triangle BCD is similar to triangle EFG. Find the measure of side FG. Round your answer to the nearest tenth if necessary.​

Answer:

mn = 4

Step-by-step explanation:

(m+n)^2 = m^2 + 2mn + n^2

(m-n)^2 = m^2 - 2mn + n^2 multply the second equation by (-1) then subtract it from first equation

m^2 + 2mn + n^2 - m^2 + 2mn - n^2 = 16

4mn = 16 divide both sides by 4

mn = 4

Answer:

should be y=-2/1x+2

Step-by-step explanation:

because the slope is going down 2 over 1 and the y-intercept is at positive 2

Answer:

side AC =[tex]10\sqrt{3}[/tex]  , angle A=30 degree   , angle B=60 degree

Step-by-step explanation:

using pythagors theorem

a^2 + b^2 =c^2

here a and b are the legs of the triangle whereas c is hypotenuse so,

10^2 + AC^2 = 20^2

100 + AC^2 = 400

AC^2 =400-100

AC^2 =300

AC=[tex]\sqrt{300}[/tex]

AC=[tex]10\sqrt{3}[/tex]

For angle A

take angle A as reference angle

using sin rule

sin A =opposite/hypotenuse

sin A=[tex]\frac{10}{20}[/tex]

sin A=[tex]\frac{1}{2}[/tex]

A=[tex]sin^{-1} (\frac{1}{2} )[/tex]

A=30 degree

For angle B

angle A + angle B + angle C =180 degree (sum of interior angles of a triangle)

30 + angle B + 90=180

120 + angle B =180

angle B =180-120

angle B =60 degree

Answer:

D. Four right angles

Step-by-step explanation:

Answer:

Step-by-step explanation:

one of the property of all rectangles is that it has four right angles

:-)

Answer:

B, I don't remember the reasoning but I know that's the answer

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Work Shown:

The order of length, width and height doesn't matter

SA = surface area of rectangular prism

SA = 2*(LW + LH + WH)

SA = 2*(2*6 + 2*9 + 6*9)

SA = 2*(12 + 18 + 54)

SA = 2*(30+54)

SA = 2*(84)

SA = 168 square cm

Answer:

The Coordinates of Point C are C(5,2)

The slope of CD is 3  

The possible coordinates of point D(a,b) are (6, 5) and (4, -1)  

Step-by-step explanation:

According to the Question,

Now, Let The Coordinates of Point C are C( x , y ) .  

The Coordinates of Point C are C( x , y ) ⇒C(5, 2).  

And, The slope of AB = (1 - 3)/(8 - 2) ⇒ -2/6 ⇔ -1/3 .

Let the coordinate of D be (a, b) then

⇒ √{ (b - 2)² +(a - 5)² } = √10

 on squaring both sides we get,

 ⇒ a² - 10a + 25 + b² - 4b + 4 = 10

 ⇒ a² + b² - 10a - 4b = - 19 ⇔⇔ (Equation 1)  

We Know, the slope of CD = 3

⇒Thus,  (b - 2)/(a - 5) = 3

⇒ b - 2 = 3a - 15

⇒ b = 3a - 13 ⇔⇔ (Equation 2)

Putting value of Equation 2 into Equation 1, We get

⇒a² + (3a - 13)² - 10a - 4(3a - 13) = - 19

⇒a² + 9a² - 78a + 169 - 10a - 12a + 52 = - 19

⇒10a² - 100a + 240 = 0

⇒a² - 10a + 24 = 0

⇒(a - 4)(a - 6) = 0

⇒a = 4 or a = 6

Now,  

When a = 4 , b = 3(4) - 13 ⇒ 12 - 13 ⇒ b = -1

When a = 6, b = 3(6) - 13 ⇒ 18 - 13 ⇒ b = 5

Therefore, the possible coordinates of point D(a,b) are (6, 5) and (4, -1).

Answer:

The answer above is 100% correct

Step-by-step explanation:

I got 100 on my quiz.

