A lighthouse blinks every 12 minutes. A second lighthouse blinks every 10 minutes. If they both blink at 8:10 P. M., at what time will they next blink together

  9:10 P.M.

Step-by-step explanation:

The least common multiple (LCM) of 12 and 10 is 60. The lighthouses will blink together again 60 minutes later, at 9:10 P.M.

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Comment on finding the LCM

The LCM can be found several ways. One way is to factor out the greatest common factor (GCF) and write each number in terms of that:

  12 = 2×6

  10 = 2×5

Then the LCM is the product of the unique factors:

  LCM(12, 10) = 2×6×5 = 60

This is equivalent to dividing the product of the two numbers by their GCF:

  LCM(12, 10) = 12×10/GCF(12, 10) = 12×10/2 = 60

One can also write each number in terms of its prime factors, then form the product of each of those to its highest power:

  12 = 2²×3

  10 = 2×5

  LCM(12, 10) = 2²×3×5 = 60

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.