MATHEMATICS MIDDLE SCHOOL

Is the HCF of a^3-8, a^4+16 and a^3+2a^2+4a just 1?
Please answer........

Answers

Answer 1
Answer: first we find the factors
a^3-8 is the differnce between 2 perfect cubes and is factored out to
(a-2)(a^2+2a+4)
the factors are (a-2) and (a^2+2a+4)

a^4+16
this is not factorable, unless you mistiped it and it was really a^4-16
the factor is 1


a^3+2a^2+4a
factor out the a
a(a^2+2a+4)
this is the most factored out form
the factors are (a) and (a^2+2a+4)


there are no common factors except 1 so 1 is the answer

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Alphonse is training for a marathon. He runs 6 1/2 miles every 2/3 hour. How far does he run in 2 hours?

Answers

Answer:

19.5\ miles or 19(1)/(2)\ miles

Step-by-step explanation:

we know that

Alphonse runs 6(1)/(2) miles every (2)/(3) hour

so

by proportion

Find how far does he run in 2 hours

Convert to an improper fraction first

6(1)/(2)=(6*2+1)/2=13/2

((13/2))/((2/3))(miles)/(hours) =(x)/(2)(miles)/(hours) \n \nx=(13/2)*2/(2/3)\n \nx=39/2\n \nx=19.5\ miles

Convert to mixed number

19.5\ miles=19+0.5=19+(1)/(2)=19(1)/(2)\ miles
19 1/2 miles. Because you take 6 1/2 and divide that in half which is 3 1/4, so that is 1/3 of an hour. 3 1/4 times 3 is 9 3/4. Since that is only 1 hour you double that, which is 19 1/2.

What is -3 and 5/7 expressed as an improper fraction?

Answers

This is equal to -3-5/7, or (-3*7)/7-5/7, or -21/7-5/7, or -26/7.

Distributive property/collecting like terms. 4n -2 - 2n

Answers

Distributive property: a(b + c) = ab + ac

4n - 2 - 2n = 2(2n - 1 - n)

4n - 2 - 2n = 2n - 2 = 2(n - 1)

What does -4/5 = 1 = - 13 equal

Answers

 
There are two equations there.

               -4/5 = 1
and
                   1 = -13 .

Both of them are false statements.

The question, in total, has no mathematical significance.

How is the area of a sail related to the weight of the pilot on a hang glider?

Answers

The correct answer is:

The larger the surface area of the sail, the heavier the pilot can be and safely use the glider.

Explanation:

A hang glider must be able to support the weight of the pilot.  The air pushing up under the sail (wing) of the glider helps support the weight.  The more sail (wing) that you have, the more air pushing up, and the more weight it can hold.
The area of the sail is correlated to the weight of the pilot on the hang glider because the surface area of the sail needs to be able to lift ≤ (greater than or equal to) weight of the pilot.

Ok convert one million seconds to years using multistep unit conversions. So far I have 1,000,000/1 • 1/60 • 1\60 • 1/24 • 1/168 but I'm stuck please help im really ticked off

Answers

One major problem is that you're not keeping the units like I showed you.
I think you have everything there, except that I have no idea what that '168'
is all about.

Here it is with the units:

(1million seconds / 1)x(1min/60sec)x(1hr/60min)x(1 day/24hr)x(1 yr/365da)

= (1,000,000 x year) / (60 x 60 x 24 x 365) = 0.03171 year

Except for that screwy mysterious '168', you have everything there,
and in the right place.  Again, I'm going to say that you didn't realize
it, because you dropped all the units and suddenly all you saw was a
bunch of numbers in front of you.
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