Solve the two-step equation.
21 27
4 4
DC-

Answer:

1. a) The scale factor that transform ΔKLP to ΔK'L'P' is a dilation of 3/2

b) The rule represented is that if the scale factor is larger than 1, the image formed is larger than the preimage

2. a) The scale factor of the dilation is 3/4

b) The rule represented by the dilation is a scale factor of less than 1 produces an image with a distance from a given point which is less than the distance of the preimage from the given point

Step-by-step explanation:

1. The coordinates of the triangle ΔKLP are;

K(-4, 2), L(2, 6), P(4, -6)

The coordinates of the points of triangle ΔK'L'P' are;

K'(-6, 3), L'(3, 9), P'(6, -9)

The length of segment KL = √((2 - (-4))² + (6 - 2)²) = 2·√13

The length of segment LP = √((4 - 2)² + (-6 - 6)²) = 2·√37

The length of segment KP = √((4 - (-4))² + (-6 - 2)²) = 8·√2

The length of segment K'L' = √((3 - (-6))² + (9 - 3)²) = 3·√13

The length of segment L'P' = √((6 - 3)² + (-9 - 9)²) = 3·√37

The length of segment K'P' = √((6 - (-6))² + (-9 - 3)²) = 12·√2

Therefore, K'L'/KL = 3·√13/(2·√13) = L'P'/LP = (3·√37/(2·√37)) = K'P'/KP =(12·√2/(8·√2)) =  3/2

Therefore, the scale factor that transform ΔKLP to ΔK'L'P' is a dilation of 3/2

The rule represented is that if the scale factor is larger than 1, the image formed (here ΔK'L'P') is larger than the preimage (ΔKLP)

2. The location of the preimage, W(-12, -4), the location of the image after the dilation W'(-9, -3)

Taking the origin O(0, 0), as the center of dilation, we have;

The length of the preimage W(-12, -4) from the origin = √((-12 - 0)² + (-4 - 0)²) = 4·√10

The length of the image W'(-9, -3) from the origin = √((-9 - 0)² + (-3 - 0)²) = 3·√10

Therefore, the scale factor of the dilation = W'O/WO = 3·√10/(4·√10) = 3/4

The scale factor of the dilation = 3/4

The rule represented by the dilation is that for a scale factor less than 1, the distance between the point of the image from a given point is less than the distance of the point of the preimage from the same point

Since Joe has read 30% of the book, that means that 14 pages is 70% of the book. That means that two pages equals 10%. Therefore, the book has 20 pages.

70% = 14

so 30% = 6

total pages = 14+6=20

Answer:

Commutative property of addition: Changing the order of addends does not change the sum.

Step-by-step explanation:

For example, 4 + 2 = 2 + 4 4 + 2 = 2 + 4 4+2=2+44, plus, 2, equals, 2, plus, 4.

Answer:

C

Step-by-step explanation:

The line passes through the point (2, -1/2) and has a slope of 3.

We can use the point-slope form, given by:

[tex]y-y_1=m(x-x_1)[/tex]

Where (x₁, y₁) is a point, and m is the slope.

Let (2, -1/2) be (x₁, y₁). We will substitute 3 for m. Therefore:

[tex]\displaystyle y-\Big(-\frac{1}{2}\Big)=3(x-(2))[/tex]

Simplify:

[tex]\displaystyle y+\frac{1}{2}=3(x-2)[/tex]

Therefore, our answer is C.

Answer:

65%

Step-by-step explanation:

so there were 20 total voters. 20-7 = 13 that did not vote for the tax

13/20= . 65 = 65%

Answer:

आपको अपने पापों के लिए पश्चाताप करना चाहिए । वे तुम्हें नष्ट कर देंगे । आप कोई मौका नहीं खड़े हैं । तुम उसके हाथ पर मर जाओगे । पछताना

Step-by-step explanation:

its just so simple! :D

Answer:

answer is rounded to the nearest tenth D, 6.3

Step-by-step explanation:

just plug those numbers into the distance formula

Answer

43

Step-by-step explanation:

Answer:

about 31 percent

Step-by-step explanation:

Answer:

73:42

Step-by-step explanation:

1115-73=42

G : B

73 : 42

Answer: I believe the answer is 60

Step-by-step explanation:

9/12 = 3/4

If we do cross multiplying x over 80 times 3/4 it equals 60.

I am sorry if it is not correct I'm not fully sure but I hope this helped!!

Step-by-step explanation:

1)

a-13b

2) b

3) -3d+14e

4)12x-11y

5)-3rs

6)8xy-10cs

7)

[tex] - 2 {x}^{2} - 4x + 7[/tex]

8)

[tex]8 {y}^{2} - 7[/tex]

Answer:

1. 6a - 3b

2. b + 6c

3.- 3d - 2e

4. 12x + 5y

5. -3rs - 14bc

6. 8xy - 8cs

7. -2x^2 - 8x + 3

Step-by-step explanation:

Subtract polynomials

Answer:

The answer is in Picture.

Step-by-step explanation:

Hope it is helpful....

Answer:

Answer:

Hey!

0.309<0.32<0.35<0.4

hope this helps you

The numbers in order of size start with the smallest can be done as 0.309 < 0.32 < 0.35 < 0.40.

The decimal numeral system is the most widely used system for representing both integer and non-integer values. It is the Hindu-Arabic numeral system's expansion to non-integer numbers. Decimal notation is the method of representing numbers in the decimal system.

The given number can be arranged from smallest to largest can be arranged as shown below. Therefore, we can write,

0.309 < 0.32 < 0.35 < 0.40

Hence, the numbers in order of size start with the smallest can be done as 0.309 < 0.32 < 0.35 < 0.40.

Learn more about Decimal Numbers here:

https://brainly.com/question/4708407

#SPJ2

Answer:

The answer is 60 degrees

Step-by-step explanation:

Answer:

Constants: 8 and 10

Step-by-step explanation:

Answer:

Step-by-step explanation:

negative b plus or minus the square root of b squared minus four times a times c all over 2a

Answer:

169.70

Step-by-step explanation:

Answer:

120[tex]\sqrt{2}[/tex]

Step-by-step explanation:

3[tex]\sqrt{40}[/tex] · 4[tex]\sqrt{5}[/tex] = (3[tex]\sqrt{5}[/tex]·[tex]\sqrt{4}[/tex]·[tex]\sqrt{2}[/tex]) x 4[tex]\sqrt{5}[/tex]

= 3 · 2 · 5 · 4 [tex]\sqrt{2}[/tex]

= 120[tex]\sqrt{2}[/tex]

Answer:

Step-by-step explanation:

50% of 70=35

92% of 19= 17.48

Answer:

As you can see, the -4 and -1/4 coefficient values are automatically different, and will resultantly produce different answers in the solutions.

The solutions are related, as the two numbers are reciprocals, as well as both being negative values.

Hope this helped !

Answer:

That means the missing side length is 15

Step-by-step explanation:

We use the Pythagorean theorem to find the hypotenuse. The hypotenuse for this triangle is 17. The equation for the Pythagorean theorem is a^2 + b^2 = c^2. Our equation is x^2+64 = 289. We can now subtract 64 from both sides and get 225. The square root of 225 will be 15.

Answer:

hi

Step-by-step explanation:

[tex] {c}^{2} = {a}^{2} + {b}^{2} \\ {8}^{2} + {b}^{2} = {17}^{2} \\ {b}^{2} = {17}^{2} - {8}^{2} \\ {b}^{2} = 289 - 64 \\ {b}^{2} = 225 \\ b = \sqrt{225} \\ b = 15[/tex]

hope it helps

Have a nice day

byee

Answer: midpoint is ( 1.5 , 0 )

Step-by-step explanation:

Answer:

-4(x+9)

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

Answer in your own words:

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape. Which can also be used to calculate the dimensions of the new figure or the original figure by simply substituting the values in the same formula.  

• The scale factor of a dilated figure is denoted by 'r' or 'k'.

• If the scale factor is more than 1 (k > 1), the image is enlarged.

• If the scale factor is less than 1 (0< k <1), the image is contracted.

• If the scale factor is 1 (k = 1), the image remains the same.

• The scale factor cannot be zero.

Scale factor = k

Pre-image lengths: a, b  

(perimeter = 2a + 2b)

Image lengths: ka, kb

(perimeter = 2ka + 2 kb or k (2a + 2b))

Marissa needs to say that the perimeter of the image is the perimeter of the pre-image times the same scale factor.

area of the pre-image = ab

area of the image = (ka)(kb) or k^2 (ab) (The area of the image is the area of the preimage times the square of the scale factor)

Scale factor 5 (then repeat it with scale factor 6)

length of the pre-image = 3 x 4  

(perimeter = 2 (3 + 4) = 2(7) = 14)

length of the image = (3x5) x (4x5) = 15 x 20= 300

(perimeter = 2 (15 + 20) = 2 (35) = 70 or 14 x 5 = 70  

area of the pre-image = 3 x 4 = 12

area of the image = 15 x 20 = 300

12 x (5^2) = 12 x 25 = 300  

Answer:

I really dont know

Step-by-stwp explanation:

98

Answer:

14x² + 41x + 15

Step-by-step explanation:

............

Answer:

it is kind of sequence that recursive sequence because that is a ex. of recursive sequence

Answer: Choice A.  (8, 4)

==========================================================

Explanation:

Because x = 2y, we can replace every copy of x with 2y

Let's do so in the second equation

3x - 4y = 8

3(x) - 4y = 8

3(2y) - 4y = 8 .... x replaced with 2y; now let's isolate y

6y - 4y = 8

2y = 8

y = 8/2 ..... divide both sides by 2

y = 4

Use this y value to find x

x = 2y

x = 2*4

x = 8

So we have x = 8 and y = 4 pair together to get the answer (x,y) = (8, 4) which is choice A.