I need help like asap !!!

only numbers and decimal points ​

I Need Help Like Asap !!!only Numbers And Decimal Points

Answers

Answer 1

Answer:

a = 6.63 cm

Step-by-step explanation:

Formula we use,

→ (AC)² = (BC)² + (AB)²

Now the value of a will be,

→ (12)² = a² + (10)²

→ 144 = a² + 100

→ a² = 144 - 100

→ a = √44

→ [ a = 6.63 cm ]

Hence, value of a is 6.63 cm.


Related Questions

what is the measure of EAC?

Answers

The measure of angle EAC IS 50°

What is an angle bisector?

The angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts. For example, an angle bisector of a 60-degree angle will divide it into two angles of 30 degrees each. In other words, it divides an angle into two smaller congruent angles. Given below is an image of an angle bisector of ∠AOB.

∠BAE = x + 30, ∠EAC = 3x - 10

If AE is a line that bisects BAC,

then ∠BAE = ∠EAC

which becomes,

x + 30 = 3x - 10

collecting like terms,

x - 3x = -10 - 30

-2x = -40

x = -40/-2

x = 20°

But m ∠EAC = 3x - 10

substituting x = 20°

we have ∠EAC = 3(20) - 10

                          = 60 - 10

    ∠EAC       = 50°

In conclusion, the value of  ∠EAC  = 50°

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the length of a rectangle is increasing at a rate of 6 cm/s and its width is increasing at a rate of 8 cm/s. when the length is 12 cm and the width is 10 cm, how fast is the area of the rectangle increasing (in cm2/s)?

Answers

The area of the rectangle is increasing at the rate of 156 [tex]cm^{2}[/tex]/s .

Let the length (cm) be l , width (cm) be w , area be A ([tex]cm^{2}[/tex]) and time (s) be t .

Given : dl / dt = 6 cm/s and dw / dt = 8 cm/s

Area of rectangle = l * w

Differentiating wrt. t ,

dA / dt = ( l ) ( dw / dt ) + ( dl / dt ) ( w )

Therefore , dA / dt = 8l + 6w

Hence , when l = 12 cm and w = 10 cm

dA / dt = ( 8 * 12 ) + ( 6 * 10 )

dA / dt = 156 [tex]cm^{2}[/tex]/s .

The area of the rectangle is increasing at the rate of 156 [tex]cm^{2}[/tex]/s .

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a certain car travels at a constant speed of 40 miles per hour. how far does the car travel in 45 minutes

Answers

The car travels 30 miles in 45 minutes with the speed 40 miles/hour with the constant speed.

What is speed?

Velocity is the rate and direction of an object's movement, whereas speed is the time rate at which an object is moving along a path. In other words, velocity is a vector, whereas speed is a scalar value. The distance traveled by a moving object in a specific amount of time is its speed. How quickly something is moving is determined by its speed. The distance traveled by an object in a given amount of time divided by the time gives the object's average speed.

Here,

45 minutes/60 minutes= .75 hours (this gives you the amount of time in hours)

time x speed = distance

.75 hours time x 40 mph speed = 30 miles distance

With a constant speed of 40 miles per hour, the car covers 30 miles in 45 minutes.

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Complete the square to re-write the quadratic function in vertex form:
y = 7x²56x + 117

Answers

The answer to the given quadratic equation is y =  ( x + 4 )²

How do we solve a question by completing the square method?

A(x + m)2 + n is the formula for completing the square, where m is any real number and n is a constant factor.

The following straightforward formula can be used to finish the square instead of the intricate step-by-step procedure. Find the following in order to complete the square in the phrase ax2 + bx + c:

N = c - (b2/4a) and m = b/2a

Enter these numbers where they belong: ax2 + bx + c = a(x + m)2 + n. These equations are geometrically derived.

Given : A quadratic equation y = 7x² + 56x + 117

this can also written as y = x² + 8 x + 17

y = x² + 4² - 4² + 17

y =  ( x + 4 )²

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Pls help due today!!!!!

Answers

It must be 10 as you need a way to get to 100

In a shop the price of a radio is reduced by one third. if the original price of the radio is two thousand four hundred naira,what is the reduced price

Answers

If the original price of the radio is 2,400 Naira and it is reduced by one third, then the discounted price is 1,600 Naira.

A store usually provides discount of some items to attract more customers and make greater sales.

