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
Katyanochek1 [597]
3 years ago
7

5. (05.03 LC) What is the simplified form of the quantity of x plus 5, all over the quantity of 3x plus 4 + the quantity of x pl

us 4, all over the quantity of x plus 3 ? (2 points)
A) the quantity of 2x plus 9, all over the quantity of 4x plus 7
B) the quantity of 4x squared plus 24x plus 31, all over the quantity of 3x squared
plus 13x plus 12
C) the quantity of 4x squared plus 24x plus 31, all over the quantity of 4x plus 7 D) the quantity of 2x plus 9, all over the quantity of 3x squared plus 13x plus 12
Mathematics
1 answer:
earnstyle [38]3 years ago
8 0

Answer:

B. \frac{4x^{2}+24x+31}{3x^{2}+13x+12}

Step-by-step explanation:

We have been given a rational expression \frac{(x+5)}{(3x+4)}+\frac{(x+4)}{(x+3)} and we are asked to simplify our rational expression.

We can see that our denominators are not equal. Since the two denominators do not share any common factors, the common denominator is simply the product of these two denominators.      

To keep the value of expression same we will multiply the same quantity with numerators and denominators.

\frac{(x+5)(x+3)}{(3x+4)(x+3)}+\frac{(x+4)(3x+4)}{(x+3)(3x+4)}  

Now let us simplify our expression using FOIL.  

\frac{x^{2}+3x+5x+15}{3x^{2}+9x+4x+12}+\frac{3x^2+4x+12x+16}{3x^{2}+4x+9x+12}

\frac{x^{2}+8x+15}{3x^{2}+13x+12}+\frac{3x^2+16x+16}{3x^{2}+13x+12}    

Now we have same denominators, so we can add our numerators.

\frac{x^{2}+8x+15+3x^2+16x+16}{3x^{2}+13x+12}    

Now let us combine like terms.

\frac{(1+3)x^{2}+(8+16)x+15+16}{3x^{2}+13x+12}  

\frac{4x^{2}+24x+31}{3x^{2}+13x+12}  

Therefore, the simplest form of our given rational expression will be \frac{4x^{2}+24x+31}{3x^{2}+13x+12}  and option B is the correct choice.

You might be interested in
Which is the net for this rectangular prism?
dybincka [34]

Answer:

On the left the one down below

Step-by-step explanation: I check it to make sure it was right

3 0
2 years ago
A man age is three times his sons age. ten years ago was five times his sons age. find their current age.
kow [346]

Answer:

The son is 20

The man is 60

Step-by-step explanation:

We can set up this equation with what we know. Let <em>m</em> stand for the Man's current age, and let <em>s</em> stand for his son's current age.

We know the Man's current age is three times that of his son, so this equation can be written as: <em>m = 3s</em>

Ten years ago means the man's current age <em>minus</em> 10 years. So it is <em>m-10</em>. So ten years ago he was 5 times his son's age 10 years ago, <em>5(s-10)</em>

This can be written as: <em>m-10=5(s-10)</em>

Solve with either substitution or elimination, the choice is yours, it doesn't really matter which method you use. I'll be using substitution.

<em>m-10=5(s-10)</em>

<em>3s-10= 5s-50</em>

<em>40=2s</em>

<em>20 = s</em>

The son is <em>20</em> years old.

We know the man is currently 3 times his son's age, because <em>m=3s</em>, so just solve for m since you now know the value of <em>s.</em>

<em>m=3s</em>

<em>m=3(20)</em>

<em>m=60</em>

The man is <em>60</em> years old

4 0
3 years ago
(a) How many integers from 1 through 1,000 are multiples of 2 or multiples of 9?
DENIUS [597]

Answer:

(a)There are 500 integers from 1 through 1,000 are multiples of 2.

There are 111 integers from 1 through 1,000 are multiples of 9.

(b)0.611

Step-by-step explanation:

Given the set of Integers from 1 through 1000

The least multiple of 2 is 2 and the highest multiple of 2 in the interval is 1000.

To determine the number of terms, we use the formula for the nth term of an Arithmetic Progression, since 2,4,6,... is an Arithmetic Progression,

where first term, a =2, common difference, d =2

Nth term of an A.P,

U_n= a+(n-1)d\\1000=2+2(n-1)\\1000=2+2n-2\\1000=2n\\n=500

  • There are 500 integers from 1 through 1,000 are multiples of 2.

Similarly,

Given the set of Integers from 1 through 1000

The least multiple of 9 is 9 and the highest multiple of 9 in the interval is 999.

To determine the number of terms, we use the formula for the nth term of an Arithmetic Progression, since 9,18,27,... is an Arithmetic Progression,

where first term, a =9, common difference, d =9

Nth term of an A.P,

U_n= a+(n-1)d\\999=9+9(n-1)\\999=9+9n-9\\999=9n\\n=111

  • There are 111 integers from 1 through 1,000 are multiples of 9.

(b)Probability that an integer selected at random is a multiple of 2 or a multiple of 9.

There are a total of 1000 numbers between from 1 through 1,000

n(S)=1000

n(Multiples of 2)=500

n(Multiples of 9)=111

Therefore:

P(\text{Multiples of 9}) \:OR\: P(\text{Multiples of 2})=\frac{111}{1000} + \frac{500}{1000} \\=\frac{611}{1000} \\=0.611

7 0
3 years ago
Help! Please answer!! Wil mark Brainiliest!
Mademuasel [1]
An exponential function displays either a growth or decay behavior going from a low steep to a high steep.
3 0
3 years ago
A bag contains 8 3/4 pounds of cat food . How many 3/8 pound servings can be made from the bag? please answer :(
LiRa [457]

Answer: 23 1/3

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • I'm stuck and don't know what to do
    14·1 answer
  • Someone please help me
    9·1 answer
  • V=kfovern   what does n=
    10·1 answer
  • Estimate 15.89+5.557 by first rounding each number to the nearest tenth
    5·2 answers
  • (y − 3)^2 = 4(x − 5), (6, 1). Find an equation of the tangent line to the graph at the given point.
    5·1 answer
  • 5. Order these from least to greatest.<br> 1/2,4/9, 2/3,5/6
    11·1 answer
  • 0.782 ___ 0.784<br> I Need HElP NOW!
    6·2 answers
  • How’s everyone’s day going? Mine is okayish. Not so bad but not so good either. If you are in remote learning , are you flying t
    6·2 answers
  • HELP ME PLEASEEEE THANKUU!!! I REALLY NEED IT !!!​
    10·1 answer
  • Find the total surface area of this triangular prism<br> 25 cm<br> 24 cm<br> 10 cm<br> 14 cm
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!