1,5,10.[/tex]

Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are integers. Examples of rational numbers include [tex]-\frac{1}{2},\frac{3}{4},0.75, etc.[/tex]

Irrational numbers are numbers that cannot be expressed as a simple fraction and that cannot be written as a repeating or terminating decimal. Examples of irrational numbers include [tex]\pi (3.14), \sqrt{2}, etc.[/tex]

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a) Natural number: 12

b) Integer that is not a natural number:-8

c) Rational number that is not an integer: [tex]\frac{5}{10}[/tex]

d) An Irrational number: [tex]\sqrt{5}[/tex]

A natural number is any whole number greater than zero, such as [tex]1,2,3,4,5[/tex]  etc. Natural numbers are also known as counting numbers.

An integer is a whole number (not a fraction) that can be positive, negative, or 0. Examples of integers are: [tex]-1,5, etc[/tex]

Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are integers. Examples of rational numbers include [tex]\frac{1}{2} ,0.5[/tex]

Irrational numbers are numbers that cannot be expressed as a simple fraction and that cannot be written as a repeating or terminating decimal. Examples of irrational numbers include [tex]\pi ,\sqrt{6}[/tex]

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Answer:

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

The first number is:

And the second number is -3.4.

Both numbers are rational, hence their product is rational.

Answer:

Rational as it is a terminating decimal.

Step-by-step explanation:

Given expression:

[tex]\sqrt{1024} \cdot -3.4[/tex]

Rewrite 1024 as 32²:

[tex]\implies \sqrt{32^2} \cdot -3.4[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]

[tex]\implies 32 \cdot -3.4[/tex]

Multiply the numbers:

[tex]\implies -108.8[/tex]

Therefore, the product is a terminating decimal.

A rational number is a number that can be expressed as the ratio of two integers (where the denominator does not equal zero).  

A terminating decimal can be written as a rational number.

To convert a terminating decimal into a rational number, multiply the number by a multiple of 10 that eliminates the decimal, then divide by the same number:

[tex]\implies \dfrac{-108.8 \cdot 10}{10}[/tex]

[tex]\implies -\dfrac{1088}{10}[/tex]

Reduce the fraction to its simplest form by dividing the numerator and denominator by 2:

[tex]\implies -\dfrac{544}{5}[/tex]

Therefore, the product of √1024 and -3.4 is rational as it is a terminating decimal.

Answer:

Mr. Callaway needs 120 ounces of seed to seed both lawns

Step-by-step explanation:

2400/40 = 60 ounces per square foot

3000 divided by 60 = 50 ounces

So, Mr. Callaway needs 50 ounces to cover a 3000-square-foot lawn

4200 divided by 60 = 70 ounces

So, Mr. Callaway needs 70 ounces to cover a 4200-square-foot lawn

50+ 70 = 120 ounces

So, Mr. Callaway needs 120 ounces to seed both lawns.

If you can, please give me a Brainliest; thank you, and have a good day!

Answer:

120 ounces pf grass seed

Step-by-step explanation:

[tex]\frac{40}{2400}[/tex] = [tex]\frac{x}{3000}[/tex]  Cross multiply and solve for x

120000 = 2400x  Divide both sides by 2400

\[tex]\frac{120000}{2400}[/tex] = [tex]\frac{2400x}{2400}[/tex]

50 = x

It will take 50 ounces of grass seed to cover 3,000 square foot lawn.

[tex]\frac{40}{2400}[/tex] = [tex]\frac{x}{4200}[/tex]  Cross multiply and solve for x

168000 = 2400x  Divide both sides by 2400

70 = x  

It will take 70 ounces of grass seed to cover 4200 square foot lawn.

50 + 70 = 120

Answer: 0

Step-by-step explanation:

Answer: 0

Step-by-step explanation:

Slope is a value that describes the steepness and direction of a line.

A line with a negative slope, said to be decreasing, runs downwards from left to right.

A line with a positive slops, said to be increasing, runs upwards from left to right.

A horizontal line has a slope of zero because y does not change. A vertical line has an undefined slope because you cannot divide by zero (x does not change).

I hope this helps to understand :)

0.25Q+0.05N=3.25 and Q+N=31 is the required system of equation and nickels should be 22.5 and Quarters should be 8.5

Two or more expressions with an Equal sign is called as Equation.

