5 ex to the power of 2. minus 36 ex. + 36. = 0

Consider a bag containing four red marbles, three green ones, one transparent one, three yellow ones, and three orange ones.

Otrada [13]

Answer: 21

Step-by-step explanation:

Given : Number of red marbles = 4

Number of green marbles =3

Number of transparent marbles =1

Number of yellow marbles =3

Number of orange marbles =3

If we want to count the sets of five marbles are there in which none of them are red or green, the we exclude green and red marbles from the total marbles.

i.e. Total required marbles = 1+3+3=7

Now, the number of possible sets of five marbles are there:-

$^7C_5=\dfrac{7!}{5!(7-5)!}=\dfrac{7\times6\times5!}{5!2!}=21$

Hence, the number of possible sets of five marbles =21

5 0

3 years ago

Given 36 − 9, simplify the expression using the Difference of Squares.

lisov135 [29]

Answer:

See below

Step-by-step explanation:

Using formula

x^2 - y^2 = (x + y)(x - y)

Applying to given expression

36 - 9 =
6^2 - 3^2=
(6 + 3)(6 - 3)=
9*3=
27

6 0

3 years ago

Which graph represents the equation x = 3?

a_sh-v [17]

Answer:

Top graph

Step-by-step explanation:

x=3 is a vertical line where the value of x is always 3

4 0

3 years ago

Read 2 more answers

3. Is XY Tangent to circle Z? Y 12 X (20 Z 18

Ratling [72]

Answer:

XY is a tangent

Step-by-step explanation:

Given

$XY = 12$

$WY = 20$

$WZ = 8$

Required

Is XY a tangent?

XY is a tangent if:

$WY^2 = XY^2 + WX^2$

Because XY should make a right angle at point X with the circle

Where

$WX = 2 * WZ$

So, we have:

$WY^2 = XY^2 + WX^2$

$WY^2 = XY^2 + (2*WZ)^2$

$WY^2 = XY^2 + (2WZ)^2$

$WY^2 = XY^2 + 4WZ^2$

This gives:

$20^2 = 12^2 + 4*8^2$

$400 = 144 + 256$

$400 = 400$

Yes, XY is a tangent

4 0

3 years ago

It takes a train 60 seconds to completely drive through a bridge of 1260 m, and 90 seconds to completely drive through a tunnel

Olegator [25]

The length of train is 120 meters

The speed of train is 25 meter per second

Solution:

The speed is given by formula:

$speed = \frac{distance}{time}$

Given that,

It takes a train 60 seconds to completely drive through a bridge of 1260 m

And 90 seconds to completely drive through a tunnel of 2010 m

Let the length of the train be "x"

The total distance travelled by the train across the bridge is given by:

total distance = x + 1260 + x = 2x + 1260

[ here we use x + x to represent that train completely drives through bridge ]

The time taken is given as 60 seconds

Therefore, the speed is given as:

$speed = \frac{2x+ 1260}{60}$

The total distance travelled by the train through the tunnel is given by:

total distance = x + 2010 + x = 2x + 2010

The time taken is given as 90 seconds

Therefore, the speed is given as:

$speed = \frac{2x+ 2010}{90}$

The speed of the train was the same in both cases.

Equate both speeds

$\frac{2x+ 1260}{60} = \frac{2x+ 2010}{90}$

$\frac{x+630}{30} = \frac{x+1005}{45}$

$45(x+630) = 30(x+1005)\\\\45x + 28350 = 30x + 30150\\\\45x - 30x = 30150 - 28350\\\\15x = 1800\\\\x = 120$

Thus length of train is 120 meters

Find the speed of train:

$speed = \frac{2x+ 1260}{60}\\\\speed = \frac{2(120) + 1260)}{60}\\\\speed = 25$

Thus speed of train is 25 meter per second

5 0

3 years ago