The number .0100100010001.... can be classified as

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

Create a real world right triangle in your notebook. Answer this ASAP

MakcuM [25]

-- Draw a line, any length.
-- Draw another line, any length, that makes a square corner with the first one.
- Connect the open ends of the two lines to each other.
-- Bada-bing ! You have a right triangle. And it's in YOUR notebook.

5 0

3 years ago

What is the standard form of (6x^2-8x-7)+(8x^2-76x)

Studentka2010 [4]

Answer: 14x^2 - 84x - 7

====================================================

Explanation:

The like terms 6x^2 and 8x^2 combine to 14x^2

The like terms -8x and -76x combine to -84x

Nothing pairs with the -7, so its stays as is.

Standard form is where we list the terms in decreasing exponent order. We can think of -84x as -84x^1 and the -7 as -7x^0. So 14x^2 - 84x - 7 would be the same as 14x^2 - 84x^1 - 7x^0. The exponents count down: 2,1,0.

The final answer is a trinomial since it has three terms. It is also a quadratic because the degree (highest exponent) is 2.

5 0

3 years ago

Help I don't understand this, Can someone explain this to me?

saul85 [17]

Answer:

The second answer is correct (5 x 1,000,000,000)

Step-by-step explanation:

Just count the number of zeros. Multiplying a number liket his by five doesn't change the number of zeros

7 0

2 years ago

Read 2 more answers

Many airline companies have begun implementing fees for checked bags. Economic theory predicts that passengers will respond to t

valentinak56 [21]

Answer:

Step-by-step explanation:

a. The hypothesis test is one tailed_____ test.

(Because we check whether sample weight is greater than hence one tailed or right tailed)

The test statistic follows a __t___ distribution.(Because only sample std deviation s is known)

The value of the test statistic is___Mean difference/Std error = $\frac{17.1-16}{\frac{6}{\sqrt{67} } } \\=1.58$ __

b. df = 66

Reject H0 if t ≥ 1.668

c. The p-value is_____0.059444

d. Using the critical value approach, the null hypothesis is _accepted____, because __t <1.668___ Using the p-value approach, the null hypothesis is__accepted___, because__p value <0.05 our significance level.___ Therefore, you __may___ conclude that the mean weight of the airline's passengers' carry-on items has increased after the implementation of the checked-bag fee.

4 0

3 years ago