Suppose the original price is p, the discount rate is d%, and the discounted price is q, then the discounted price can be calculated as:

q = (1 - d%) x p

Parameters given in the problem:

p = 2,400 Naira

d = 1/3

Hence,

q = (1 - 1/3) x 2400

q = 2/3 x 2400 = 1600

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Write an equation in standard form with an x-intercept of 4 and a y-intercept of 5.

Answers

Equation in standard form with an x-intercept of 4 and a y-intercept of 5 is y = -5/4(x) + 5.

Given:

x - intercept = 4

y - intercept = 5

At x intercept y = 0 and at y intercept x = 0

(4,0) and (0,5)

slope = 5-0/0-4

= 5/-4

m = -5/4

substitute (4,0) and m value,

y = mx+c

0 = -5/4*4 +c

0 = -5 + c

c = 5

y = mx + c

y = -5/4(x) + 5.

Therefore equation in standard form with an x-intercept of 4 and a y-intercept of 5 is y = -5/4(x) + 5.

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Another piece of steel is also in the shape of a triangle. One side of the triangle is 6 inches long. The lengths of the other two sides are equal and each is less
than 6 inches long. The lengths of the unknown sides of the triangle are whole numbers of inches.
What are all the possible lengths, in inches, of the unknown sides of the triangle? Explain the process you used to find all the possible lengths.

Answers

According to the triangle inequality, the length of a triangle's third side must be greater than the sum of any two other triangle lengths, so the length of the steel piece will likely be 4 or 5 inches.

What is triangle inequality?

Triangle inequality is a theorem in Euclidean geometry that states any two triangle sides added together must be greater than or equal to the third side; it is represented by the symbols a + b≥ c. The basic tenet of the theorem is that a straight line connects any two points.

Here,

If they are an integer number of inches long and less than six, the following lengths are possible: 4 ,5

According to the triangle inequality, any two other triangle lengths must be greater than the third side of a triangle's length:4+4 = 8 > 6

4+6 = 10 > 4

5+5 = 10 > 6

6+5 = 11 > 5

According to "The Triangle Inequality," which states that the length of a triangle's third side must be greater than the sum of any two other triangle lengths, the piece of steel's potential length will be 4 or 5 inches.

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HELPPPP I'm so confused!!! 60 POINTSSSS!!!

Answers

Answer:

que tienes que realizar no se entiende tu pregunta lo siento

Sam spends exactly £20 on petrol. The petrol costs £1.45 per litre. Work out the number of litres of petrol she buys.

Answers

Answer: 13,8 litres

Step-by-step explanation:

£1.45 ------------ 1 L

 £20 ------------- ?

?= [tex]\frac{20 *1}{1.45} = 13,79310345 L[/tex] = 13,8 L

how many copies for every 10 minutes

Answers

What’s the question?
I don’t know… ????????

Set up the form for the partial fraction decomposition. Do not solve for A, B, C, and so on.

Answers

Answer:

For part a you would decompose the fraction into two independent fractions with the following form:

() = ()/( x^2+5)(x ^2+3x−4)  = (Ax + B)/(x^2+5) + (Cx + D)/(x ^2+3x−4)

Combining these fractions we get:

((Ax + B)*(x ^2+3x−4) + (Cx + D)*( x^2+5))/( x^2+5)(x ^2+3x−4) = ()/( x^2+5)(x ^2+3x−4)

Thus we can say: (Ax + B)*(x ^2+3x−4) + (Cx + D)*( x^2+5) = ()

You then simplify the equation on the left by combining like terms and solve the system of equations that arise corresponding with ().

You would follow a similar process for part b as well.

Step-by-step explanation:

37=18q+1 show work pls

Answers

Answer:

37=18q+1

subtract 1 on both sides

then divide both sides by 18

q=2

Step-by-step explanation:

Answer:

q = 2

Step-by-step explanation:

[tex]\sf 37=18q+1[/tex]

[tex]\sf 18q+1=37[/tex]

Subtract 1 from both sides:-

[tex]\sf 18q+1-1=37-1[/tex]

Simplify:-

[tex]\sf 18q=36[/tex]

Divide both sides by 18:-

[tex]\sf \cfrac{18q}{18}=\cfrac{36}{18}[/tex]

[tex]\sf q=2[/tex]

_____________________

Hope this helps!

Have a great day!



