Activity
Valerie is remodeling her home. She decides to replace the old carpet in the living room and wants to know how much carpet she needs. You can see from the diagram of the living room that this is not a simple shape. Complete the steps below to find the area of the room, which is the amount of carpet Valerie needs for her project.


Part A
Help Valerie decompose the shape into the fewest simple shapes. Which shapes can you divide the figure into? How many of each shape do you get?
Part B
In how many different ways can you divide the shape to get the same number and type of shapes you obtained in part A?
Part C
On a separate piece of paper, draw the different ways you can divide the given shape into simpler shapes. Describe each result.
Part D
What are the dimensions of the simple shapes you obtained in part C? List dimensions for all your decompositions (sets of shapes).
Part E
Using the dimensions from part D, find the area of each simple shape. Do this for all your decompositions (sets of shapes).
Part F
Add the areas of the simple shapes you found in part E to find the area of the composite shape. Do this separately for both decompositions. What do you notice about the two answers?
Part G
What is the amount of carpet Valerie needs for her living room?

(a) List all the possible outcomes

A dice has 6 sides, ranging from numbers 1 to 6.

As such, the possible outcome for 1 dice is 1, 2, 3, 4, 5 and 6.

Since 2 dice are used, the possible outcome increases, ranging from 2 to 12.

Working:

1 + 1 = 2 (MIN)

6 + 6 = 12 (MAX)

Therefore, the possible outcomes is from 2 to 12.

(b) Find the probability of getting an even number as a score

Total number of score = 11

Total number of even score = 6

P (even number) = 6 / 11

I believe this should be the correct answer... seems logical to me. HAHA. Anyway, do let me know if I am correct or have any queries :)

Answer:

c, and b.

Step-by-step explanation:

because it's the same as the ordered pair.

Answer:

40%

Step-by-step explanation:

Discount price = 22 - 13.20 = $8.80

Discount percentage = [tex]\frac{8.80}{22}*100\\[/tex]

                                   = 40%

Answer:

B

Step-by-step explanation:

(2.5,0)

Answer:

They had 20 of them

Step-by-step explanation:

sorry if its wrong

Answer:

159.82

Step-by-step explanation:

262          100              let unknown be "x"

x                61

262 x 61 = 100x

15982= 100x

15982/100 = x

x= 159.82

Answer:

(3,-4)

Step-by-step explanation:

Yaaaaaaaaaaa a a a

Answer:

(3,-4)

Step-by-step explanation:

x axis goes first y axis second

Answer:

16 boxes will be needed for 122 books.

Step-by-step explanation:

Given that,

Each box can hold 8 books.

We need to find the number of boxes needed for 122 books. It can be calculated as follows :

[tex]\dfrac{122}{8}[/tex] = 15.25

It means 15 boxes can be filled and 16 boxes will be needed for 122 books.

Answer:

Please refer to the above attachment...

(sorry for bad handwriting:P)...

Step-by-step explanation:

I hope it helps...:)

Answer:

[tex]Solution,\\PQ = \sqrt{(1-3)^2+(3-1)^2} = \sqrt{2^2+2^2} = \sqrt{8} = 2\sqrt{2} \\P'Q' = \sqrt{(3-9)^2+(9-3)^2} = \sqrt{6^2+6^2} = \sqrt{72} = 6\sqrt{2}\\Also,\\RQ = \sqrt{(1-3)^2+(1-1)^2} = \sqrt{2^2} = 2\\R'Q' = \sqrt{(3-9)^2+(3-3)^2} = \sqrt{6^2} =6\\Again,\\PR = \sqrt{(1-1)^2+(3-1)^2} = \sqrt{2^2}=2\\P'R' = \sqrt{(3-3)^2+(9-3)^2} = \sqrt{6^2} = 6\\Here, P'R' = 3PR, P'Q'=3PQ ~and~ Q'R'=3RQ~\\In~other~words~each~side~of~triangle~P'Q'R' ~is~three~times~the~length~of~triangle~PQR.\\[/tex][tex]So,~the~algebraic~rule~of~diliation(enlargement)~is~(x,y)----(3x,3y)[/tex]

If my answer did not help you, comment below but please don't delete it.

Responder:

x = 4.48

y = 4.86

z = -1.04

Explicación paso a paso:

Dadas las ecuaciones simultáneas;

6X + 8Y - 4Z = 5 .... 1

1X + 2Y + 5Z = 9 ... 2

9X - 3Y + 3Z = 6 .... 3

Primero necesitamos reducir el sistema de ecuaciones

Ecuación 1 * 1

Ecuación 2 * 4

__________

6X + 8Y - 4Z = 5

4X + 8Y + 20Z = 36

Restar

6x-4x - 4z-20z = 5-36

2x-24z = 31 ... 4

también

ecuación 2 * 3

ecuación 3 * 2

_______________

1X + 2Y + 5Z = 9 * 3

9X - 3Y + 3Z = 6 * 2

_______________

3x + 6y + 15z = 27

18x - 6 años + 6z = 12

Agregar

3x + 18x + 15z + 6z = 27 + 12

21x + 21z = 39 ...... 5

Resolviendo 4 y 5

2x-24z = 31 ... 4 * 21

21x + 21z = 39 ...... 5 * 2

____________

42x - 504z = 651

42x + 42z = 78

Sustraer

-504x - 42z = 651-78

-546z = 573

z = -573/546

z = -1.05

Sustituye z = -1.05 en 4

De 4;

2x-21z = 31

2x - 21 (-1,05) = 31

2x + 22,04 = 31

2x = 31-22.04

2x = 8,96

x = 8,96 / 2

x = 4,48

Obtener y

De 2:

X + 2Y + 5Z = 9

4.48 + 2y + 5 (-1.04) = 9

2 años + 4,48-5,2 = 9

2y = 9 + 0,72

2 años = 9,72

y = 9,72 / 2

y = 4,86

Por tanto, la solución (x, y, z) es (4.48, 4.86, -1.04)

Answer:

This would be a, b, and d.

