I need some help with my math homework...?

Question

Working on my math homework, I came across a couple of problems.

#1 Factoring

n^2-6n+8=0

I know to bring it to (n+4)(n+2)=0, but I'm never sure what to do from there.

#2 Substitutions

Evaluate: 2s^2+4sh when s=√6 and h=1/2√6

Since there is no square root, I wasn't sure where to start here.

#3 More substitution

Evaluate: √(x-5)^2+(y-3)^2 when x=1 and y=0

For this one, I started with √(1-5)^2 + (0-3)^2, which brought me to (-4)+(-3), which is -7. However, in the back of the book, it says the answer is 5. What am I doing wrong?

Thanks in advance!!!

Answer 1

The first should be (n - 4)(n - 2) = 0

Then since if two numbers multiply to be zero, one must be zero, you know that either n - 4 = 0 making n = 4, or n - 2 = 0 making n = 2.

#2, if s = √6 then s^2 = 6 so 2s = 12

and √6 times 1/2 √ 6 is 1/2 times 6 or 3, then that times the 4 is 12

so 12 + 12 = 24

On #3 you need to square the -4 and 3. So they are 16 and 9 then add them getting 25 then do the square root getting 5

Final one: the rule for an exponent followed by another exponent is to multiply the exponents so you'd get x^ -4,

which like you said flips to be 1 over x^4

Answer 2

I'll give the solution for the last one

   (x ^2 )^ -2                                            

   = x^(2* -2)    

   =  x^ -4                                                  

   =  1/x^4

power of power means multiplication of indices  which are 2 & -2.

Answer 3

1

n^2-6n+8=0

n^2-4n-2n+8=0

n(n-4)-2(n-4)=0

(n-2)(n-4)=0

if ab=0, either a or b must be 0.

thus, either n-2 or n-4 must be 0.

If:

n-2=0, n=2

n-4=0, n=4

So the solutions are n=2 and n=4

#2.

There is a bit of confusion, is it:

h=1/(2√6)

or

h=(1/2)√6?

We know:

s=√6

So,

s^2=6

sh=1/2 if the first h is correct

sh=3 if the second h is correct

So,

2s^2=12

2s^2+4sh=12+4sh=4(3+sh)

if the first is correct:

4(3+sh)=4(3+1/2)=4(7/2)=(4/2)7=2*7=14

If the second is correct:

4(3+sh)=4(3+3)=4(6)=24

#3:

Again a bit of confusion, i believe it is:

√[(x-5)^2+(y-3)^2]

rather than what you have put.

So,

x=1, x-5=1-5=-4, (x-5)^2=(-4)^2=-4*-4=16

y=0, y-3=-3, (y-3)^2=(-3)^2=-3*-3=9

So, the expression becomes:

√(16+9)=√25=5

#4.

Note:

(a^b)^c=a^(bc)

a^-d=1/(a^d)

So, using those rules,

(x^2)^-2=1/(x^2)^2=

1/x^(2*2)=1/x^4=

x^-4

Hope this helped. email for qs. peace

Answer 4

Ok let's review every execersice

Factoring n²-6n+8=0   this is equal to

(n-4)(n-2)=0 there are no positive signsas you put on the question

After this, you equal each braquet to 0

n-4=0

n=4

n-2=0

n=2

#2

2s²+4sh   s=sqrt 6 h=1/2sqrt 6

2(sqrt6)²+4(sqrt6)(1/2sqrt6)        (sqrt6)²=6 the power cris cross with the square root

2(6)+4(1/2)(sqrt6)²

12+2(6)

12+12

24

#3

sqrt ((x-5)²+(y-3)²)    x=1  y=0

sqrt((1-4)²+(0-3)²)

sqrt((-4)²+(-3)²)

sqrt(16+9)

sqrt (25)

5

Last one

(x²)^(-2)  Power of power their exponents are multiplied

x^(-4) or 1/x^4

I hope this can useful

David

Answer 5

Sorry. Not sure about Number 2 or 3.

But I will help you with number 1.

First off, your factoring is incorrect.

Because it is -6n your binomials will be (n-4)(n-2)

Because -4 and -2 multiply to positive 8 and they add to -6  =]

Now.  you have  (n-4)(n-2)=0

I'm not sure how you learned but I have learned to make each binomial equal to zero.

so..  n-4=0   and   n-2=0  And solve those mini- equations

and you will get the value of N.

So your answers are N=4 and N=2