Write down the two district properties between parellelograml and trapezium

Answers

Properties of Trapezium

The base of the trapezium is parallel to each other. In the above case, AD // BC.None of the sides, diagonals and angles are equal to each other.

Properties of Parallelogram

The opposite sides of a parallelogram are parallel to one another and are also equal to one another.The angles are also congruent.The adjacent angles are supplementary.The diagonals bisect each other and the diagonal divides the parallelogram into two congruent triangles.If one of the angles in the parallelogram is a right angle, then all the other angles are a right angle.

You can see pic..

if l || m, solve for x and y

I NEED HELP ASAP

Answers

8x-14=5x+34

3x=48
x=16

If x= 16°

8(16)-14+5y+16=180
130+5y=180
5y=50
y=5°

R is inversely proportional to A.
R = 12 when A = 1.5
a) Work out the value of R when A = 5.
b) Work out the value of A when R = 9

Answers

The value of R when A equal 5 is 3.6 and the value of A when R equal 9 is 2 as R is varies inversely to A.

What is the value of R when A equal 5 and value of A when R equal 9?

Proportional relationships are relationships between two variables where their ratios are equivalent.

If R is inversely proportional to A.

R ∝ 1/A, then

R = k/A

Where k is the proportionality constant.

Given that;

R = 12 A = 1.5Proportionality constant k = ?

First, we determine the proportionality constant.

R = k/A

Plug in R = 12 and A = 1.5 and solve for k

k = R × A

k = 12 × 1.5

k = 18

a) The value of R when A = 5 will be;

R = k/A

R = 18 / 5

R = 3.6

b) The value of A when R = 9

R = k/A
R × A = k

A = k/R

A = 18 / 9

A = 2

Therefore, the value of A when R equal 9 is 2.

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The system of conics has two solutions.

(x−4)^2 + (y+1)^2 = 9
(x−4)^2/9 + (y+1)^2/81 = 1

What are the solutions to this system of conics?

Answers

The system of equations has its solutions to be (1, -1) and (7, -1)

How to solve the system of equations?

The system of equations is given as

(x−4)² + (y+1)² = 9

(x−4)²/9 + (y+1)²/81 = 1

Make (y + 1)² the subject in the equation (x−4)² + (y+1)² = 9

So, we have

(y+1)² = 9 - (x−4)²

Substitute (y+1)² = 9 - (x−4)² in (x−4)²/9 + (y+1)²/81 = 1

This gives

(x−4)²/9 + [9 - (x−4)²]/81 = 1

Split

(x−4)²/9 + 9/81 - (x−4)²/81 = 1

Collect the like terms

(x−4)²/9 - (x−4)²/81 = 1 - 9/81

Evaluate the like terms

[9(x−4)² - (x−4)²]/81 = 72/81

So, we have

9(x−4)² - (x−4)² = 72

Evaluate the difference

8(x−4)² = 72

Divide by 8

(x−4)² = 9

Take the square roots

x - 4 = ±3

So, we have

x = 4 ± 3

Evaluate

x = 1 or 7

Substitute x = 1 or 7 in (y+1)² = 9 - (x−4)²

(y + 1)² = 9 - (1−4)² or (y + 1)² = 9 - (7−4)²

This gives

(y + 1)² = 0 or (y + 1)² = 0

This gives

y + 1 = 0

Evaluate

y = -1

Hence, the solution is (1, -1) and (7, -1)

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a) Work out the gradient of the line y=5x-3 (1)

Gradient = (Answer here)

b) Work out the gradient of the line 3y-12x+7=0 (1)

Gradient = (Answer here)

Answers

Answer:

5 and 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the gradient and c the y- intercept )

(a)

y = 5x - 3 ← is in slope- intercept form

with gradient m = 5

(b)

3y - 12x + 7 = 0 ( add 12x to both sides )

3y + 7 = 12x ( subtract 7 from both sides )

3y = 12x - 7 ( divide through by 3 )

y = 4x - [tex]\frac{7}{3}[/tex] ← in slope- intercept form

with gradient m = 4

-4x+3y=2
3x-9y=3
Is (4,1) a solution of the system?

