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Scrat [10]
3 years ago
6

Factor the polynomial. 8g + 16h

Mathematics
1 answer:
AVprozaik [17]3 years ago
6 0

Answer:

8g+16h=8(g+2h)

Step-by-step explanation:

The given expression is

8g+16h

To factor this polynomial, we just need to extract the common factor. Or you can see as the greatest common factor.

What is the greatest common factor between 8 and 16?

16: 1, 2, 4, 8, 16.

8: 1, 2, 4, 8.

You can observe that the greatest common factor is 8, so we extract it from both numbers

8g+16h=8(g+2h)

Notice that we placed the GCM in the front as a product, if we don't do that, it would be completely wrong, because we can change the equivalence of the expression. Now, notice that each variable have different coefficients, that is because if you extract the GCM, you need to placed its quotients as coefficients.

Therefore, the factor of the polynomial is

8g+16h=8(g+2h)

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A light bulb consumes 2400 watt-hours per day. how long does it take to consume 9000 watt- hours?
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Answer:

3.75

Step-by-step explanation:

Set up the following ratio:

2400 watt-hours           1 day

-------------------------   =    ----------

9000 watt-hours           x days

Then do criss-cross-apple-sauce:

x*2400=9000*1

And then solve for x:

2400x=9000

x=9000/2400

x=3.75

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15 POINTS: A motorboat traveling downstream covers the distance between port M and port N in 6 hours. Once, the motorboat stoppe
pav-90 [236]

Answer: S=18

Step-by-step explanation:

D = distance between M and N  

S = speed of the boat  

S + 2 = speed down streem  

S - 2 = speed upstream  

T = time on the downstream leg until the boat made its turn  

9-T= time on the upstream leg  

6(S + 2) = D  

T (S + 2) = D - 40  

(9-T)(S-2) = D - 40  

now we have 3 equations and 3 uknowns  

lets multply everything out  

6S + 12 = D  

ST + 2T = D - 40  

9S - 18 - ST + 2T = D - 40  

add the second 2 together to get rid of the ST term  

9S - 18 + 4T = 2D - 80  

and lest subtract them from one annother  

2ST - 9S + 18 = 0  

if we can find T in terms of S we will have a quadratic equation, and will be able to use the quadratic formula / factor

9S - 18 + 4T = 2(6S + 12) - 80  

9S - 18 + 4T = 12 S + 24 - 80  

4T = 3S - 38  

T = 0.75 S - 9.5  

2S(0.75 S - 9.5) - 9S + 18 = 0  

1.5 S^2 - 28 S + 18 = 0  

S = 18, 2/3  

now it doesn't make sense for S to equal -2/3 as it suggests the boat moves backward when it is going up stream. (and that it travels downstream for negative time)  

S = 18

8 0
3 years ago
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