Given:

The equations are:

[tex]a=b+9[/tex]

[tex]b=c-2[/tex]

To find:

The equation that show the relationship between a and c.

Solution:

We have,

[tex]a=b+9[/tex]               ...(i)

[tex]b=c-2[/tex]               ...(ii)

Equation (i) can be rewritten as:

[tex]a-9=b[/tex]              ...(iii)

From (ii) and (iii), we get

[tex]a-9=c-2[/tex]

[tex]a-c=9-2[/tex]

[tex]a-c=7[/tex]

Therefore, the required equation is [tex]a-c=7[/tex].

Answer:

x = 7

y = 4

Step-by-step explanation:

y + 12 = 3x - 5

5y - 4 = 3x - 5

So y + 12 = 5y - x

To solve the equation above, y =4

Sub y = 4,

x = 7

Answer:

197.92

Step-by-step explanation:

pretty simple not hard bub

Complete question is;

The blueprint of a deck has a scale of 2 centimeters equals 9 feet.

A) What are the actual lengths of the sides of the deck?

B) Decking costs $1.75 per square foot. How much will it cost to build the deck?

Answer:

A) actual lengths are;

27 ft, 36 ft and 45 ft

B) cost of entire deck = $850.5

Step-by-step explanation:

A) From the attached image, we see that the sides of the triangle deck are;

8cm, 10cm and 6 cm

Now, we know that 2cm represents 9 ft.

Thus;

8cm will be; 8 × 9/2 = 36 ft

10 cm will be; 10 × 9/2 = 45 ft

6 cm will be; 6 × 9/2 = 27 ft

Thus, actual lengths are;

27 ft, 36 ft and 45 ft

B) Area of deck is Area of triangle = ½ × base × height.

In this diagram, base = 6 cm = 27ft

Height = 8 cm = 36 ft

Thus;

Area of deck = ½ × 27 × 36

Area of deck = 486 ft²

We are told that the Decking costs $1.75 per ft²

Thus;

Cost of entire deck = 1.75 × 486 = $850.5

Answer:

Step-by-step explanation:

Sum of angles of a triangle = 180

d+ 2d + 60 = 180

3d = 180 - 60

3d = 120

d = 40

The angles are 40, 80, 60

Answer:

A

Step-by-step explanation:

The midsegment is half the sum of the parallel bases, that is

21 - x = [tex]\frac{1}{2}[/tex] (17 + 11)

21 -x = [tex]\frac{1}{2}[/tex] × 28 = 14 ( subtract 21 from both sides )

- x = - 7 ( multiply both sides by - 1 )

x = 7 → A

The value of x is 7

The midpoint theorem states that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of the length of the third side. This theorem is used in various places in real life, for example in the absence of a measuring instrument, we can use the midpoint theorem to cut a stick into half.

In math, we also have a midpoint theorem formula which has its applications in coordinate geometry. It can also be known as the midpoint theorem of a line segment. It states that if we have a line segment whose endpoints coordinates are given as (x1, y1) and (x2, y2), then we can find the coordinates of the midpoint of the line segment by using the formula given below:

Let (xm, ym) be the coordinates of the midpoint of the line segment. Then,

(xm, ym) = ( (x1 + x2)/2 , (y1 + y2)/2 )

This is known as the midpoint theorem formula.

As, midsegment is half the sum of the parallel bases

21 - x = 1/2 (17 + 11)

21 - x= 12* 28

21-x= 14

x= 7

Learn more about mid point theorem here:

https://brainly.com/question/13677972

#SPJ5

Given:

Consider the given equation is:

[tex]y=-\dfrac{7}{2}x+\dfrac{11}{3}[/tex]

To find:

The slope of the line that is represented by the given equation.

Solution:

The slope intercept form of a line is:

[tex]y=mx+b[/tex]                                      ...(i)

Where, m is the slope and b is y-intercept.

We have,

[tex]y=-\dfrac{7}{2}x+\dfrac{11}{3}[/tex]           ...(ii)

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

[tex]m=-\dfrac{7}{2}[/tex]

Therefore, the slope of the given equation is [tex]-\dfrac{7}{2}[/tex].

