Math help please?

Question

squ means squared by

1. (4x squ 2 Y -squ 2) squ -2

2. 5/x + 1/3x divided by 4/3x + 3/2x

3. - (3/x) + 3/2x

4.Sandra can paint a kitchen in 3 hours and James can pait the same kitchen in 4 hours. How long does it take to paint the kitchen if they both work together.

5.4/f+3 + 4/f squ 2 - 9

6. x+5/x+2 = x+4/ x+6

7. x squ 2/ x+6 x x squ 2 + 7x+6/x squ 2+x

PLEASE HELP REALLY NEED THESE BY MONDAY!!!!!!!!!!!!!!!

Answer 1

2). 5/x + 1/3x divided by 4/3x + 3/2x
LCF(x, 3x, 2x) = 6x
(30 + 2 : 8 + 9) = 32: 8 + 9 = 4 + 9 = 13/6x = 2 1/6x
x different of zero

3) -(3/x) + 3/2x = -3/2x
4) (3 + 4) : 2 = 3,5 hours
5) 4/f+3 + 4/f squ 2 - 9
4/f + (4/f)² -6
16/f² + 4/f - 6 = 0
16 - 4.16.-6 = 400

f = (-4 +/- \/400) : 2.16
f = (-4 + 20) : 32
f' = 16/32 = 1/2
f" = (-4 - 20) : 32
f" = -24 : 32
f" = -3/4
Answer: {f E R | f' = 1/2 and f = -3/4}
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6) x+5/x+2 = x+4/ x+6
x² + 7x + 10 = x² + 10x + 24
x² - x² + 7x -10x + 10 - 24 = 0
-3x - 14 = 0
-3x = 14
x = -14/3

Answer 2

1. (4x^2 -y^2)^-2 If this is what you mean, then:
= 1/(4x^2-y^2)^2
= 1/[(2x-y)(2x+y)]^2

2.(5/x +1/3x)/(4/3x +3/2x)
= (15/3x+1/3x)/(8/6x + 9/6x)
= (16/3x)/(17/6x) = (16/3x)(6x/17) = 32/17
Now, in the above problem, I have assumed that 1/3x means 1 divided by 3x and not 1/3 times x. If my assumption is wrong, then the answer is wrong. Always use parentheses to makke clear what you mean!!

3. - (3/x) + 3/2x
= -6/2x +3/2x = -3/2x.

4.Sandra can paint a kitchen in 3 hours and James can pait the same kitchen in 4 hours. How long does it take to paint the kitchen if they both work together.

These type of problems are most easily solved by taking the product over the sum. Thus time if both work together is :
(3)(4)/(3+4)= 12/7 = 1 5/12 hours.


5.4/f+3 + 4/f squ 2 - 9
This time I'm assuming that 4/f +3 means 4/(f+3)
4/(f + 3) + 4/(f^2 -9)
=4/(f+3) +4/[(f+3)(f-3)]
= 4(f-3)/[(f+3)(f-3)] + 4/[(f+3)(f-3)]
=(4f +12 +4)/[f+3)(f-3)]
=(4f +16)/[(f-3)(f+3)] = (4f +16)/(f^2-9)

6. x+5/x+2 = x+4/ x+6
(x+5)/(x+2) = (x+4)/(x+6)
cross multiply to get:
(x+2)(x+4) = (x+5)(x+6)
x^2 +6x + 8 = x^2 +11x +30
6x -11x = 30 - 8
-5x=22
x = -22/5 = -4.4

7. x squ 2/ x+6 x x squ 2 + 7x+6/x squ 2+x
x^2/(x+6) + (x^2 +7x) +6/(x^2+x) is my interpretation. The two x's in a row is confusing so I'm thinking the 1st x is + sign.
= x^2/(x+6) + (x^2 +7x) + 6/[(x(x+1)]
The common denominator is x(x+1)(x+6), so
=[x^2 (x)(x+1) +(x^2+7x)(x)(x+1)((x+6) + 6(x+6)]/[x(x+1)(x+6)]
=[x^4 +x^3 +x^4+7x^2+x^3 +7x+6x+36][/x(x+1)(x+6)]
=(2x^4+2x^3+7x^2+13x +36)/[x(x+1)(x+6)] = final answer.

