Why do you think a dilation with 0 < k < 1 results in a reduction?

Answers

Answer 1

Multiplying x by any positive number smaller than 1 will result in some smaller value.

For example, if the scale factor is k = 0.5, then we can think of this as the fraction k = 1/2. Multiplying by 1/2 will make any number smaller, namely, exactly half as much.

1/2 times 100 = 501/2 times 78 = 391/2 times 600 = 300

We are taking a fractional part of the original number, so its expected the result is smaller. It's like having a whole cake and we only take slices of that cake to end up with the new value. There's no way having one or more slice be larger than the original whole amount.

Because things are getting smaller, we call this type of dilation to be a reduction or we can call it shrinking. This is in contrast to an enlargement when k > 1.

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More info (optional section)

Claim:  For some positive number k such that k < 1, we have xk < x when x is positive.

The proof of this claim is fairly straight forward.

We multiply both sides of k < 1 by x to get

k < 1

x*k < x*1

xk < x

The inequality sign does not flip because we're multiplying both sides by a positive number x.

So because xk < x, this shows that the original value x gets smaller to xk when we apply the positive scale factor k such that k < 1. This is the same as saying 0 < k < 1. Furthermore, xk < x is the same as 0 < xk < x.


Related Questions

om and Tamir applied to the same university. They looked up the average SAT score of students admitted to that university. Tom’s SAT score was 260 points above the average score. Tamir’s SAT score was 20 points below the average score. Which expression represents the difference in their scores?

-❘260 - 20❘
❘-20 - 260❘
❘260 - 20❘
-❘260❘ - ❘20❘

Answers

Answer:

a.-260-20 this is the answer because Tom was 260 above average that means average plus 260 was tom s marks

so tamirs marks were 20 behind average that means average minus 260 minus 20

Answer:|-20-260|

Step-by-step explanation:

Tom with above average score of 260, so that will represent 260 in the equation

Note that the average score will be represented with 0

Tamir score is below average of 20 which represents -20 in the equation

To find the difference we need to subtract -20 with 260, -20-260. Which will equal -280

Note it's not possible for tom to have a below average score, so we must add a absolute value to get 280 to make it make sense

So we get the final equation of |-20-260|

help me pls thank u <3

Answers

The correct answer is A

Write two equations in standard form for two lines that will have the same solution as

4x -5y = 7

Answers

Answer:

5y-4x=7

Step-by-step explanation:

4567576537458675473489568743895

Hurry I need it pleaseeee come helpp

Answers

Answer:

43

Step-by-step explanation:

180-123=57

180-(57+80)=43

Answer:

x=43

Step-by-step explanation:

the other two angles measure 80 (vertical angles are equal) and 57, (straight lines make 180 degree angles)

so x = 43 because 180-(80+57)=43 (180 degrees in a triangle)

factor 5x^3 - 2x^2 using the GCF

Answers

Answer:

x^2(5x-2)

Step-by-step explanation:

The gcf of the whole expression is x^2. You then factor out it from the expression to get x^2(5x-2)

Beach towels are on sale for $1.50 off of the regular price. Ms. Ortiz buys 4 beach towels on sale for a total of $33.96. Use equations to determine the regular price of a beach towel.

Answers

Answer: $9.99

Step-by-step explanation:

From the question, we are informed that beach towels are on sale for $1.50 off of the regular price and that Ms. Ortiz buys 4 beach towels on sale for a total of $33.96.

The amount for each beach towel bought will be:

= $33.96/4

= $8.49

Since there's $1.50 off the normal price, that means the normal price for each will have been:

= $8.49 + $1.50

= $9.99

At the youth center, the committee has decided to create a circular shaped flower bed. They plan to cover the flower bed with mulch. A flower bed with a 12' diameter will cost $150 to cover with mulch. A flower bed with an 18' diameter will cost $300 to cover. Which is the better value?

Answers

Answer:

12 in diameter bed will  give better value

Step-by-step explanation:

Given:

Cost of cover 12 in diameter bed = $150

Cost of cover 18 in diameter bed = $300

Find:

Better value

Computation:

Area of bed = πr²

Area of 12 diameter of bed = (22/7)(6)²

Area of 12 diameter of bed = 113.14 in²

Area of 18 diameter of bed = (22/7)(9)²

Area of 18 diameter of bed = 113.14 in²

Area of 18 diameter of bed = 254.57 in²

Compare cost of bed 1 = 113.14 / 150 = 0.75 in per dollar

Compare cost of bed 2 = 254.57 / 300 = 0.84 in per dollar

So,

12 in diameter bed will  give better value

Find the area of a right triangle with a height of 8 1/2 feet and a base of 15 feet

Answers

Answer:

63.75

Step-by-step explanation:

The equation for finding the area of a triangle is 1/2b x h

b = base

h = height

b = 15

h = 8.5

15(1/2) x 8.5

7.5 x 8.5 = 63.75

Answer:

A = 63.75 ft^2, or 63 3/4 ft^2

Step-by-step explanation:

The formula for the area of a triangle of base b and height h is

A = (1/2)(b)(h).

With h = 8.5 ft and b = 15 ft, the area of the triangle in question is

A = (1/2)(8.5)(15)ft^2, or

A = 63.75 ft^2, or 63 3/4 ft^2

someone 10 points...?​

Answers

Answer:

Frequently consuming unusually large amounts of food in one sitting and feeling that eating behavior is out of control is a binge eating disorder and a binge eating is when you eat a lot of snacks but u know how to control how much to eat.

Step-by-step explanation:

i forgot to make it an answer my bad

pls help Will give Brainliest

Answers

Answer: 15

Step-by-step explanation:

5x = 75

x = 15

Angles are the same since they are vertical angles

Help please! 50 Points! PLEASE DONT RESPOND IF YOU DO NOT KNOW.
find the area of the shaded region. round to the nearest hundredths if necessary.
You can answer just 1 of them and thats fine but id really appreciate if all could get answered!

Answers

Answer:

e.869.58units^2

f. 96m^2

g. 184m^2

Step-by-step explanation:

e.

484 square

176 triangle

209.58 equilateral triangle

f. 196 total are - mini square 25+25+25+25= 96m^2

g. 22+66+80+16=184m^2

given:2y-1/-3=-5 prove:y=8

Answers

Answer:

2y + 1/3 = 5

2y = -5 -1/3

2y = -16/3

Y = -8/3

Step-by-step explanation:

im pretty sure thats the answer but good luck!

$60 simple interest is received on a loan each year. When the rate of interest is increased by 0.5%, the simple interest is $70. What is the amount of the loan?​

Answers

Answer:

Step-by-step explanation:

I=Pr

P(r+.005-r)=70-60

.005P=10

P=$2000

Answer:

Step-by-step explanation:

$60 simple interest is received on a loan each year. When the rate of interest is increased by 0.5%, the simple interest is $70. What is the amount of the loan?​

On a bicycle you can travel 20 miles in 4 hours. What is the unit rate in this situation? * 100 miles per hour 80 miles per hour 5 miles per hour O 24 miles per hour​

Answers

The unit rate is, 5 miles per hour

Answer:

Unit rate: 5 miles per hour

Step-by-step explanation:

Unit rate:  20 m / 4h  =  5m per hour

i really need help please ​

Answers

Answer:

Step-by-step explanation:

85/3

Can anybody help me?

Answers

Answer:

[see below]

Step-by-step explanation:

We are given the two points (0,3) and (2,0). We can use the slope formula to find the slope.

[tex]\frac{0-3}{2-0}=\frac{-3}{2}=-\frac{3}{2}[/tex]

The slope is negative three-halves.

Since the point passes the point (0,3), 3 would be the y-intercept.

Hope this helps.

In a public park the number of deer doubles every year. In the year 2000, there were 25 deer in the park. The function represents
(2) 25 = N number of deer in the park years after the year 2000 what will be the number of deer in 2006?

A) 1600

B) 300

C) 89

D) 37

D A​

Answers

Answer:

A) 1600

Step-by-step explanation:

double the number for the first year then double that number ect untill you do six years

simon is ironing shirts it takes him 15 minutes to iron 2 shirts how long would it take him to iron 26 shirts give your answer in hours and minutes

Answers

Answer:

3 hours 15 minutes

Step-by-step explanation:

Simon is ironing shirts it takes him 15 minutes to iron 2 shirts.

2 shirts = 15 minutes

1 shirt = (15/2) minutes

For 26 shirts,

[tex]26\ shirts = 26\times \dfrac{15}{2}\ min\\\\=195\ minutes[/tex]

or

Time = 3 hours 15 minutes

Hence, it will take 3 hours 15 minutes to iron 26 shirts.

John bought a crate of floor tiles $100. The crate had 5 boxes of floor tiles. Each box contained 40 floor tiles. Write an equation to determine the cost per tile, t.

Answers

Answer:

5x+40=100

Step-by-step explanation:

The equation to determine the cost per tile, t will be [tex]\rm 200 \times t =100[/tex] and the cost per tile, t = 1/2$.

The total cost of a crate of floor tiles was $100 which had 5 boxes of floor tiles and each box contained 40-floor tiles. we have to determine the equation for the cost per tile, t.

What is the cost per tile?

Here, Cost per tile = $t

Per Box Contain 40 tiles.

So, Price for 1 box = [tex]\rm 40\times t[/tex]

and Total price of crate = [tex]\rm 40 \times t \times5[/tex]

Therefore,  [tex]\rm 40 \times t \times5=100[/tex]

[tex]\rm 200 \times t =100[/tex]

[tex]\rm t = \frac{1}{2}[/tex]

Hence, the cost per tile, t = 1/2.

