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
horrorfan [7]
3 years ago
12

Can someone help me with algebra 2 with an explanation?

Mathematics
1 answer:
sammy [17]3 years ago
4 0

Answer: This took me a long time to type, hope you read it and find it helpful and easy to understand...

1. x=1

2. x=\frac{3}{2}

3. x=1

4. x=\frac{6}{5}

Step-by-step explanation:

1.

\frac{1}{x}-\frac{x-2}{3x}=\frac{4}{3x}

To make it easier to add / subtract fractions, we are looking for common denominators. I can see that if I move the fraction on the left with a denominator 3x to the right, I'll be able to add two equations with like denominator.

Let's add \frac{x-2}{3x}

\frac{1}{x}=\frac{4}{3x}+\frac{x-2}{3x}

Add the numerators and keep the same denominator.

\frac{1}{x}=\frac{4+x-2}{3x}

\frac{1}{x}=\frac{2+x}{3x}

To get rid of the denominator x on the left side, we can multiply by x.

(x)\frac{1}{x}=\frac{2+x}{3x}(x)

1=\frac{2+x}{3}

Now multiply by 3.

(3)1=\frac{2+x}{3}(3)

3=2+x

Subtract 2.

3-2=x\\1=x

The value of x is 1.

Proof.

\frac{1}{x}-\frac{x-2}{3x}=\frac{4}{3x}

\frac{1}{1}-\frac{1-2}{3(1)}=\frac{4}{3(1)}

1-\frac{-1}{3}=\frac{4}{3}

1+\frac{1}{3}=\frac{4}{3}

\frac{1*3+1}{3} =\frac{4}{3}\\\frac{4}{3}=\frac{4}{3}

I can't show the proof to the following problems because I have a 5000 character limit.

-----------------------------------------------------------------------------------------

2.

\frac{5x-5}{x^2-4x} -\frac{5}{x^2-4x}=\frac{1}{x}

Again, we have like denominators, therefore, we can simply subtract the numerators and keep the same denominator.

\frac{5x-5-5}{x^2-4x}=\frac{1}{x}

\frac{5x-10}{x^2-4x}=\frac{1}{x}

Again, we can multiply by x to get rid of the x in the denominator.

(x)\frac{5x-10}{x^2-4x}=\frac{1}{x}(x)

Do not distribute the x in the numerator yet because we're gonna eliminate it later.

\frac{(x)(5x-10)}{x^2-4x}=1

Factor the denominator.

\frac{(x)(5x-10)}{(x)(x-4)}=1

Simplify x's.

\frac{5x-10}{x-4} =1

Multiply by x-4 to get rid of the denominator.

(x-4)\frac{5x-10}{x-4} =1(x-4)

5x-10=x-4

Add 10

5x=x-4+10

Subtract x

5x-x=-4+10

Combine like terms;

4x=6

Divide by 4.

\frac{4x}{4}=\frac{6}{4}

x=\frac{6}{4}

Simplify by 2.

6/2 = 3

4/2 = 2

x=\frac{3}{2}

-----------------------------------------------------------------------

3.

\frac{x^2-7x+10}{x}+\frac{1}{x}=x+4

Same denominator, add numerators.

\frac{x^2-7x+10+1}{x}=x+4

\frac{x^2-7x+11}{x}=x+4

Multiply by x to get rid of the x.

(x)\frac{x^2-7x+11}{x}=(x+4)(x)

x^2-7x+11=x^2+4x

Subtract -x^2-4x

x^2-7x+11-x^2-4x=0

Combine like terms;

-11x+11=0

Subtract 11.

-11x=-11

Divide by -11

x=\frac{-11}{-11} \\x=1

-------------------------------------------------------------------------

4.

\frac{x^2+7x+10}{5x-30}+\frac{x}{x-6}=\frac{x^2-13x+40}{5x-30}

It's easier if you move the operation with denominator x+6 to the right side with negative sign and bring the operation on the right side to the left side with negative sign as well.