Answers

Answer:

not a solution

Step-by-step explanation:

we can just fill it in on both equations

-4(4)+3(1)=2

-16+3=2

-13=2

It doesn’t work for this equation so it’s not a solution

Hopes this helps please mark brainliest

Answer:

No

Step-by-step explanation:

For (4, 1 ) to be a solution then both equations must be true

substitute x = 4 and y = 1 into both equations

- 4(4) + 3(1) = - 16 + 3 = - 13 ≠ 2

3(4) - 9(1) = 12 - 9 = 3

Since both equations are not true then (4, 1 ) is not a solution of the system.

Karama can paint a staircase banister in 50 minutes. Find the rate per minute at which Karama can paint banisters

Answers

The rate per minute at which Karama can paint banisters is 0.02.

In the given question,

Karama can paint a staircase banister in 50 minutes.

We have to find the rate per minute at which Karama can paint banisters.

Since we have to find the rate per unit. Rate per unit means how much Karama can paint in one minute.

To find the rate per unit we divide 1 by 50.

As we know that Karama can paint one staircase banister in 50 minute.

So we can write it as

50 minute = 1 staircase banister paint

Now in 1 minute.

1 minute = 1/50 staircase banister paint

Simplifying

1 minute = 0.02 staircase banister paint

Hence, the rate per minute at which Karama can paint banisters is 0.02.

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The pitch at Old Trafford in Manchester,
England is 105 meters long and 68 meters
wide. What is the distance from one corner of
the field to the opposite corner, as denoted by
the dashed line in the picture to the left

Answers

The distance from one corner of the field to the opposite corner, using the Pythagorean Theorem, is of:

125 meters.

What is the Pythagorean Theorem?

The Pythagorean Theorem is a geometry axiom relating the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the equation presented as follows:

[tex]h^2 = l_1^2 + l_2^2[/tex]

From the situation described in this problem, we have that:

The legs are the length and the width of the field, of 105 meters and 68 meters, respectively.The hypotenuse is the length from one corner to the opposite corner.

Hence the distance from one corner of the field to the opposite corner is obtained as follows:

d² = 68² + 105²

d = sqrt(68² + 105²)

d = 125 meters.

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Lora's phone records data for screen time each week. Last week, she used 840 minutes. This week, Lora used 504 screen time minutes on the phone. Calculate the percent decrease in screen time this week.

17%
34%
40%
67%

Answers

The percent decrease in screen time this week is 40%. Therefore, option C is the correct answer.

Given that, last week, Lora used 840 minutes. This week, Lora used 504 screen time minutes on the phone.

What is percentage?

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 "%".

Now,

Difference=840-504

= 336

Percentage decrease = Difference in value/Original value ×100

= 336/840 ×100

= 0.4 ×100

= 40%

The percent decrease in screen time this week is 40%. Therefore, option C is the correct answer.

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The art teacher gave each student half of a sheet of paper. Then she asked the students to colored one one fourth of their pieces of papper. what do the number represent? what information was given?

Answers

The number 1/8 represent the fraction of full sheet of paper the teacher asked each student to color.

The information given are;

Paper given to each student by the teacherPart the teacher asked each student to color

What fraction of paper did the student colored?

The information given are

The full sheet of paper = xPaper given to each student by the teacher = 1/2x

Part the teacher asked each student to color = one fourth of their pieces of papper

= 1/4 of 1/2x

= 1/4 × 1/2x

= 1/8x

So therefore, the student colored 1/8 of the original piece of paper.

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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease y=210(1.092)^x

Answers

The change  y=210(1.092)^x represent exponential growth

The percentage rate of increase is 9.2 percent increase

How to determine exponential growth

Exponential functions are functions that consist of three part say c(b)^d

the part that says whether the function is growth or decay is b

b is called the base function and it is used as follows to determine growth or decay function

b < 1 gives a decay functionb > 1 gives a growth function

Comparing with the given function 1.092 > 1 hence a growth function

The percentage is solved as follows

1.092 * 100 = 109.2%

109.2% is also referred to as 9.2 percent increase since it is an increment of 9.2%. this is shown below

100% + 9.2% = 109.2%

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Just 2 questions.
Explaining the Converse of the Pythagorean Theorem
Task 1
Part A
The Pythagorean Theorem states that for any given right triangle, a2 + b2 = c2. Using the Pythagorean Theorem, what should be the relationship between the areas of the three squares?
Task 2
Part E What does this show about the relationship between the two triangles?

Answers

The Pythagorean Theorem indicates the following relationship between the squares and triangles.

