Covert the measurements 3km 312m

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

Mice21 [21]

Answer:

LCM = $8y^{4}(y+ 10)^{2}(y + 8)$

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 factorization 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 factorization 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. HCF is $2y^{2} (y+ 10)$ .

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

$HCF \times LCM = p \times q$

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

Hence, LCM = $8y^{4}(y+ 10)^{2}(y + 8)$

5 0

3 years ago

Please help me solve this practice SAT question!

lord [1]

Answer:

t=5

Step-by-step explanation:

∵ (t,17) lies on (x,y) plane y=x²-3x+7,t>0

∴ 17=t²-3t+7

t²-3t+7-17=0

t²-3t-10=0

t²-5t+2t-10=0

t(t-5)+2(t-5)=0

(t-5)(t+2)=0

t=5,-2

t>0

so t=5

6 0

3 years ago

HEEELEP ASAP PLZ 15 POINTS + BRAINLIEST

skad [1K]

1334 / 23 = 58
mean (average) = 58 miles per hour

answer
58 miles per hour

3 0

3 years ago

X I ㅗ ] Factor: -2/3 out of -3X - 12

sesenic [268]

Answer:what is this

Step-by-step explanation:

bruh

3 0

2 years ago

PLEASE HELP Provide 3 examples of how Franklin Delano Roosevelt changed the course of history 5-8 sentences PLEASE SOMEONE WHO W

Vesna [10]

Well, there are a lot of ways in which President Roosevelt impacted the US. He brought a nation to the brink of disaster from the Great depression and helped overcome it with his New deal which gave a lot of people jobs and helped rebuild America because of the CCC, among other programs in the New Deal. He also guided America through World War 2 and created peace between nations by signing the Atlantic Charter which then was the basis for the United Nations. As you can see President Roosevelt did alot to help America, he was a very good president

8 0

3 years ago