\frac{x^2+7x+10}{5x-30}-\frac{x^2-13x+40}{5x-30}=-\frac{x}{x-6}

Now, since we have the same denominators, we can simply subtract numerators.

\frac{x^2+7x+10-(x^2-13x+40)}{5x-30} =-\frac{x}{x-6}

Distribute the negative sign.

\frac{x^2+7x+10-x^2+13x-40}{5x-30} =-\frac{x}{x-6}

Combine like terms;

\frac{20x-30}{5x-30}=-\frac{x}{x-6}

Factor.

I can see that I can factor a 5 on both numerator and numerator. This will allow me to simplify them.

\frac{(5)(4x-6)}{(5)(x-6)} =-\frac{x}{x-6}

Simplify.

\frac{4x-6}{x-6}=-\frac{x}{x-6}

Multiply by x-6

(x-6)\frac{4x-6}{x-6}=-\frac{x}{x-6}(x-6)

This will simplify the denominators.

4x-6=-x

Add x and 6.

4x+x=6\\

Combine like terms;

5x=6

Divide by 5.

x=\frac{6}{5}

You might be interested in
I need help please?!!!!!
sergiy2304 [10]

the answer is 9/16 the power is distributed among both numbers

6 0
3 years ago
Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x=12. y=
kramer
Y = 20x + 7 for instance
then just substitute the values
4 0
3 years ago
Denise gets 450 minutes each month to use on her cell phone. Last month, she used 360 minutes. What percent of her minutes did s
guajiro [1.7K]

Answer:

80%

Step-by-step explanation:

Denise used 360 minutes out of 450 minutes. You would set this up as a fraction. Then, you would have to find out the percentage of how much Denise used. You would put 360/450 across from x/100. You find the value of x by multiplying 360*100 which equals 36000. You then would divide it by 450 to get a product of 80. This is how you would get 80%.

8 0
3 years ago
Read 2 more answers
Which of the following is an example of parallel line
mote1985 [20]

c) opposite edges of a computer screen

6 0
3 years ago
Read 2 more answers
The following frequency distribution shows the yearly tuitions (in $1,000s) of a sample of private colleges.
hoa [83]

Answer:

19.714

Step-by-step explanation:

Given :

Yearly Tuition Frequency

12-16 5

17-21 4

22-26 3

27-31 2

We calculate the midpoint (x) = (lower + upper) / 2

The mean yearly tuition :

The midpoint (x) :

X ___ F ___ Fx

14 __ 5

19 __ 4

24 __ 3

29 __ 2

The mean = Σfx / Σf

Σfx / Σf = (14*5 + 19*4 + 24*3 + 29*2) / (5+4+3+2)

Mean = 276 / 14

Mean yearly tuition = 19.714

8 0
3 years ago
Other questions:
  • What’s the answer for -3(r-4)_>0
    8·1 answer
  • 2. The Soccer Club is selling T-shirts and washing cars to raise money for a summer trip. Last week, the club raised $292.50 by
    6·1 answer
  • What is 100 to the 20th power called?
    13·2 answers
  • Campare the graphs of y=ax^2 and y=(cx)^2 to the graph of the parent function y=x^2 for a=c>0​
    6·1 answer
  • If f (x)=1/3(6)x what is f(2)
    10·1 answer
  • Someone help me with this ASAP
    13·2 answers
  • Devin is going to deposit $3,000 in an account that earns 3.5% interest for 10 years. How much more INTEREST will he earn if the
    5·1 answer
  • HELP!!! Andre reads 2 1/2 pages in 1/4 hour. What is the complex fraction and unit rate?
    14·1 answer
  • PLS HELP I WILL GIVE BRAINLIEST <br><br> HELP ASAP
    12·2 answers
  • Please help me find the area for this hexagon (please show work to) ,:)
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!