Part A

The relationship between the areas of the squares is that the area of the large square is the sum of the areas of the other two squares.

Part E

The point that the length c on one triangle is equal to the length n on the other triangle and that the other two sides of both triangles are congruent, the two triangles are congruent by SSS congruency rule.

What is the Pythagorean Theorem?

Pythagoras theorem can be stated as follows; The square of the length of the hypotenuse side of a right triangle is equal to the sum of the squares of the other two sides.

Part A

The possible squares in the question are the three squares arranged on the three sides of the triangle, and having a side length which is the same as the length of the side of the triangle to which the square is attached

The relationship between the three squares of side length a, b, and c according to Pythagorean theorem is; a² + b² = c²

Therefore, the area of the largest square that is located on the hypotenuse side of the triangle is equal to the sum of the areas of the other two squares.

Part E

The length of the sides of the triangles, obtained from a similar question on the site are; a, b, and c and a, b, and n

It was shown that c² = n²

Therefore;

c = n

This shows that the two triangles are congruent

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best ontime airlines: hawaiian airlines topped the list of the most punctual u.s. airlines for full-year 2014, according to data released by the bureau of transportation statistics. the on-time arrival performance was 91.9% another aviation data service believes that this percentage now is even higher. the team of researchers chose 130 randomly selected flights and find that 120 of the flights arrived on time. can a hypothesis test be used to determine whether the proportion of hawaiian airlines flights that arrive on-time is higher than 91.9%? group of answer choices yes, because the sample is random. thus, it is representative of the population of flights for the airlines. yes, because the sample is random and (130)(0.923) and (130)(0.077) are both at least 10. this means the normal model is a good fit for the sampling distribution. yes, because the sample is random and (130)(0.919) and (130)(0.081) are both at least 10. this means the normal model is a good fit for the sampling distribution.

Answers

1.because sample is random and (130)

(0.923) and (130)(0.077) are both at least 10.

This means the normal model is a good fit for the sampling distribution.

Consider the provided information.

130 randomly selected flights and find that

120 of the flights arrived on time.

n=130

The on-time arrival performance was 91.9%

p=0.923 and q=1-0.923=0.077

np = 130 x 0.923

np = 120 ≥ 10

nq = 130 × 0.077

nq = 10 = 10

Hence, Yes, because sample is random and

(130)(0.923) and (130)(0.077) are both at least 10. This means the normal model is a good fit for the sampling distribution.

2.because sample is random and (130)

(0.919) and (130)(0.081) are both at least 10.

This means the normal model is a good fit for the sampling distribution.

Consider the provided information.

130 randomly selected flights and find that

120 of the flights arrived on time.

n=130

The on-time arrival performance was 91.9%

p=0.919 and q=1-0.919=0.081

np = 130 x 0.919

np = 119.5 ≥ 10

nq = 130 × 0.081

nq = 10.5 ≥ 10

Hence, Yes, because sample is random and

(130)(0.919) and (130)(0.081) are both at least 10. This means the normal model is a good fit for the sampling distribution.

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Write a polynomial of least degree with roots 1 and -9. un Write your answer using the variable x and in standard form with a leading coefficient of 1. ​

Answers

Answer:

  y = x² +8x -9

Step-by-step explanation:

You want the least-degree polynomial with roots 1 and -9, written in standard form.

Factors

Each root p means there is a factor (x-p). The two roots make the factored form of the polynomial be ...

  y = (x -1)(x +9)

Expanding this to standard form, we get ...

  y = x² +8x -9

__

Additional comment

A quadratic that has two roots, p and q, will have the standard form ...

  y = (x -p)(x -q) = x² -(p+q)x +pq

That is, the linear term coefficient is the opposite of the sum of the roots, and the constant is their product. This means you can write down the equation directly from the roots:

  y = x² -(1-9)x +(1)(-9) = x² +8x -9

Activity 8. Counting the roots of polynomial equation

by inspection determine the number of real roots of each polynomial equation. Roots multiply n are counted n times

1. (x-4)(x+3)^2(x-1)^3=0
2. X^2(x^3-1)=0
3. X(x+3)(x-6)^2=0
4. 3x(x^3-1)^2=0
5. (x^3-8)(x^4+1)=0​

patulong po plss.

Answers

The number of real roots found are-

1. (x-4)(x+3)^2(x-1)^3=0 ; 6 real roots.

