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Elan Coil [88]
3 years ago
12

15 points hurry please

Mathematics
1 answer:
gavmur [86]3 years ago
3 0

Answer:

the third and fifth one

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Find the least common multiple (LCM) of 8y^6+ 144y^5+ 640y^4 and 2y^4 + 40y^3 + 200y^2.
Mice21 [21]

Answer:

<em>LCM</em> = 8y^{4}(y+ 10)^{2}(y + 8)

Step-by-step explanation:

Making factors of 8y^{6}+ 144y^{5}+ 640y^{4}

Taking 8y^{4} common:

\Rightarrow 8y^{4} (y^{2}+ 18y+ 80)

Using <em>factorization</em> method:

\Rightarrow 8y^{4} (y^{2}+ 10y + 8y + 80)\\\Rightarrow 8y^{4} (y (y+ 10) + 8(y + 10))\\\Rightarrow 8y^{4} (y+ 10)(y + 8))\\\Rightarrow \underline{2y^{2}} \times  4y^{2} \underline{(y+ 10)}(y + 8)) ..... (1)

Now, Making factors of 2y^{4} + 40y^{3} + 200y^{2}

Taking 2y^{2} common:

\Rightarrow 2y^{2} (y^{2}+ 20y+ 100)

Using <em>factorization</em> method:

\Rightarrow 2y^{2} (y^{2}+ 10y+ 10y+ 100)\\\Rightarrow 2y^{2} (y (y+ 10) + 10(y + 10))\\\Rightarrow \underline {2y^{2} (y+ 10)}(y + 10)        ............ (2)

The underlined parts show the Highest Common Factor(HCF).

i.e. <em>HCF</em> is 2y^{2} (y+ 10).

We know the relation between <em>LCM, HCF</em> of the two numbers <em>'p' , 'q'</em> and the <em>numbers</em> themselves as:

HCF \times LCM = p \times q

Using equations <em>(1)</em> and <em>(2)</em>: \Rightarrow 2y^{2} (y+ 10) \times LCM = 2y^{2} \times  4y^{2}(y+ 10)(y + 8) \times 2y^{2} (y+ 10)(y + 10)\\\Rightarrow LCM = 2y^{2} \times  4y^{2}(y+ 10)(y + 8) \times (y + 10)\\\Rightarrow LCM = 8y^{4}(y+ 10)^{2}(y + 8)

Hence, <em>LCM</em> = 8y^{4}(y+ 10)^{2}(y + 8)

5 0
3 years ago
Find the product write the product as a mixed number
Helga [31]

Answer:

\frac{9}{10}  \times 54 =  \frac{9 \times 54}{10}  =  \frac{486}{10}  = 48 \frac{6}{10}  =  \frac{243}{5}

3 0
3 years ago
Answers: <br> a) 74<br> b) 108<br> c)49<br> d)51
lisabon 2012 [21]

Answer:

51

Step-by-step explanation:

sum of exterior angles = 360

64  + 60 + 69 + 42 + x + x +23 = 360

2x + 258 = 360

2x = 360 - 258

2x = 102

x = 51

5 0
3 years ago
Read 2 more answers
Ed is on a road trip. He has already traveled 208 miles and is driving at a rate of 70 miles per hour. Which equation could be u
Dmitriy789 [7]

The answer would be B. 208x+70=695

6 0
3 years ago
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A store sells posters. Each poster costs the same amount. During a sale, the store reduces the price of each poster by $1. 25. C
grandymaker [24]

Answer:

4.44

Step-by-step explanation:

I used a calculater to divide $17.76 by 4

4 0
3 years ago
Read 2 more answers
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