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denis-greek [22]
3 years ago
5

What is the greatest common factor of 8m, 36m", and 12?

Mathematics
1 answer:
wlad13 [49]3 years ago
4 0

Answer: 4

Step-by-step explanation:

8m = 2*2*2*m

36m^3 = 2*2*3*3*m*m*m

12 = 2*2*3

GCF=2*2

Hope this helps!!

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During its first year in business, Alice's restaurant shows a loss of $12,000. During its second year, the restaurant makes a pr
galina1969 [7]

Answer:

$10,000

Step-by-step explanation:

-12,000+23,200-1,200= 10,000

8 0
3 years ago
The sum of 4 consecutive multiples of 6 is 540. What is the greatest of these numbers?
pychu [463]

Answer:

144

Step-by-step explanation:

First: 6x

Second: 6x+6

Third: 6x+12

Fourth: 6x+18

- Since they're multiples of 6

6x+6x+6+6x+12+6x+18=540

24x+36=540\\

Subract 36 from each side give us...

24x=504\\x=21

21(6)+18=144

Hope this helped! Please mark brainliest :)

4 0
3 years ago
Find the quotient.
posledela
Answer :

B. 16 {a}^{2}c

step-by-step explanation :

48 {a}^{3}b{c}^{2} \div 3abc

This can be rewritten as:

\frac{ 48 {a}^{3}b {c}^{2} }{3abc}

Now,

\frac{48}{3}=16

The law of indices states that:

\frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}

It implies that, when dividing two expressions with the same bases, repeat one of the bases and subtract the exponents.

Therefore,

\frac{ {a}^{3} }{a}= {a}^{3 - 1} = {a}^{2}

\frac{b}{b} = {b}^{1 - 1} = {b}^{0} = 1

Note: Any non-zero number exponent zero is 1

Also

\frac{ {c}^{2} }{c} = {c}^{2 - 1} = {c}^{1} = c

Hence:

\frac{ 48 {a}^{3}b {c}^{2} }{3abc} = 16 {a}^{2}c
3 0
3 years ago
Math help can’t solve please
frez [133]

Answer:

See below

Step-by-step explanation:

a) 43.8 - 38 = 5.8 yrs

b) SD = 8.9 yrs    5.8 / 8.9 = .6517 SD   <u> below</u> the mean

(A z score merely shows how many standard deviations a score (age) is above or below the mean in SD units)

c) Z =     - .6517     Negative because it is <u>BELOW</u> the mean                                                                                   ( FYI    from z-score table: this is .2578  in percentage )

d) usual       ( it  (-.6517)  is between -2   and + 2  )

7 0
2 years ago
A force of 5 pounds stretches a spring 1 foot. A mass weighing 6.4 pounds is attached to the spring, and the system is then imme
Rudiy27

Answer:

x(t) = e ^{-3t} [-cos (4t) - \frac{3}{4}sin (4t)]

Step-by-step explanation:

A force of 5 pounds stretches a spring 1 foot.

This implies that, the string constant (K) = 5 lbs? ft

Mass (m) = \frac{6.4}{32}

= \frac{1}{5}

The damping force F_d = -1.2 v

The negativity of the damping force is due to the fact that it opposes the motion.

Then the force due to the spring is :

F_5 = -kx    

where;

x = the mass distance from the equilibrium point.

Total Force F = F_d + F_s

⇒ F = -1.2v - 5.0 x

⇒ mx = -1.2v - 5.0 x

where v = x' and a = x"

Hence, the equation becomes mx" =  -1.2x' - 5.0 x

⇒  \frac{1}{5} x"+1.2x'+5v = 0

⇒ x" +6x'+25x =0

The auxiliary equation is can be written as:

r^2 +6x+25=0

⇒ r = \frac{-6 \pm\sqrt{36-100} }{2}

r = -3\pm4i

r = -3+4i  OR   -3-4i

Now,the general equation of motion is :

x(t)=e^{-3t}(C_1cos(4t)+C_2sin(4t))

x'(t)=-3e^{-3t}(C_1cos(4t)+C_2sin(4t)) + e^{-3t}(-4C_1sin(4t)+4C_2 cos(4t))

Initial Conditions are:

x(0) = -1 and x' (0) = 0

x(0) = -1

⇒ -1 = C_1

x' (0) =0 ⇒ 0 = -3(-1) + (4C_2)

⇒ C_2 = -\frac{3}{4}

Thus:

x(t) = e ^{-3t} [-cos (4t) - \frac{3}{4}sin (4t)]

7 0
3 years ago
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