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denis23 [38]
1 year ago
11

Please answer this question ASAP!

Mathematics
1 answer:
kvasek [131]1 year ago
3 0

Answer:

  8:07:12 am

Step-by-step explanation:

The lights will change simultaneously after any multiple of the least common multiple of their cycle times.

<h3>LCM</h3>

The least common multiple of a set of numbers is the product of the highest powers of their prime factors.

  48 = 2⁴×3

  72 = 2³×3²

  108 = 2²×3³

The highest power of the factor 2 is 4. The highest power of the factor 3 is 3, so the LCM of the numbers 48, 72, and 108 is ...

  LCM = 2⁴×3³ = 16×27 = 432

The lights will change simultaneously after each period of 7 minutes 12 seconds. They will change simultaneously again at 8:07:12 am.

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X-y+4z=5<br> 4x+z=2<br> x+5y+z=17
JulsSmile [24]

Answer:x = 0, y = 3, z = 2

Step-by-step explanation:

The given system of equations is expressed as

x - y + 4z = 5 - - - - - - - - - - - - - -1

4x + z = 2

z = 2 - 4x- - - - - - - - - - - - - -2

x + 5y + z = 17- - - - - - - - - - - - - -3

From equation

Substituting equation 2 into equation 1 and equation 3, it becomes

x - y + 4(2 - 4x) = 5

x - y + 8 - 16x = 5

x - 16x - y = 5 - 8

- 15x - y = - 3 - - - - - - - - - - - - - -4

x + 5y + 2 - 4x = 17

x - 4x + 5y = 17 - 2

- 3x + 5y = 15- - - - - - - - - - - - - -5

We would eliminate y by multiplying equation 4 by 5 and equation 5 by 1. It becomes

- 1

- 75x - 5y = - 15

- 3x + 5y = 15

Adding both equations, it becomes

- 78x = 0

x = 0

Substituting x = 0 into equation 2, it becomes

z = 2 - 4 × 0

z = 2

Substituting x = 0 and z = 2 into equation 1, it becomes

0 - y + 4 × 2 = 5

- y + 8 = 5

y = 8 - 5

y = 3

6 0
3 years ago
10,13,16,19<br> What is the 30th term?
Komok [63]

Step-by-step explanation:

An=A1+(n-1)d

A30=10+(30-1)3

A30=10+(29)3

A30= 10+87

A30=97

it takes me a centuary to type

6 0
3 years ago
Factor completely 4p^2-25q^2
Alexxandr [17]

Answer:

(2p - 5q) (2p + 5q)

5 0
3 years ago
Select the correct answer.
vagabundo [1.1K]

Answer

D.  `(y+4) = (5)/(3)(x+ 1)`


Step by step explanation

The given points are (-1, -4) and (2, 1)

Slope = (y2 - y1)/(x2 - x1)

= (1 - (-4)) / (2 - (-1))

= (1 + 4) / (2 +1)

m = 5/3

When two points are given, the equation of the line is

(y - y1) = m (x - x1)

y -(-4) = 5/3 (x - (-1))

y + 4 = 5/3 (x + 1)

The answer is (y+4) = (5)/(3)(x+ 1)

Thank you.

5 0
2 years ago
Read 2 more answers
You downloaded a video game to your computer. You have a 60-minute free trial of the game. It takes 5 1/6 minutes to set up the
igomit [66]

Answer:

B.

Step-by-step explanation:

Given,

The time for set up the game =  5\frac{1}{6} minutes,  

Also, the time for each level of game is 7\frac{1}{3\\} minutes,  

If there are l levels of games,  

Then the time taken in all levels of game = (7\frac{1}{3}) l<em> </em>

Hence, the total time ( in minutes ) = Set up time + time in all level

= 5\frac{1}{6} +(7\frac{1}{3}) l

We have 60-minute of free trial of the game,

So, the total time taken can not be exceed to 60 minutes,

= 5\frac{1}{6} +(7\frac{1}{3}) l\leq 60

Which is the required inequality.  

Option 'B' is correct.

5 0
2 years ago
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