Answer:

x=9

Step-by-step explanation:

angle A =angle B (because they are corresponding angles)

5x-5=3x+13

5x-3x=13+5

2x=18

x=18/2

x=9

angle A=5x-5

=5*9-5

=45-5

=40

angle B=3x+13

=3*9+13

=27+13

=40

Answer:

A = B

5X-5 = 3X+13

5X-3X. =13+5

2X =18

X = 9

5X-5

(5×9)-5

45-5

=40

ANGLE A=ANGLE B =40

Step-by-step explanation:

any two methods that you can use to graph the equation are

y+4/3=x

y+4=3x

Answer: 0.421, 0.422, 0.423, 0.43, 0.434

Step-by-step explanation:

Answer:

En la clase hay 25 alumnos.

Step-by-step explanation:

La regla de tres es una forma de resolver problemas de proporcionalidad entre tres valores conocidos y una incógnita, estableciendo una relación de proporcionalidad entre todos ellos.

De todos los estudiantes en la clase, 5 quieren una fiesta de helado. Sabiendo que el 20% de los estudiantes de la clase quiere una fiesta de helado, se puede aplicar la regla de tres: si el 20% de los estudiantes de la clase son 5 estudiantes, el 100% (totalidad de los alumnos) cuántos alumnos son?

[tex]totalidad de los alumnos=\frac{100*5}{20}[/tex]

totalidad de los alumnos= 25

En la clase hay 25 alumnos.

Answer:

A) 151 in³ or 151 cubic inches

Step-by-step explanation:

Volume of rocket = Volume of Cylinder + Volume of Cone

Step 1

Find the volume of the cylinder

Volume of a cylinder = πr²h

r = Diameter/2

= 5/2 = 2.5 inches

h = 6 inches

Hence,

π × 2.5² × 6

= 117.81 cubic inches

Step 2

Find the volume of the cone

Volume of a cone =1/3 πr²h

h = 11 inches - 6 inches

= 5 inches

r = 2.5 inches

Hence,

1/3 × π × 2.5² × 5

= 32.72 cubic inches

Therefore:

Volume of rocket = Volume of Cylinder + Volume of Cone

= 117.81 cubic inches + 32.72 cubic inches

= 150.53 cubic inches

Approximately to the nearest inch = 151 in³ or 151 cubic inches

Option A is correct

Answer:

NOPE, the surface area is bigger than the volume, the answer must be C

Step-by-step explanation:

18+18+36+36+72+72 = 252

Answer:

252 cm^2

Step-by-step explanation:

SA = 2 ( lw+wh+hl)

where l is the length , h is the height and w is the width

SA = 2 ( 6*12+ 12*3 + 3*6)

SA = 2 (72+36+18)

SA = 2(126)

SA =252

Answer:

Step-by-step explanation:

(2). 1 yd ≈ 0.9144 m

1 yd³ ≈ 0.76455 m³

2 yd³ ≈ 1.53 m³ ≈ 2 m³

(3). 1 ft ≈ 0.3048 m

1 ft² ≈ 0.0929 m²

162 ft² ≈ 15.1 m²

(4). 1 mi ≈ 1.60934 km

1 mi² ≈ 2.59 km²

503 mi² ≈ 1302.8 km²

Answer:

Step-by-step explanation:

so u gotta do 1=1/9nk

Answer:

True, a translation is a slide of a congruent shapes.

Step-by-step explanation:

If the size and shape of the figure is not changed, then the figures are congruent.

Answer:

x = 110 degree

Step-by-step explanation:

Hope this helps u !!

Answer:B)360

Step-by-step explanation:

Answer:

B 360

Step-by-step explanation:

Step-by-step explanation:

the answer is in the image above

Answer:

6 boxes wide

6 boxes wide

or 2high 2high 2high 2high 2high 2high

Step-by-step explanation:

6 wide and 6 wide to make 12. 6x2=12

2 high ×6 2×6=12