A train travelling at 30km/hour reaches a tunnel which is 9 times as long as the train. If the train takes 2 minutes to completely clear the tunnel, how long is the train?​

Answer:

113.1 cm²

Step-by-step explanation:

V = [tex]\frac{1}{3}[/tex] [tex]\pi[/tex] r² h

h = 12 cm , r = 3 cm , [tex]\pi[/tex] = [tex]\frac{22}{7}[/tex]

V ≈ 113.1 cm²

Answer:

a.

[tex]{ \tt{3x - 6y + 8 = 0}} \\ { \tt{ 6y = 3x - 8}} \\ { \boxed{ \bf{y = \frac{1}{2} x - \frac{4}{3} }}}[/tex]

b.

[tex]{ \tt{ - 2x - 5y - 2 = 0}} \\ { \tt{5y = - 2x + 2}} \\ { \boxed{ \bf{y = - \frac{ 2}{5} x + \frac{2}{5} }}}[/tex]

Answer:

Step-by-step explanation:

The missing length is 13 because,

Lets say the top triangle is A and the bottom triangle is B.

Triangle A gives us the side GF, and Triangle B gives us the sides TU and ST. Since the triangles are similar(as stated in the problem), we can pair 2 sides GF(A) and TU(B) which is 11:22.(one way I usually figure which sides are similar is by first- matching the hypotenuse, then checking which of the remaining two is longer.. if that made any sense). You can see that their relationship is x2 or /2 (In another word, from A to B is multiplication- ex: 11 * 2 is 22, and from B to A is division- ex 22/2 is 11.) Since the missing number is the hypotenuse of triangle A and you know the Hypotenuse of triangle B all you have to do is divide side TS by 2 to get side SF. So the missing side is 13.

Answer: 13

Answer:

→ m∠ABE + m∠EBC =180°

→ m∠ABF + m∠FED + ∠DBC =180°

→ ∠ABF ≅ ∠EBC

→ ∠ABE ≅ FBC

~OAmalOHopeO

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Given a quadratic equation in standard form

ax² + bx + c = 0 , then the sum of the roots is

α + β = - [tex]\frac{b}{a}[/tex]

Here 2x² - x - 3 = 0 is in standard form

with a = 2 and b = - 1 , then

sum of roots = - [tex]\frac{-1}{2}[/tex] = [tex]\frac{1}{2}[/tex]

Answer: (b)

Step-by-step explanation:

Given

There are five consecutive integers and the least minus twice the greatest equals to -3

Suppose [tex]x,x+1,x+2,x+3,x+4[/tex] are the five consecutive integers

According to the question

[tex]\Rightarrow x-2(x+4)=-3\\\Rightarrow x-2x-8=-3\\\Rightarrow -x=8-3\\\Rightarrow x=-5[/tex]

option (b) is correct.

Answer:

x=2, x=-2, x=-3

Step-by-step explanation:

-check if anything simplifies

(x-1)(x-3)²(x+1)² / (x-2)(x+2)(x-1)(x+3), simplify (x-1)

(x-3)²(x+1)² / (x-2)(x+2)(x+3)

-make the denominator 0 to find the asymptotes

(x-2)(x+2)(x+3) = 0

(x-2) =0 gives x = 2 asymptote

(x+2) =0 gives x= -2 asymptote

(x+3) = 0 gives x=- 3 asymptote

Answer:

1 hour

Step-by-step explanation:

2 ÷2=1 speed divide by distance

Answer:

20,160 pounds

Step-by-step explanation:

bricks in each row * number of rows * pound of each brick

Answer:

20160 lbs

Step-by-step explanation:

To find the amount of bricks, multiply 36 by 140 which equals 5040. Then, multiply 5040 by the weight: 4. 5040×4=20160

Answer:

the Mode Is 3

Step-by-step explanation:

You Have To Put the numbers from ascending order to descending order..The Numbers that appears the most is the mode

Answer:

A=2

B=4

C=6

D=5

E=7

F=8

G=3

H=1

Step-by-step explanation:

explanation is in the picture!

