The blueprint of a deck has a scale of 2 centimeters equals 9 feet. The scale drawing is shown below.
8 cm
10 cm
6 cm
Part A
What are the actual lengths of the sides of the deck?
6 cm
8 cm =
10 cm =
Part B
Decking costs $1.75 per square foot. How much will it cost to build the deck?

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Answers:

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Explanation:

The tickmarks show that WZ and XY are the same length. The arrows show that WX is parallel to ZY. This is an isosceles trapezoid.

For any isosceles trapezoid like this, the diagonals are the same length. We can prove it using the SAS congruence theorem.

So,

WY = XZ

15x-2 = 9x+10

15x-9x = 10+2

6x = 12

x = 12/6

x = 2 .... first answer

Use that value of x to find the length of each diagonal.

Both diagonals are 28 units long, which helps confirm we have the right x value.

Given:

The volume of a cube = [tex](2+3p)^3\ \text{cm}^3[/tex]

To find:

The total surface area of the cube in terms of p.

Solution:

Volume of a cube is:

[tex]V=a^3[/tex]            ...(i)

Where, a is the side length.

It is given that,

[tex]V=(2+3p)^3\ \text{cm}^3[/tex]         ...(ii)

On comparing (i) and (ii), we get

[tex]a=2+3p\text{ cm}[/tex]

Now, the total surface area of a cube is:

[tex]A=6a^2[/tex]

Where, a is the side length.

Putting [tex]a=2+3p[/tex], we get

[tex]A=6(2+3p)^2[/tex]

Therefore, the total surface area of the cube in terms of p is [tex]6(2+3p)^2\ \text{cm}^2[/tex].

Answer:

5$

Step-by-step explanation:

Answer:

a)  67.4°

Step-by-step explanation:

since this is a right triangle you can use the sine trigonometric ratio of opposite/hypotenuse

sin⁻¹(Ф) = 12/13 which equals 67.4°

Answer:

No

Step-by-step explanation:

We can use the Pytaghorean theorem to verify it

4.4^2 + 5.5^2 = 6.6^2

19.36 + 30.25 = 43.56

49.61 = 43.56 (false)

Answer:

x = 33

Step-by-step explanation:

(x + 13) + (4x + 2) = 180

x + 13 + 4x + 2 = 180

5x + 15 = 180

5x = 180 - 15

5x = 165

x = 165/5

x = 33

Check:

(x + 13) + (4x + 2) = 180

(33 + 13) + 4(33) + 2 = 180

46 + 132 + 2 = 180

46 + 134 = 180

Answer:

Refer to the attached file

Hope it helps..

Answer:

y=5x-9

Step-by-step explanation:

-5(-3)+b=6

15+b=6

B=-9

Answer:

51

Step-by-step explanation:

51 is elaginlent to 44 and 33 12 garde things

Answer:

y = 2/3x - 5

Step-by-step explanation:

If two lines are parallel, they have the same slope. This means the line we are looking for has a slope of 2/3. Since we are also given a point, we can start by writing the equation in point-slope form which is represented by

[tex]y-y_{1} =m(x-x_{1} )[/tex]

Where m is the slope and (x1, y1) is a point. We have both, so we can substitute the values and simplify:

y + 1 = 2/3 (x - 6)

y + 1 = 2/3x - 4

y = 2/3x - 5

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

Explanation:

We can apply the remote interior angle theorem. Some math books or teachers may refer to this as the "exterior angle theorem". They're the same idea just with different names.

According to that theorem, the interior angles x and 53 add up to the exterior angle 158

x+53 = 158

x = 158-53

x = 105

This theorem only works if neither interior angle is adjacent to the exterior angle. Hence the "remote" part.

----------

If you wanted a slightly longer approach, then let y be the missing angle that isn't marked in the diagram. Angle y is adjacent to the 158 degree angle.

We can find y by noting how 158 and y are supplementary

158+y = 180

y = 180-158

y = 22

Then we use the fact that adding three angles of any triangle always gets us 180 degrees

x+y+53 = 180

x+22+53 = 180

x+75 = 180

x = 180-75

x = 105

Effectively, this example helps reinforce why the remote interior angle theorem is true.

