In Exercises 1-4, determine whether the dilated figure or the original figure is closer to the center of dilation. Use the given location of the center of dilation and scale factor k.
1. Center of dilation inside the figure; k = 3
Center of ditation inside the figure, k = 1/2
3. Center of dilation outside the figure: = 120%
4. Center of dilation outside the figure; k = 0.1

Answers

Answer 1

When the Center of dilation is inside the figure

The original figure is closer to the center of dilationThe dilated figure is closer to the the center of dilation

When the Center of dilation is outside the figure

    3. The original figure is closer to the the center of dilation

    4. The dilated figure is closer to the center of dilation

The center of dilation is the fixed point from which the distances in a dilation are measured

The scale factor is ratio of the side lengths of an original figure or preimage to  the side lengths of the newly formed image

Center of dilation is inside the figure

Where the center of dilation is inside the figure, and the scale factor is larger than 1, k = 3 > 1,  we have;

The distance of a point on the dilated figure, including the distances from the center of dilation is 3 times the distances of points on the original image from the center of dilation

Therefore, the original figure has a shorter distance to and is therefore closer to the the center of dilation than the dilated figure

     2. Where the center of dilation is inside the figure, and the scale factor is a fraction between 0 and 1 k = 1/2, we have;

The distance of a point on the dilated figure, including the distances from the center of dilation is 1/2 times the distances of points on the original image from the center of dilation

Therefore, the dilated figure has a shorter distance to and is therefore closer to the the center of dilation than the original figure

Center of dilation outside the figure

     3. Given that the center of dilation is outside the figure and the scale factor is larger than 1, k = 120% = 120/100 = 1.2 > 1, we have;

The distance of the dilated figure from the center of dilation is 120% of the distance of the original figure from the center of dilation, therefore, the original figure is closer to the the center of dilation than the dilated figure

     4. Where the center of dilation is outside the figure and the scale factor is a fraction between 0 and 1, k = 0.1 < 1

The distance of the dilated figure from the center of dilation is only 0.1 times the distance of the original figure from the center of dilation, and therefore, the dilated figure is closer to the center of dilation

Learn more about scale factors and center of dilation here;

https://brainly.com/question/12162455


Related Questions

please answer this question!!​

Answers

Answer:

a

Step-by-step explanation:

all angles of an equilaterall triangle are equal therefore 180÷3 = 60

equivalent expression: 3 + 4(2z - 1)

Answers

Answer:

8z - 1

Step-by-step explanation:

Given

3 + 4(2z - 1) ← multiply each term in the parenthesis by 4

= 3 + 8z - 4 ← collect like terms

= 8z - 1

Answer:

-1 + 8z

Step-by-step explanation:

First use the distributive property of multiplication (Just multiply 4 with all numbers in the parenthesis):

3 + 4(2z - 1)

3 + 8z - 4

Group like terms:

3 + 8z - 4

-1 + 8z

The answer is -1 + 8z

Hope this helped.

what is the relation that represents the relation

Answers

Answer:

what can i help u with

Step-by-step explanation:

I really can't help u with that sorry i am bad at math

How many solutions does the system have?








x+y=3
5x+5y=15

Answers

x=3-y

5(3-y) + 5y=15

15y-5y+5y=15

15y=15

Y= 15/15

Y= 1


X+(1)=3

X=3-1

X=2




Final answer: x=2 and y=1

Method: simultaneous equations

If I start a road trip with 10,425 miles on my auto meter and I end it with 23,840 miles showing how many miles was my trip

Answers

Answer:

13,415 miles

Step-by-step explanation:

Final position - initial position = Miles traveled:

23,840 miles - 10,425 miles = 13,415 miles

Solve 4 sinx + 9 cosx=0 for 0° ​

Answers

4 sin(x) + 9 cos(x) = 0

4 sin(x) = -9 cos(x)

tan(x) = -9/4

x = arctan(-9/4) + … … … (in radians)

or

x = arctan(-9/4) + 180n ° … … … (in degrees)

where n is any integer.

I'm guessing you're solving for x over some domain, probably 0° ≤ x < 360°. In that case, you would have two solutions for n = 1 and n = 2 of

x ≈ 113.96°   and   x ≈ 293.96°

Help anyone can help me do the question,I will mark brainlest.​

Answers

Answer:

Step-by-step explanation:

S=pi*R^2=(area of the sector)*(360/angle of AOB)

so 22/7*9^2=99*360/angle of AOB

-> AOB=140

perimeter of circle: 2*pi*R

permiter of sector : 2*pi*140/360*R+ 2R=22+9*2=40

find the missing length indicated​

Answers

Answer:

x = 240

Step-by-step explanation:

Apply the leg rule to find the value of x.

