1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
laiz [17]
2 years ago
10

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

Mathematics
1 answer:
Mice21 [21]2 years ago
5 0

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)

You might be interested in
I use 3 fifth size strips to model 3/5.I want to use tenth size strips to model an equivalent fraction.How many tenth size strip
Yuri [45]
3/5= 3 fifth size strips
You want to find an equivalent fraction with the denominator of ten, correct? Then you would multiply the fraction in a way that will allow you to have a denominator of ten.
So...
3/5*2/2=6/10
You would need 6 tenth size strips.
5 0
3 years ago
Triangle with a height of 25 feet and base of 12 feet. What is the area of the triangle?
Dafna1 [17]

Answer:

150 ft

Step-by-step explanation:

triangle area formula= (b*h)/2

25 time 12 is 300. divide 300 by 2 and get 150.

3 0
3 years ago
Read 2 more answers
How do I solve/ set up equation? Will give brainliest pls help
slamgirl [31]

Answer:

See below ~

Step-by-step explanation:

<u>Finding x</u>

  • 2x - 28 = x/2
  • 3/2x = 28
  • 3x = 56
  • x = 56/3 = 18.66666667

  1. The exact side length of the small square is <u>18.66666667 cm</u> and the exact side length of the big square is <u>37.3333334 cm</u>.
  2. The approximate side length of the small square is <u>18.7 cm</u> and the approximate side length of the big square is <u>37.3 cm</u>.
4 0
1 year ago
Write the equation of a line in slope intercept form that is perpendicular to the line y = –4x and passes through the point (2,
Gnesinka [82]

1. If the line that we are searching for is perpendicular to the line y = -4x, this means that the gradient of our line and the gradient of the perpendicular line will multiply to give -1. Thus if we call the gradient of our line m, then:

m*(-4) = -1

-4m = -1

m = 1/4

2. Since we know that m = 1/4 and we have a point (2,6) on our line, we can use the formula y - y1 = m(x - x1) to find the equation of our line, where (x1, y1) is the coordinates of a point on the line. Thus:

y - y1 = m(x - x1)

y - 6 = (1/4)(x - 2)

y - 6 = (1/4)x - 2/4 (Expand (1/4)(x - 2))

y = (1/4)x - 1/2 + 6 (Simplify 2/4 and add 6 to each side)

y = (1/4)x + 11/2 (Evaluate -1/2 + 6)

Slope-intercept form is given by y = mx + c. As our equation is already in this form, there is nothing more to do. Thus, the answer is y = (1/4)x + 11/2

6 0
2 years ago
Chloe wants to buy some apples at holmeberg's orchard. She can purchase 3 pound bag of apples for $7.50 or she can buy a 10 poun
Gnom [1K]
What’s the questpn lol
6 0
3 years ago
Other questions:
  • Amount financed $500,
    7·1 answer
  • Identify the slope of the line shown in the graph below:
    7·2 answers
  • Jen bought 5 CD’s for $57.50. What was the unit rate?
    7·1 answer
  • Boat A and Boat B are racing across a bay. Boat A is 6 miles ahead of Boat B. Boat A has a top speed of 36 miles per hour, but B
    9·1 answer
  • Evaluate the algebraic expression 5 + 9(x-8)2 for x = 9.<br> When x = 9,5+9(x-8)2 =
    15·1 answer
  • An oil storage tank is a cylinder with a height of 50 feet and a diameter of 20 feet. What is the volume of the tank? Use 3.14 f
    15·1 answer
  • Why did I get different answers to find x?
    12·1 answer
  • 100 points &amp; brainliest if you get it correct!
    6·1 answer
  • What is the length of segment
    10·1 answer
  • Evaluate the expression:<br> -17-14=
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!