Answer:

4,8,12 hope that helps heeeeheheʘ‿ʘ

Answer:

4) 2x3 + 10x2−x−18

5) 2x3+5x2−7x−1

6) 2x2+5x−3

7) −3x2−6x+1

Step-by-step explanation:

4) (4x2 - x - 7) + (2x3+ 6x2– 11)

Combine Like Terms:

=4x2+−x+−7+2x3+6x2+−11

=(2x3)+(4x2+6x2)+(−x)+(−7+−11)

=2x3+10x2+−x+−18

5) (2x3– x + 4) + (5x2– 6x – 5)

Combine Like Terms:

=2x3+−x+4+5x2+−6x+−5

=(2x3)+(5x2)+(−x+−6x)+(4+−5)

=2x3+5x2+−7x+−1

6) (3x2+ 2x + 1) – (x2– 3x + 4)

Distribute the Negative Sign:

=3x2+2x+1+−1(x2−3x+4)

=3x2+2x+1+−1x2+−1(−3x)+(−1)(4)

=3x2+2x+1+−x2+3x+−4

Combine Like Terms:

=3x2+2x+1+−x2+3x+−4

=(3x2+−x2)+(2x+3x)+(1+−4)

=2x2+5x+−3

7)(2x2– 3x + 7) – (5x2+ 3x + 6)

Combine Like Terms:

= (2x2 −5x2 )+(−3x−3x)+(7−6)

straight angle because the supplementary angle and straight angle is same.

Answer:

7th graders in the school

Step-by-step explanation:

if she wants to know what 7th graders like, ask 7th graders since no one els would know as good as 7th graders themselves

Answer:

A.7th graders in the school

Step-by-step explanation:

Because she specifically wants to find the favorite activity of 7th grade students she should sample only 7th grade students to get the best and most accurate results.

Answer:

why was it ‍♂️

All of his grades were down below c level

hehe

=)

Answer:

14

Step-by-step explanation:

x * 2 = 8

y * 3 = 6

6 + 8 = 14

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

Explanation:

Consider a square on paper that is 3 inches by 3 inches. It's area would be 3*3 = 9 square inches.

The ratio 1 to 38 means that 1 inch on paper corresponds to 38 inches in real life (assuming the "1 to 38" doesn't have any verbal units attached to it; if so, then refer to the note below). So a 3 by 3 square corresponds to a 114 by 114 square because 3*38 = 114.

The area of the second larger square is 114*114 = 12,996 square inches.

Now divide the two areas: (12,996)/(9) = 1444

It's probably not entirely obvious, but through a bit of playing around with various numbers, you should find that 38^2 = 1444. It's not a coincidence that this happens. The linear scale factor is 38 which means the area scale factor is 38^2 = 1444.

In short, the larger square in real life has area that is 1444 times that of its scaled down counterpart.

Or put another way:

large area = 1444*(small area)

------------------

Side note: This all assumes that the numbers in "1 to 38" are both the same unit. If we had a mixed ratio of units like "1 inch to 38 feet", then the answer would be different. You would need to convert from feet to inches, and then follow the steps above to get a different answer.

Answer:

2,197.8

Step-by-step explanation:

Answer:

The value of x is 15 inch.

Step-by-step explanation:

Area, A = 81 square inch

Perimeter, P = 48 inch

let the side is y.

[tex]y^2 = 81\\\\y = 9 inch[/tex]

Let the other side is d.

P = 4 d = 48

d = 12 inch

the length x is given by

[tex]x^2 = 9^2 + 12^2\\\\x^2 =81 + 144 = 225\\\\x = 15 inch[/tex]

So, x = 15 inch.

Answer: 0.4%

Step-by-step explanation:

First, a porportion needs to be set up.

part/whole = percent/100

28/7,000 = x/100

Second, cross multiply.

2800=7,000x

x=0.4

Answer:

C, y=2x(x-4)

Step-by-step explanation:

All the other equations can be graphed as lines, but C is the only one that is a parabola (a curve).

Answer:

21cm^2

Step-by-step explanation:

Area of Square-Area of semi circles (makes one full circle)

Squares Area = 100

LxW or (10x10)=100

Circle Area = 25/pi

/pi (radius)^2 or /pi(5)^2 = 25/pi

100cm^2-25cm^2 = 21.4601…cm^2 rounded to 21.5 cm^2

The area of the shaded region is 21.5 cm²

'In geometry, a semicircle is a plane figure that is formed by dividing a circle into exactly two parts.'