Step-by-step explanation:

we see, for x=-1 we get 3³

x=0 we get 3²

x=1 we get 3¹

so the function is definitely a 3 to the power of x version.

but we need to adapt the exponent a bit and correct x, so that at least for these 3 values of x the result is "running backwards".

the easiest way : 2-x as exponent.

it fits.

for x=-1 we get 2 - -1 = 3 as exponent.

for x=0 we get 2-0 = 2 as exponent.

for x=1 we get 2-1 = 1 as exponent.

so, the exponential function passing through these 3 points is

[tex]f(x) = {3}^{2 - x} [/tex]

The square root of 100 is 10.

To check, solve 10 x 10.

Hope this helps! Please mark me as brainliest!

Have a great day!

1. 2

2. The X axis

3. 3 right and 1 up (3, 1)

Answer:

2 or A

x-axis or y = 0

I'm not sure the answer choices for the third one so I'm heading out.

Step-by-step explanation:

If your device is capable of taking screenshots from your laptop/desktop, then take a screenshot, like on Windows OS, it's Windows Key + Shift + S, and on Mac OS, it's Command + Control + Shift + 4, I think.

Taking a picture from a phone takes longer to upload and has bad quality since it's from a further distance and the individual pixels are more spread out.

Welp....there's your answer

Answer:

y=(3/4)x+2

Step-by-step explanation:

write the equation in slope-intercept form: y=(3/4)x - 3

since it is parallel the slope is the same so we have y=(3/4)x + b

then plug in the point (-1) = (3/4)(-4) + b

-1 = -3 +b, b=2

y= (3/4)x + 2

Answer:

27 litros de leche de búfalo equivalen a 45.9 litros de leche de vaca.

Step-by-step explanation:

Sabiendo que un litro de leche de búfala equivale a 1.7 litros de leche de vaca, podemos calcular el equivalente de capacidad de la vaca para 27 litros de leche de búfala mediante Regla de Tres Simple:

[tex]x = 27\,L\times \frac{1.7\,L}{1\,L}[/tex]

[tex]x = 45.9\,L[/tex]

27 litros de leche de búfalo equivalen a 45.9 litros de leche de vaca.

Answer:

{2,4,5,6,8,10,15,20}

Answer:

{ 2,4,5,6,8,10,15,20}

Step-by-step explanation:

D ∪ E

This means the union of the two sets or what is in both circles with no duplicates

{ 2,4,5,6,8,10,15,20}

Answer:

10/1

Step-by-step explanation:

5/6÷1/12

5/6×12/1 (do a inverse of 1 upon 12)

10/1

cancel 12 by 6

[tex]\\ \sf\longmapsto 2(5m-4)-3(m-5)^2[/tex]

[tex]\\ \sf\longmapsto 10m-8-3(m^2-10m+5^2)[/tex]

[tex]\\ \sf\longmapsto 10m-8-3(m^2-10m+25)[/tex]

[tex]\\ \sf\longmapsto 10m-8-3m^2+30m-75[/tex]

[tex]\\ \sf\longmapsto -3m^2+30m+10m-75-8[/tex]

[tex]\\ \sf\longmapsto -3m^2+40m-83[/tex]

Answer:

Step-by-step explanation:

If polygons are similar ratio of sides will be same

[tex]\\ \sf\longmapsto \frac{6}{14} = \frac{3}{x} \\ \\ \sf\longmapsto 6x = 14 \times 3 \\ \\ \sf\longmapsto 6x = 42 \\ \\ \sf\longmapsto x = \frac{42}{6} \\ \\ \sf\longmapsto x = 7[/tex]

Answer:

x=12

Step-by-step explanation:

Since the polygons are similar, we can write a ratio to solve

red side / yellow side

4      2

--- = ---

x       6

Using cross products

4*6 = 2x

24 = 2x

Divide by 2

24/2 =2x/2

12=x

Answer:

12

Step-by-step explanation:

When two shapes are similar, you need to find the scale factor of two existing corresponding sides.

For example, you can do 6 and 2.

Divide:

6/2 = 3

The scale factor: 3

Now multiply 4 and the scale factor (3):

4 × 3 = 12

So, x = 12.

Hope this helped.

Answer:

Step-by-step explanation:

a1=-8

a2=3

D=11

n=-8+11(n-1)

Answer:

x=35/78

Step-by-step explanation:

3/2x-11/5=(7/8)*(64/49)

3/2x-11/5=8/7

3/2x=8/7+11/5

3/2x=117/35

x=(35*3)/(2*117)

x=35/78

Answer:

The length of the third side is 7.81 inches and the perimeter of the triangle is about 18.81 inches

Step-by-step explanation: