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Answer:

The scale factor that transforms quadrilateral ABCD to quadrilateral A'B'C'D' is 3

Step-by-step explanation:

Quadrilateral ABCD has the following coordinates

A(1, 5), B(2, 6), C(3, 3) and D(1, 3)

The image A'B'C'D' has the following coordinates;

A'(-3, 1), B'(0, 4), C'(3, -5), D'(-3, -5)

The length of segment [tex]\overline {AB}[/tex] = √((2 - 1)² + (6 - 5)²) = √2

The length of segment [tex]\overline {BC}[/tex] = √((3 - 6)² + (3 - 2)²) = √10

The length of segment [tex]\overline {CD}[/tex] = √((1 - 3)² + (3 - 3)²) = 2

The length of segment [tex]\overline {DA}[/tex] = √((1 - 1)² + (3 - 5)²) = 2

For quadrilateral, we have;

A'(-3, 1), B'(0, 4), C'(3, -5), D'(-3, -5)

The length of segment [tex]\overline {A'B'}[/tex] =  √(0 - (-3))² + (4 - 1)²) = 3·√2

The length of segment [tex]\overline {B'C'}[/tex] = √((3 - 0)² + (-5 - 4)²) = 3·√10

The length of segment [tex]\overline {C'D'}[/tex] = √((-3) - 3)² + (-5 - (-5))²) = 6

The length of segment [tex]\overline {D'A'}[/tex] = √((-3) - (-3))² + ((-5) - 1)²) = 6

The scale factor that transforms quadrilateral ABCD to A'B'C'D' is given as follows;

[tex]The \, scale \, factor \, of \, transformation = \dfrac{\overline {A'B'}}{\overline {AB}} = \dfrac{\overline {B'C'}}{\overline {BC}} = \dfrac{\overline {C'D'}}{\overline {CD}} = \dfrac{\overline {D'A'}}{\overline {DA}} = 3[/tex]

Therefore, the scale factor that transforms quadrilateral ABCD to A'B'C'D' = 3

Given:

Consider the complete question is "A field provides grazing for 18 sheep for 8 days. How many days grazing would it provide for 24 sheep?".

To find:

The number of days the field provides grazing for 24 sheep.

Solution:

We have,

If number of sheep = 18, then, number of days = 8.

If number of sheep = 24, then, number of days = x.

Now, the products of number of sheep and number of days are equal because they represent the total work done.

[tex]18\times 8=24\times x[/tex]

[tex]\dfrac{18\times 8}{24}=x[/tex]

[tex]\dfrac{144}{24}=x[/tex]

[tex]6=x[/tex]

Therefore, the field provides grazing for 24 sheep for 6 days.

Answer:

the answer is B

Step-by-step explanation:

since 10 isn't a perfect square

Answer:

16.3, 14, 8, -3

Step-by-step explanation:

Any number less than 16.3 and 16.3 are acceptable answers

Answer:

[tex]\frac{26}{52}[/tex], [tex]\frac{13}{52}[/tex], [tex]\frac{52}{52}[/tex], [tex]\frac{1}{52}[/tex]

Step-by-step explanation:

In a deck of playing cards there are 52 cards total.

13 clubs

13 hearts

13 spades

13 diamonds

half are red and half are black

all of the cards are red or black

plz mark me brainliest ;)

Answer:

18

Step-by-step explanation:

C = 2πr

r = 3

2π(3) = 18.85

Answer:

$22.17

Step-by-step explanation:

105.36 multiplyed by 0.22 ( you need to change the 22% to a decimal so just make it 0.22) then once you multiplyed them then you get your answer.

Answer:

the last one

Step-by-step explanation:

a square's sides should be the same angle

Answer:

i believe its the last one but im not 100% sure

Step-by-step explanation:

Answer:

[tex]c^2 = 9dp[/tex]

Step-by-step explanation:

Given

[tex]dx^2 + cx + p = 0[/tex]

Let the roots be [tex]\alpha[/tex] and [tex]\beta[/tex]

So:

[tex]\alpha = 2\beta[/tex]

Required

Determine the relationship between d, c and p

[tex]dx^2 + cx + p = 0[/tex]

Divide through by d

[tex]\frac{dx^2}{d} + \frac{cx}{d} + \frac{p}{d} = 0[/tex]

[tex]x^2 + \frac{c}{d}x + \frac{p}{d} = 0[/tex]

A quadratic equation has the form:

[tex]x^2 - (\alpha + \beta)x + \alpha \beta = 0[/tex]

So:

[tex]x^2 - (2\beta+ \beta)x + \beta*\beta = 0[/tex]

[tex]x^2 - (3\beta)x + \beta^2 = 0[/tex]

So, we have:

[tex]\frac{c}{d} = -3\beta[/tex] -- (1)

and

[tex]\frac{p}{d} = \beta^2[/tex] -- (2)

Make [tex]\beta[/tex] the subject in (1)

[tex]\frac{c}{d} = -3\beta[/tex]

[tex]\beta = -\frac{c}{3d}[/tex]

Substitute [tex]\beta = -\frac{c}{3d}[/tex] in (2)

[tex]\frac{p}{d} = (-\frac{c}{3d})^2[/tex]

[tex]\frac{p}{d} = \frac{c^2}{9d^2}[/tex]

Multiply both sides by d

[tex]d * \frac{p}{d} = \frac{c^2}{9d^2}*d[/tex]

[tex]p = \frac{c^2}{9d}[/tex]

Cross Multiply

[tex]9dp = c^2[/tex]

or

[tex]c^2 = 9dp[/tex]

Hence, the relationship between d, c and p is: [tex]c^2 = 9dp[/tex]

Answer:

-4

Step-by-step explanation:

Here, we want to get the greatest integer less than -3

The integer less than -3 that is the greatest is -4

It is the internet directly after it to the left of the number line

Answer:

3x^2+11x-20

Step-by-step explanation:

step 1 3x(x+5)-4(x+5)

step 2 3x(x+5)-4(x+5)= 3x^2+15-4(x+5)

step 3 3x^2+15x-4x+20

Answer:$5.85

Step-by-step explanation: you divide 52.65 divided by 9 and it will equal $5.85

Answer:

$5.85. Hope this helped! :')

Step-by-step explanation:

1. Use the algorithm method.                              

          5      . 8 5

9 |        5 2 . 6 5

            4 5 .  

                7 . 6

                7 . 2

                      4 5

                      4 5

2. Therefore, 52.62 divided by 9=5.85

5.85

Answer:

the slope is 3/4x

Step-by-step explanation:

if you need it in slope intercept form too its y=3/4x-1

Answer:

x= 58

Step-by-step explanation:

$1500 = $25x + $50

minus 50

1450 = 25x

divide by 25

58 = x

hope this helps!

Answer:

$58

Step-by-step explanation:

1,500-50=1450

1450/25=58

Answer:

x = 3.5

Step-by-step explanation:

3.5 x 3 is 10.5. Triangle two has been expanded each side by 1.5. So multiply 7 (the side with 3x on the other triangle) x 1.5 to get 10.5. To fid x divide 10.5 by 3. This gives you 3.5 as x.

Hope it helps!

Answer:

x = 3.5

Step-by-step explanation:

What we know that the scale factor is 1.5 going from DEF to XYZ (4.5/3 = 1.5; 7.5/5 = 1.5)

So, multiply 7 by 1.5 to get ZX's length. It would be 10.5 units long.

We now know the equation, which is 3x = 10.5

3x = 10.5

Cancel out the multiplication by dividing both sides by 3

x = 10.5/3

Divide 10.5 by 3 to get 3.5

x = 3.5 in this case.

Answer:

150 = 0.50y + 1.00x

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

To rotate a figure 90 degrees clockwise the figure needs to be moved from (x,y) to (y,-x)

The original figure lies at A (5,5) B (5,1) C (2,1) D (1,5)

Rotating the figure 90 degrees clockwise would be A' (5-,5), B' (1,-5), C' (1,-2), D' (5-1)

Answer:

I think False umm...

i'm so so sorry if im rong

Step-by-step explanation:

Answer:

y =  -5/6x - 7

Step-by-step explanation:

Answer

x = 18 cm

Step-by-step explanation:

Here, we want to calculate the value of x

let half of x = b

so b is the base of each right-triangle

As we can see, the triangle is isosceles

we can calculate the length of the base of one of the smaller right angled triangle and multiply by 2 to get the full x length

According to Pythagoras’ , the square of the hypotenuse equals the sum of the squares of the two other sides

15^2 = 12^2 + b^2

225 = 144 + b^2

b^2 = 225-144

b^2 = 81

b = √81

b = 9

but x = 2b

x = 2(9)

x = 18 cm

Answer:

(1 yard) 3 = 1 3 yard*yard*yard = 1 yard*yard*yard = 1 cubic yard. Since 1 yard = 3 feet, we have.

1 cubic yard = (1 yard) 3 = (3 feet) 3 = 33 feet*feet*feet = 27 cubic feet.

Step-by-step explanation:

Answer:

(59°F − 32) × 5/9 = 15°C

Step-by-step explanation:

Simply follow the equation and you will get your answer.

Answer:

B

Step-by-step explanation:

They both are the same equation with the same slope and y intercept which means that they are the same line, thus concluding that they will have infinite points of intersection.

Answer:

2

Step-by-step explanation:

2 is a value of x that would not make the set a function because a function can't have multiple coordinates wit hthe same domain (x-coordinate). 2 is a domain that has already been used in the point (2,7). If this is used in (x,5), the point would become (2,5) and repeat a domain.

Note:

The x-coordinate could also be 1 or 6 because they have been used as domains as well.

Hope it helps!

Answer: 21 Nickels

21 dimes

8 pennies

Step-by-step explanation:

Answer:

Answer is

Step-by-step explanation:

D

Lala!smzl!smzkaka

Answer:

[tex]\frac{1}{18}[/tex]

Step-by-step explanation:

[tex]\frac{1}{2} / \frac{9}{1} = \frac{1}{2} (\frac{1}{9} ) = \frac{1}{18}[/tex]