Leg rule is given as:

Hypotenuse/leg 1 = leg 1/part 1

Hypotenuse = 400

Leg 1 = x

Part 1 = 144

Plug in the known values into the formula

400/x = x/144

Cross multiply

x*x = 144*400

x² = 57,600

Take the square root of both sides

√x² = √57,600

x = 240

solve the quadratic equation
give your answer to 2 decimal places
: 3x^2+x-5=0

Answers

Given:

The quadratic equation is:

[tex]3x^2+x-5=0[/tex]

To find:

The solution for the given equation rounded to 2 decimal places.

Solution:

Quadratic formula: If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then:

[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

We have,

[tex]3x^2+x-5=0[/tex]

Here, [tex]a=3,b=1,c=-5[/tex]. Using the quadratic formula, we get

[tex]x=\dfrac{-1\pm \sqrt{1^2-4(3)(-5)}}{2(3)}[/tex]

[tex]x=\dfrac{-1\pm \sqrt{1+60}}{6}[/tex]

[tex]x=\dfrac{-1\pm \sqrt{61}}{6}[/tex]

[tex]x=\dfrac{-1\pm 7.81025}{6}[/tex]

Now,

[tex]x=\dfrac{-1+7.81025}{6}[/tex]

[tex]x=1.13504167[/tex]

[tex]x\approx 1.14[/tex]

And

[tex]x=\dfrac{-1-7.81025}{6}[/tex]

[tex]x=-1.468375[/tex]

[tex]x\approx -1.47[/tex]

Therefore, the required solutions are 1.14 and -1.47.

If the length of the shorter arc AB is 22cm and C is the center of the circle then the circumference of the circle
is:

Answers

Answer:

22= 2(pi)(r)(45/360)

28.01

C=176

Step-by-step explanation:

32 x square Y - 2 y cube

Answers

Answer:

207y

Step-by-step explanation:

Find all complex numbers z such that z^4 = -4.

Note: All solutions should be expressed in the form a+bi, where a and b are real numbers.

Answers

26 and yeah just need points ignore this answer so sorry

4. Which property of similarity can be used to prove triangles DEF and GHI are similar?

Answers

Answer:

SSS

Step-by-step explanation:

We know all three sides of both triangles. The common ratio of DEF to GHI is 2/3.

Answer:

SSS

Step-by-step explanation:

Similar triangles must have congruent corresponding angles and proportional corresponding sides.

express the ratio 7day to 6weeks as a decimal fraction

Answers

Answer:

6 weeks=6*7 days=42days

7/42 =1/6 =0.16667

OR

7 days=1 week

therefore 1/6=0.16667

Note that both must be in the same unit.

traders fix the price of cosmetic items 30% above the cost price when he sold an item at 25% discount there was a loss of Rs 15 find the cost price and marked price of the item​

Answers

Cost price is Rs600 and marked price is Rs780.

Must click thanks and mark brainliest

Determine, to one decimal place, the length, width & height of the rectangular prism that would have the greatest volume, with a surface area of 200 cm^2.

Answers

Answer:

The length = The width = The height  ≈ 5.8 cm

Step-by-step explanation:

The volume of a rectangular pyramid, V = l × w × h

The surface area of the pyramid = 2 × l × h + 2 × w × h + 2 × l × w = 200

∴  l × h + w × h + l × w = 200/2 = 100

We have that the maximum volume is given when the length, width, and height are equal and one length is not a fraction of the other. Therefore, we get;

At maximum volume, l = w = h

∴ l × h + w × h + l × w = 3·l² = 100

l² = 100/3

l = 10/√3

Therefore, the volume, v = l³ = (10/√3)³

The length = The width = The height = 10/√3 cm ≈ 5.8 cm

Pressure varies inversely as volume. When the pressure is 8 Pascals, the volume is 22 liters. What would the volume be if the pressure were increased to 16 pascals?

Answers

Answer:

we can use 2 formule to solve your question: One is P*V=n(mol)*R*T(KELVIN)

Step-by-step explanation:

And other is P(first)*V(first)=P(last)*V(last)

8*22=16*?

the ?=11

Determine what type of model best fits the given situation: the temperature of a cup of coffee decreases by 5 F every 20 minutes.