According to the given problem,

Side length of the square = 10

Area of the square = ( 10 × 10 )

                               = 100 cm²

Now, for the semi-circle,

Diameter = 10 cm

Radius = [tex](\frac{10}{2}[/tex][tex])[/tex] cm

            = 5 cm

Area of the semicircle =  [tex]\frac{\pi r^{2} }{2}[/tex]

                                     = [tex]\frac{\pi * 5^{2} }{2}[/tex]

Since, there are two semicircles in the square, we multiply the area with 2,

⇒ [tex]\frac{\pi *5^{2} }{2}*2[/tex]

= 25[tex]\pi[/tex]

Area of the shaded region = ( 100 - 25π )

                                            = ( 100 - 78.53 )

                                            = 21.46

                                            ≈ 21.5 cm²

Hence, we can conclude, the area of the shaded region is 21.5 cm².

Learn more about semi-circles here: https://brainly.com/question/14429410

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Answer:

Hello! answer: 268 square meters

Step-by-step explanation:

To find the total surface area you find the area of each face then add them up so...

10 × 3 = 30

10 × 3 = 30

8 × 3 = 24

8 × 3 = 24

10 × 8 = 80

10 × 8 = 80

Now that I found the area for each face I will just add them up so...

30 + 30 + 24 + 24 + 80 + 80 = 268 therefore the area is 268 square meters Hope that helps!

[tex] \large\mathrm {\boxed{ \boxed{268 \: \: m {}^{2} }}}[/tex]

The above pieces will form a cuboid, having dimensions :

[tex] \mathrm{\longrightarrow length = 10 \: m}[/tex]

[tex] \mathrm{\longrightarrow width = 8 \: m}[/tex]

[tex] \mathrm{\longrightarrow height = 3 \: m}[/tex]

We know that Surface area of Cuboid is :

[tex] \large \longmapsto \mathrm{{2(lw + wh + lh)}}[/tex]

Let's solve,

[tex]\longrightarrow2[(10 \times 8) + (8 \times 3) + (10 \times 3)][/tex]

[tex]\longrightarrow2[80 + 24 + 30][/tex]

[tex]\longrightarrow2 \times 134[/tex]

[tex]\longrightarrow268 \: m {}^{2} [/tex]

[tex] \circ { \underline{ \boxed{ \sf{ \color{green}{ \mathfrak{hope \: \: it \: \: helps \: \: you.....}}}}}}∘[/tex]

Answer:

18X-2+12X+2=360-180

30X=180

X=6

The value of the variable x is 6, in the given rhombus.

A quadrilateral having the following characteristics is called a rhombus:

From the properties of a rhombus,

The sum of all angles is 360°.

Thus, in the given case,

18x-2+12x+2+ 90° +90° = 360°

18x- 2 + 12x +2 = 180°

30x = 180

x = 6

Therefore, the value of the x is 6.

Learn more about Rhombus here:

https://brainly.com/question/27870968

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Answer:

3,16,729

Step-by-step explanation:

Answer:

she would be able to buy 40 lunches

Step-by-step explanation:

Subtract  100  from both sides of the inequality

Divide each term by   −2  and simplify.

The solution to the inequality 100 – 2x < 20 is x > 40

How to find solution to an inequality?

She set aside $100 to buy school lunches for the year. Each school lunch cost $2.

Therefore, the inequality can be used to find the number of school lunches Gloria can buy before she has less than $20 left.

100 – 2x < 20

The solution of the inequality is as follows;

100 – 2x < 20

subtract 100 from both sides

100 - 100 - 2x < 20 - 100

-2x < - 80

divide both sides by -2

x > 40

learn more on inequality here: https://brainly.com/question/11872626

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Answer:

O perímetro do outro triângulo deve ser ou de 30 unidades de comprimento, ou de 3.33 unidades de comprimento.

Step-by-step explanation:

Dois triângulos semelhantes possuem razão entre suas áreas igual a 9.

O perímetro tem grau um, enquanto a área tem grau 2. Isto implica que a razão entre os perímetros é a raiz quadrada da razão entre as áreas, então a razão entre os perímetros é de 3.

Se o perímetro de um deles é 10, o perímetro do outro deve ser:

Ou 10*3 = 30, ou [tex]\frac{10}{3} = 3.33[/tex]

O perímetro do outro triângulo deve ser ou de 30 unidades de comprimento, ou de 3.33 unidades de comprimento.