The equation to determine the cost per tile, t will be [tex]\rm 200 \times t =100[/tex] and the cost per tile, t = 1/2$.

Learn more about the linear equation here:

https://brainly.com/question/11897796

The center of a clock is at (0,0) in a coordinate system, and the minute hand is 10 inches long. Find the approximate coordinates of the tip of the minute hand at: 12:05 p.M.

Answers

Answer:

(5, 8.66)

Step-by-step explanation:

Let x represent the x coordinate of the clock tip and y represent the y coordinate of the clock tip.

At 12:05 pm, the clock tip forms an angle of 60° with the x axis. Therefore:

θ = 60°

[tex]tan\theta=\frac{y}{x} \\\\tan60=\frac{y}{x} \\\\y=1.732x\\\\y-1.732x=0\ \ \ (1)[/tex]

Since the minute hand is 10 inches long, hence:

[tex]\sqrt{x^2+y^2}=10\\\\x^2+y^2=100\\\\substituting\ y=1.732x, gives\\\\x^2+(1.732x) ^2=100\\\\x^2+3x^2=100\\\\4x^2=100\\\\x^2=25\\\\x=5[/tex]

To find y, substitute x = 5:

y = 1.732(5) = 8.66

This means that the coordinate of the tip of the minute hand at: 12:05 p.M. is (5, 8.66)

Triangle LMN has a perimeter of 9cm. If triangle LMN is dilated by a scale factor of 3 about a given point, what is the perimeter of triangle L'M'N

Answers

9514 1404 393

Answer:

  27 cm

Step-by-step explanation:

Dilation multiplies all linear measures by the same dilation factor. The perimeter will be 3 times that of triangle LMN.

Perimeter of L'M'N' = 3(9 cm) = 27 cm.

Answer:

27cm

Step-by-step explanation:

Which statement about these triangles is true?
Pre-Image
Image
12 + 3
12
5
5+3

Answers

Answer:

The answer will be B

Step-by-step explanation:

I think that the answer would be b

Help me with this!!!! ( fake answers will be reported :)) )

Answers

Answer:

16

Step-by-step explanation:

3x-2x=8

x=8

QR=8*2=16

Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a radius of 15 feet and a height of 20 feet. Container B has a radius of 19 feet and a height of 19 feet. Container A is full of water and the water is pumped into Container B until Container A is empty.


To the nearest tenth, what is the percent of Container B that is full after the pumping is complete?

pleaseee help meee

Answers

9514 1404 393

Answer:

  65.6%

Step-by-step explanation:

The question is essentially asking the ratio of the volumes.

  Va = πr²h = π(15²)(20)

  Vb = πr²h = π(19²)(19)

The ratio of volumes is ...

  Va/Vb = π(15²)(20)/(π(19³)) = (15²)(20)/19³ ≈ 0.65607

Container B will be about 65.6% full when container A is empty.

help out for these two questions please

Answers

Answer:

23 - A

24 - x = -3 and x = 1

Step-by-step explanation:

Hey There!

So if you didnt know the " zeroes" are the coordinates of where x=0

For the first one the zeroes would be 1 because that's where the line is at x=0

For the second one the zeroes would be x=-3 and x=1 because that's where x=0 if that makes sense

department store sells a pair of shoes with a 33% discount coupon. If the store orignially sold the shoes for $55.25, what is the sale price?

Answers

Answer:

The sale price is $37.02.

Step-by-step explanation:

With the information provided, you can find the sale price by calculating 33% of the price which is the discount and subtracting that amount from the price:

$55.25*33%=$18.23

$55.25-$18.23=$37.02

According to this, the answer is that the sale price is $37.02.

Which algebraic expression represents the phrase "7 more than three multiplied by
c"?

Select one:

A. 7 + 3c

B. 7 x (3c)

C. 7c + 3

D. 3 + 7c

Answers

Answer:

7x(3c)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

7 more then, start with +7. 3 multiplied by c is 3c. Therefore, it would be 7+3c

A car traveled 187 miles in 4 hours and 16 minutes. What was the average speed of the car in miles per
hour?

Answers

Answer:

43.83mph

step-by-step-explanation

Find value of X

Thank you

Answers

Answer:

x = 98

Step-by-step explanation:

If angle D is the center then

x + 4 = 2 × (x - 47)

x + 4 = 2x - 94

4 + 94 = 2x - x

98 = x

which value of x is a solution of 8> (x-6)-2

Answers

Answer:

The answer is x < 16.

Step-by-step explanation:

1) Remove parentheses.

[tex]8 > x - 6 - 2[/tex]

2) Simplify x - 6 - 2 to x - 8.

[tex]8 > x - 8[/tex]

3) Add 8 to both sides.

[tex]8 + 8 > x[/tex]

4) Simplify 8 + 8 to 16.

[tex]16 > x[/tex]

4) Switch sides.

[tex]x < 16[/tex]

Therefor, the answer is x > 16.

The answer is x is equal to 16
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