From given,

3.35$ in quarters and nickels. If you have 31 coins

0.25Q+0.05N=3.25..(1)

Q+N=31

Q=31-N

Now substitute Q value in (1)

0.25(31-N)+0.05N=3.25

7.75-0.25N+0.05N=3.25

7.75-0.2N=3.25

Subtract 7.75 on both sides

-0.2N=3.25-7.75

-0.2N=-4.5

Divide both sides by 0.2

N=22.5

and Q+22.5=31

Q=31-22.5

Q=8.5

Hence, 0.25Q+0.05N=3.25 and Q+N=31 is the required system of equation and nickels should be 22.5 and Quarters should be 8.5

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Answer:

Step-by-step explanation:

40/20= 20

39/x=x

that woudl be how you would find it

The evaluation of the given fraction expression is 1 11/16. The correct option is the last option

From the question, we are to evaluate the given expression.

The given expression is

[tex]12 \div (2+\frac{2}{3})^{2}[/tex]

Evaluating the expression

[tex]12 \div (2+\frac{2}{3})^{2}[/tex]

[tex]12 \div (\frac{8}{3})^{2}[/tex]

[tex]12 \div (\frac{8^{2}}{3^{2}})[/tex]

[tex]12 \div \frac{64}{9}[/tex]

= [tex]12 \times \frac{9}{64}[/tex]

= [tex]\frac{108}{64}[/tex]

= [tex]\frac{27 \times 4}{16 \times 4}[/tex]

= [tex]\frac{27}{16}[/tex]

= [tex]1\frac{11}{16}[/tex]

Hence, the fraction is 1 11/16

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Answer: Hugo should buy car A

Step-by-step explanation:

Car A

Take 702 divided by 12 = 58.5 miles per gallon of gas

Car B

Take 873 divided by 15 = 58.2 miles per gallon of gas.

So Hugo should buy car A

The circle's perimeter is determined by F = -9π, according to green's theorem.

The simple formula for Green's theorem is the link between the total amount of microscopic circulation inside curve C and the macroscopic circulation revolving around it.

Remembering that we are talking about two dimensions, if C is a straightforward closed curve in the plane, it will enclose the region D (shown in red) in the plane.

So, knowing that this exercise should be solved using Green's theorem, then:

[tex]\begin{aligned}& \int 4 y d x+2 x y d y=\iint(d / d x)(2 x y)-(d / d y)(4 y) d A \\& =\iint 2 y-4 d A\end{aligned}[/tex]

You must convert in this manner to polar coordinates, and the result will be:

[tex]\begin{aligned}& \int_0^3 \int_0^{2 \pi}(2 r \sin (\theta)-4)(r) d \theta d r \\& =\int_0^3(-2 r \cos (\theta)-4 \theta)(-2 r \pi) d r \\& =-(\pi)\left(r^2\right)=-9 \pi\end{aligned}[/tex]

Therefore, the circle's perimeter is determined by F = -9π, according to green's theorem.

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Correct question;
Suppose F⃗ (x,y)=4yi⃗ +2xyj⃗ . Use Green's Theorem to calculate the circulation of F⃗ around the perimeter of a circle C of radius 3 centered at the origin and oriented counter-clockwise.

The length of the midsegment of the triangle DEF is 47 units.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the midsegment of a triangle is half of the length of the parallel side.

∴ GH = (1/2)DF.

3x - 4 = (1/2)(9x - 59).

6x - 8 = 9x - 59.

- 3x = - 51.

x = 17.

So, The length of GH is 3(17) - 4 = 51 - 4 = 47 units.

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Answer: A Geometric sequence is a type of sequence in which each subsequent term after the first term is determined by multiplying the previous term by a constant (not 1), which is referred to as the common ratio.

Step-by-step explanation: Hope this was helpful

Step-by-step explanation:

The sequence

a, ar, ar^2, .....ar^n-1,...

where a is the first term and any two consecutive numbers differ by a factor r, is called a Geometric progression (G.P.).

Geometric progression also known as Geometric sequence.

Using the system of equation, the cost of one dinning table is 145 dollars.

James is buying furniture for her new apartment. She buys one dining room table and four chairs and cost $265. Mark buys 2 tables and 6 chairs for the total cost of $470.

The system of equation that represent the situation is as follows:

let

x = cost of one dinning room table

y = cost of one chair

Therefore,

x + 4y = 265

2x + 6y = 470

using substitution method,

x = 265 - 4y

2(265 - 4y) + 6y = 470

530 - 8y + 6y = 470

-2y = 470 - 530

-2y = -60

y = -60 / -2

y = 30

Hence,

x = 265 - 4(30)

x = 265 - 120

x = 145

Therefore,

cost of one dinning table  = 145 dollars

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Answer:

Step-by-step explanation:

b(x)=6x^2

That is the same as b(x)=6*x*x

when x=16

b(16)=6*16*16=1536

F= k*a*v^2

a= 250

v=190

30300=k*250*{190^2}

k= 0.003357

F= 0.003357*250*180*180

F=27135

The lifting force is 27135

The total area that all of a 3D object's faces cover is the surface area. The surface area of a cube is its surface area, for instance, if we are trying to determine how much paint is needed to paint it. Always expressed in square units.