I hope my interpretations were correct. Even if they were wrong, you should have learned something from all this.

I hope so and good luck on Monday.

Answer 3

1. (4x squ 2 Y -squ 2) squ -2

As near as I can tell, you mean

(4x^2y^-2)^-2

where ^ means 'raised to the power of'

y^-2 = 1/y^2, so

(4x^2/y^2)^-2

1/[(4x^2/y^2)]^2

1/(a/b) = b/a, so

[(y^2/4x^2)]^2

y^4/16x^4


2. 5/x + 1/3x divided by 4/3x + 3/2x

[5/x + 1/3x]/[4/3x + 3/2x]

Multiply the big numerator and big denominator by 6x (the LCD of the little fractions) to clear the little fractions

[30 + 2]/[8 + 9] = 32/17


3. - (3/x) + 3/2x

If we multiply the left fraction by 2/2 then both fractions have the same denominator

- 6/(2x) + 3/(2x) = - 3/(2x)


4.Sandra can paint a kitchen in 3 hours and James can pait the same kitchen in 4 hours. How long does it take to paint the kitchen if they both work together.

The rate for Sandra is one kitchen in 3 hours, or 1/3
The rate for James is 1/4

Together they can do 1 kitchen in x hours, or 1/x, and this rate is the sum of their rates

1/3 + 1/4 = 1/x

To clear the fractions, multiply by 12x

4x + 3x = 12
7x = 12
x = 12/7 = 1 5/7


5.4/f+3 + 4/f squ 2 - 9

You probably mean

4/(f + 3) + 4/(f^2 - 9)

f^2 - 9) is a difference of two squares, and factors into (f + 3)(f - 3)

Multiply the left fraction by (f - 3) so the fractions will have the same denominator

4(f - 3)/[(f + 3)(f - 3)] + 4/[(f + 3)(f - 3)]

(4f - 12 + 4)/[(f + 3)(f - 3)]

(4f - 8)/[(f + 3)(f - 3)]

4(f - 2)/[(f + 3)(f - 3)]


6. x+5/x+2 = x+4/ x+6

(x + 5)/(x + 2) = (x + 4)/(x + 6)

You can clear the fractions by multiplying both sides by (x + 2)(x + 6)

The same result is reached by cross-multiplication = multiply the numerator on the left by the denominator on the right, and multiply the numerator on the right by the denominator on the left

(x + 5)(x + 6) = (x + 4)(x + 2)

x^2 + 6x + 5x + 30 = x^2 + 2x + 4x + 8
x^2 + 11x + 30 = x^2 + 6x + 8
11x + 30 = 6x + 8 {subtract x^2 from both sides}
5x = - 22 {subtract 6x and 30}
x = - 22/5


7. x squ 2/ x+6 x x squ 2 + 7x+6/x squ 2+x

Cann't decifer this one - suggest you amend your post using ^ and ( ) where appropriate

Answer 4

3. - (3/x) + 3/2x
=(-6+3)/2x=(-3/2)x

4.Sandra can paint a kitchen in 3 hours and James can pait the same kitchen in 4 hours. How long does it take to paint the kitchen if they both work together.
theiri hours job together=1/3+1/4=7/12
so togetherthey canfinish in 12/l hrs= 1 5/7 hrs

5.4/f+3 + 4/f squ 2 - 9


6. x+5/x+2 = x+4/ x+6
(x+6)(x+5)=(x+2)(x+4)
x^2+11x+30=x^2+6x+8
adding -x^2-6x-8
5x+22=0
adding-22
5x=-22
dividing by 5
x=-22/5
=-4 2/5

unless you present the sums understandably it becomes difficult to solve.use parenthesis

Answer 5

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