A. liner
B. exponential
C. quadratic
D. none of these

Answers

Answer: T = -t / 4 + T0   where t is the temperature in minutes elapsed, T is the final temperature, and T0 is the initial temperature

Explanation: This is a linear equation in T and t

(-1 / 4 represents -5 deg / 20 min  = - 1 deg / 4min

Write an equation of the graph (shown below) in slope intercept form.

Answers

This is not a valid question and, therefore, cannot be answered. (Reason: No graph is attached.) Try revising it or giving more information. Hope this helps! ❤️

ncert maths class 10 solution 5.1 4

Answers

Can you attach a picture to your question?

I would love to help you out.

Answer:

Step-by-step explanation:

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.1

           where is question ??

Convert 5π∕6 radians to degrees. Question 1 options: A) 25° B) 150° C) 150π° D) 1080°

Answers

Step-by-step explanation:

Hi there!

Given;

= 5(π\6)

We have;

π = 180°

Keeping value of π in the question;

= 5(180°/6)

= 5*30°

= 150°

Therefore, answer is option B.

Hope it helps!

If a wheel has a radius of 5cm
how much is one rotation of the wheel
How many rotations can the wheel do within a distance of 50km

Answers

Answer:

circumference = 2*PI*radius

circumference = 2 * PI * 5 cm

circumference = 31.4159265358979 cm

50 km = 500,000 centimeters

rotations = 500,000  / 31.4159 cm

15,915.51  rotations

Step-by-step explanation:

log 55 is the power to which ---- must be raised in order to produce a value of 55

Answers

Answer:

10

Step-by-step explanation:

just took the quiz

Jim removed 27 gallons of water from a rainwater storage tank. There are 59 gallons left in the tank. What equation can Jim use to find how much water was in the tank earlier? Use x to represent the amount of water originally in the tank.

Answers

Answer: X = 86 gallons

Step-by-step explanation:

X-27=59

X=59+27

Determine the quotient of .     ​

Answers

of what?? the hamburgler??

Can anyone help plz?

Answers

Answer:

just add a small amount and and square the new number

between 2.82 and 2.83 seems a bit closer

Step-by-step explanation:

x      x^2

2.8         7.84

2.81         7.8961

2.82 7.9524

2.83 8.0089

2.84 8.0656

2.85 8.1225

2.86 8.1796

2.87         8.2369

Rob cuts a circular hole out of a rectangular piece of paper. The paper measures 20 centimeters by 30 centimeters. The hole is 10 centimeters in diameter. How much of the piece of paper, in square centimeters, is left over after the hole is cut out?

Answers

Answer:

521.25

Step-by-step explanation:

the circle is 78.75 in area and the square is 600 so 600- 78.75 = 521.25

Prove that 1/√2 is irrational

Answers

Answer:

Step-by-step explanation:

Let's assume that it is rational , so this number can be represented as

[tex]\Large \boldsymbol{}\bf \dfrac{p^{^/is \ an \ integer}}{q^{ / natural}} -irreducible \ \ fraction[/tex]

[tex]\Large \boldsymbol{}\bf \dfrac{1 ^{/ an \ integer }}{\sqrt{2}^{ / not \ \ integer } }[/tex]  -Since the denominator is not a natural number then the  1/√2   is respectively an irrational number

Please Help !


Which of the following describes point D? (-4, 0) (0, -4) (0, 4) (4, 0)

Answers

Answer:

D(0 , 4)

Step-by-step explanation:

Point D is on the y axis. So, x-coordinate  = 0

y- coordinate is the vertical length from origin which is 4

Answer:

D(0 , 4)

Step-by-step explanation:

To paint a wooden cube, Pinocchio needs 4 grams of paint. When it is dry, he cut the cube into 8 smaller pieces of smaller size. How much paint additional paint does Pinocchio need to paint the unpainted surfaces of the smaller cubes

Answers

Answer:

9 grams of paint

Step-by-step explanation:

6×8=48

48÷4= 12

48-12=36

36÷4=9

first multiply 6 by 8 because a cube has six faces and you cut that cube eight times

second after you cut that you will have 48 faces and for every six faces there are 4 grams of paint so you divide 48 by 4 and you get 12 this means that 12 of the faces are painted

next you subtract 12 from 48 and you get 36 this means that 36 faces are not painted

lastly you divide 36 by 4 and you will get 9 grams of paint

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