I NEED HELP PLEASE!!!

I give you a tricky one Express 108 ×125as a product of prime factors in exponential form

lana [24]

Answer:

$108 \times 125=2^2 \times 3^3 \times 5^3$

Step-by-step explanation:

To express the given product (108 X 125) as a product of prime factors

Step 1: Express each of the numbers as a product of its prime factors.

$108=2^2 \times 3^3\\125=5^3$

Step 2: Write the product together, and combine any like terms if any

Therefore,

$108 \times 125=2^2 \times 3^3 \times 5^3$

8 0

3 years ago

There are six wires which need to be attached to a circuit board. A robotic device will attach the wires. The wires can be attac

lesya692 [45]

Answer:

$S=720$

Step-by-step explanation:

From the question we are told that

Six wire are attached to a circuit board

Generally using multiplication rule

Let number of possible sequence be given as S

Mathematically

$S=6! =6*5*4*3*2*1=720$

Therefore

Number of possible sequence $S=720$

5 0

3 years ago

The length of a rectangle is 5 meters less than twice the width. If the area of the rectangle is 273 meters, find the dimensions

AleksandrR [38]

The length of the rectangle = 16 meters

The width of the rectangle = 10.5 meters

Step-by-step explanation:

Given that,

The Area of the rectangle is 273.

Step 1 :

Let, the width of the rectangle be 'x'

The length of the rectangle is 2x - 5

Step 2 :

Area of the rectangle = length $\times$ width

273 = (2x - 5) x

273 = 2x^2 - 5x

Step 3 :

The equation formed is 2x^2 - 5x -273 = 0

a= coefficient of x^2 = 2

b= coefficient of x = -5

c = constant = -273

Find the roots of the equation, to find the width.

Step 4 :

Find the roots using factorizing method,

ac = 2 $\times$ -273 = -546 and b= -5

Factorizing -546 as -26 $\times$ 21

The product of -26 $\times$ 21 = -546

The sum of -26 + 21 = -5

Step 5 :

The roots of the equation 2x^2 - 5x -273 = 0 are x= -26/2 and x= 21/2

The values of x are x= -13 and x= 10.5

Since the width cannot be a negative value, neglect x= -13

Step 6 :

Therefore,

The width of the rectangle = 10.5 meters

The length of the rectangle = 2x-5

= 2(10.5) - 5

= 21 - 5

length = 16 meters

5 0

3 years ago

A card is drawn from a well shuffled deck of 52 cards. Find the probability that the card is a red card or a 2.

tamaranim1 [39]

$|\Omega|=52$

There are 26 red cards and four 2's. But two 2's are red, so $|A|=26+4-2=28$

$P(A)=\dfrac{28}{52}=\dfrac{7}{13}\approx54\%$

3 0

2 years ago

Determine the measure of angle A, to the nearest degree.

Effectus [21]

Answer:

(a) 17°

(b) 78°

Step-by-step explanation:

(a) sin A= 0.2896

to calculate for "A" check for sin inverse of 0.2896

A= sin^-1(0.2896) = 16.83

to the nearest degree A= 17°

(b) tan A = 4.7046

A= tan^-1(4.7046)

A = 77.99

to the nearest degree A = 78°

4 0

2 years ago