Step-by-step explanation:

When graphed, the slope line of each of these would look like a straight vertical line, meaning their slope would be undefined. There has to be a change in x to create a defined slope.

Answer:

its 1,645.32

Step-by-step explanation:

search one twelfth of 3,478.50, then one twelfth of 1,186 and add those answers with 1,645.32

Answer:

$1094.40

Step-by-step explanation:

684 increase 60% =

684 × (1 + 60%) = 684 × (1 + 0.6) = 1094.4

Answer:

h=8

Step-by-step explanation:

h = -16t^2 + 20t + 32

h = -16(2)^2 + 20(2) + 32

h = -16(4) + 40 + 32

h = -64 + 72

h = 8

Answer:

2 seconds

Step-by-step explanation:

i got it right, no explanation <3

Answer:

the probability of a rating that is between 200 and 275 is 0.4332

Step-by-step explanation:

Given the data in the question;

if an applicant is randomly selected, the probability of a rating that is between 200 and 275

mean μ = 200

standard deviation σ = 50

P( 200 < X < 275 ) = P( X-μ / σ  < x-μ / σ <  X-μ / σ )

P( 200 < X < 275 ) = P( 200-200 / 50  < x-μ / σ <  275-200 / 50 )

= P( 0/50 < Z <  75/50 )

= P( 0.00 < Z < 1.50 )

P(Z < 1.50) - P(Z < 0.0)

from the standard normal table

P(Z < 1.50) = 0.9332

P(Z < 0.0) = 0.5000

so

P( 200 < X < 275 ) = 0.9332 - 0.5000

P( 200 < X < 275 ) = 0.4332

Therefore, the probability of a rating that is between 200 and 275 is 0.4332

Answer:

706.5 cm²

Step-by-step explanation:

Surface area of the open cylinder with only one base = surface area of cylinder - area of one of the base

= 2πr(h + r) - πr²

Where,

r = 9 cm

h = 8 cm

π = 3.14

Plug in the values into the equation

Area of the open cylinder with one base = 2*3.14*9(8 + 9) - 3.14*9²

= 56.52(17) - 254.34

= 960.84 - 254.34

= 706.5 cm²

Answer:

one inch on the plan represents 2.3 feet in real life

Step-by-step explanation:

Set up a proportion

[tex]\frac{4}{9.2} \\[/tex]=[tex]\frac{1}{x}[/tex]

[tex]4x=9.2[/tex]

[tex]x=2.3[/tex]

Answer:

67°

Step-by-step explanation:

Corresponding angles are equal in parallel lines.

Here, ∠acb and ∠aed are corresponding angles for lines bc and de

hence ∠aed = ∠acb = 39

in triangle ade,

x + 74 + 39 = 180 (angle sum property of a triangle)

x = 67°

Answer:

It is between B and C but what I would choose is C.

The radius, area and circumference of the circle is invariant properties of the circle. Option a, c and d to be chosen.

Properties to be determine that would not change after the rotation of circle.

Circle is locus of the point whose distance from the fixed points i.e. center is fixed.

Here, circle has unit radius and center at origin. If the circle is rotated along the point any where in the space the propertied that would be fixed is its radius, area  and circumference.

Thus, the radius, area and circumference of the circle is invariant properties of the circle.

Learn more about circle here:
https://brainly.com/question/11833983

#SPJ2

Answer: 897

Step-by-step explanation: \frac{a}{\sin A}=\frac{b}{\sin B}

sinA

a

​

=

sinB

b

​

From reference sheet.

\text{Find other angle:}

Find other angle:

\angle X=180-139-20=21^{\circ}

∠X=180−139−20=21

∘

X

Y

Z

x = 940

z = ?

139°

20°

21°

\frac{z}{\sin 20}=\frac{940}{\sin 21}

sin20

z

​

=

sin21

940

​

Plug in. Opposite sides go together.

z=\frac{940\sin 20}{\sin 21} \approx 897.12 \approx 897

z=

sin21

940sin20

​

≈897.12≈897

Answer:

yes

Step-by-step explanation:

2+3 is equal to 5 so he will make less that 6 cups

Answer:

correct

Step-by-step explanation:

it should be correct

Answer: great adventure theme park is more expensive

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:afvStep-by-step explanation:

Answer:

Question 3

C. [tex] y-9 =1/2(x-1)[/tex]

Question 4

D. [tex] y+5 =3(x+2)[/tex]

Step-by-step explanation:

Question 3:

Equation of line in point slope form is given as:

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

Plug m = 1/2, [tex] x_1 = 1, \:y_1 = 9 [/tex] in the above equation, we find:

[tex] y-9 =1/2(x-1)[/tex]

This is the required equation of the line.

Question 4:

Equation of line in point slope form is given as:

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

Plug m = 3, [tex] x_1 = - 2, \:y_1 = - 5[/tex] in the above equation, we find:

[tex] y-(-5) =3[x-(-2)][/tex]

[tex] y+5 =3(x+2)[/tex]

This is the required equation of the line.