The entire surface of a three-dimensional shape is referred to as its surface area. A cuboid with six rectangular faces has a surface area equal to the sum of the areas of each face. Alternatively, you can label the cuboid's length, width, and height (l, w, and h), then calculate its surface area (SA) using the formula: SA=2lw+2lh+2hw.

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Answer:

The two numbers we are looking for are a rational number and an irrational number.

Step-by-step explanation:

To find the two numbers that, when multiplied by the square root of 360, give a rational number, we can consider the prime factorization of 360. 360 can be written as 2^3 * 3^2 * 5, so the square root of 360 is equal to √(2^3 * 3^2 * 5) = 2√(3 * 5) = 2√15.

Now, suppose we want to find a rational number that is equal to x * √15. We can rewrite this expression as x * √(3 * 5) = x * √3 * √5. For this expression to be rational, both x and √3 must be rational or both must be irrational.

If x is rational, then the expression x * √3 * √5 is rational. Therefore, one of the two numbers we are looking for is x, which is a rational number.

If x is irrational, then the expression x * √3 * √5 is irrational. Therefore, the other number we are looking for is √3, which is an irrational number.

Therefore, the two numbers we are looking for are a rational number and an irrational number.

a) The mean of the sampling distribution of p is of 0.2.

b) The standard deviation of the sampling distribution of p is of: 0.0231, which is the amount that the sample proportions may differ from 0.2.

c) The shape of the sampling distribution of p is approximately normal.

The sampling distribution of p is defined according to the Central Limit Theorem, which states that the sampling distribution of a proportion p in a sample of size n has:

The parameters for this problem are given as follows:

p = 0.2, n = 300.

The 10% condition is given as follows:

Then the standard error of the sampling distribution of p is calculated as follows:

[tex]s = \sqrt{\frac{0.2(0.8)}{300}} = 0.0231[/tex]

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The line parallel to the line x + 2y = 8 is y = -(1/2)x - 7 Or (1/2)x + 7 = - 7.

The slope is the rate of change of the y-axis with respect to the x-axis.

The equation of a line in slope-intercept form is y = mx + b, where

slope = m and y-intercept = b.

We know the greater the absolute value of a slope is the more steeper is it's graph or rate of change is large.

The given line is x + 2y = 8 ⇒ 2y = - x + 8 ⇒ y = -(1/2)x + 8.

We know line parallel to each other have the same slope and it passing through (-2, - 6).

∴ - 6 = -(1/2)(-2) + b.

- 6 = 1 + b.

b = - 7.

So, The required line is y = -(1/2)x - 7.

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Given a function with one vector parameter scores, if scores may be very large, and the function will modify the parameter, the parameter would be defined as pass by reference but not constant.

Pass-by-reference refers to passing the reference of an argument in the calling function to the corresponding formal parameter of the called function. The called function can modify the value of the argument by using its reference passed in. It refers to an alias or reference to the actual parameter that is passed to the method. Pass by reference makes the parameter modifiable, but constant prevents the parameter from being modified.

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For a random day with the standard deviation, the probability that there are less than 300 shoppers on a random day, is 0.00585.

Probability is a measure of the likelihood that an event will occur.

The average total number of shoppers on a grocery store in 1 day is 505; the standard deviation is 115.

Let, X be the random variable denoting the number of shoppers on a random day.

Then, X follows normal with mean 505 and standard deviation of 115.

Then, we can say that,

Z=(X-505)/115 follows standard normal with mean 0 and standard deviation of 1.

We have to find

P (250 <X< 450)

= P {(250-505)/155} < Z < {(450-505)/155}

= P (-1.64 <Z< -0.03)

Where, Z is the standard normal variate.

ρ = -1.64 <ρ< -0.03

Where, ρ is the distribution function of the standard normal variate.

From the standard normal table, this becomes

=0.00585

For a random day, the probability that there are less than 300 shoppers on a random day, is 0.00585.

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△DEF is congruent to △D'E'F' because you can map △DEF to △D'E'F' using a reflection across the x-axis, which is a rigid motion.

What does a math congruent mean?

Congruent refers to having precisely the same form and size. Even after the shapes have been flipped, turned, or rotated, the shape and size ought to remain constant.

1)  Reflections, rotations and translations are rigid transformations, because they do not modify the lengths of the segments nor the angles, so the images and the preimages are congruents.

2) Let's see what transformation map △DEF is to △D'E'F' by analyzing the vertices of preimage and image:

Preimage         Image

D (-3, -1)            D' (-3, 1)

E (2, -4)             E' (2, 4)

F (4, -4)             F' (4, 4)

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