2. X^2(x^3-1)=0 ; 3 real roots.

3. X(x+3)(x-6)^2=0 ; 4 real roots.

4. 3x(x^3-1)^2=0 ; 3 real roots.

5. (x^3-8)(x^4+1)=0​ ; 1 real roots.

Define the term roots of polynomial?If a root is not imaginary (defined as a number as in form a + bi, whereby I is a number which is not on any real number line, which is why the name imaginary), it is said to be real.

Consider the given cases-

1. (x-4)(x+3)^2(x-1)^3=0,

Put each equals zero.

x – 4 = 0 or (x + 3)^2 = 0 or (x – 1)^3 = 0,

Thus,

x = 4

x = –3 twice

x = 1 thrice

All are real numbers, thus given polynomial has 6 real roots.

2. x^2(x^3-1)=0

Put each equals zero.

x² = 0

x³ – 1 = x³ – 1³ = (x – 1)(x² + x + 1) = 0

The quadratic expressions has 2 imaginary roots.

Use the discriminant formula to find-

D = b² – 4ac = 1² – 4(1)(1) = 1 – 4 = –3 < 0.

Thus, roots that are not real.

So, the real roots of this polynomial : 0(twice) and 1.

Hence, thus given polynomial has 3 real roots.

3. x(x+3)(x-6)^2=0

Put each equals zero.

x = 0

x = 3

x = 6 twice

Hence, thus given polynomial has 4 real roots.

4. 3x(x^3-1)^2=0

Put each equals zero.

3x = 0 and  x = 0

(x^3 – 1)² = [(x – 1)(x² + x + 1)]² = (x – 1)²(x² + x + 1)² = 0,

Here, only two roots are real

The quadratic expression do have unreal roots, thus 1 twice are the real roots.

Hence, thus given polynomial has 3 real roots..

5. (x^3-8)(x^4+1)=0

Put each equals zero.

x³ – 8 = x³ – 2³ = (x – 2)(x² + 2x + 4) = 0

There is only one real root i.e, 2, the quadratic expression do have imaginary roots

Check using the discriminant formula

D = b² – 4ac = 2² – 4(1)(4) = 4 – 16 = – 12 < 0.

x⁴ + 1 = 0 has imaginary roots.

Hence, thus given polynomial has 1 real roots..

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On this assignment I am just writing about what the student did wrong. Please help me. LOOK AT THE PICTURE ABOVE ^^^^^^^^^^^^^^^^^^^^^^^^^

QUESTIONS:

1. What math did Ann do well?? EXPLAIN

2. What mistake has Ann made? EXPLAIN​

Answers

ann made a rectangle with the

right perimeter & area

ann doesn't try any other

rectangles to see if their areas are

different.

splitting the land , ann confuses perimeter and area

mapmathshellorg

Complete both transformations below. Then enter the final coordinates of the figure. A (1.-2)
B (4,-1)
C (5.-3)
1) < -2.4 >
2) Dilate K = 3​

Answers

Applying the transformation rule (x - 2.y + 4) and using the scale factor k = 3 for dilation gives

preimage      translation image     Dilation image

A (1.-2)             A' (-1, 2)                   A'' (-3, 6)  

B (4,-1)             B' (2, 3)                    B'' (6, 9)

C (5.-3)            C' (3, 1)                     C'' (9, 3)

What is transformation?

Transformation is a term used in mathematics to refer to the movements made by objects.

Translation refers to a type of transformation that involve a linear movement.

Applying the transformation rule (x - 2.y + 4 ) gives

A (1.-2) = (1 - 2, -2 + 4) = (-1, 2)

B (4,-1) = (4 - 2, -1 + 4) = (2, 3)

C (5.-3) = (5 - 2, -3 + 4) = (3, 1)

preimage        image

A (1.-2)             A' (-1, 2)

B (4,-1)             B' (2, 3)

C (5.-3)            C' (3, 1)

Dilation involves making the image bigger or smaller. In this case K > 1 hence the image is bigger

Using the scale factor k = 3 for dilation rule (kx, ky) gives

A' (-1, 2) = (-1 * 3, 2 * 3) = (-3, 6)

B' (2, 3) = (2 * 3, 3 * 3) = (6, 9)

C' (3, 1) = (3 * 3, 1 * 3) = ( 9, 3)

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