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
7nadin3 [17]
2 years ago
7

The denominator of a fraction is 3 more than its numerator. If 2 is added to both the numerator and the denominator, the 2 new f

raction is equivalent to Find the 3 original fraction. (Hint: Let the numerator of the original fraction be x)​
Mathematics
1 answer:
Julli [10]2 years ago
7 0

Answer:

  4/7

Step-by-step explanation:

Using the hint, we have an original fraction of x/(x+3). The given manipulations and relations can be used to find the value of x, and the original fraction.

__

<h3>adding 2 to each term</h3>

The new fraction is ...

  \dfrac{x+2}{(x+3)+2}=\dfrac{x+2}{x+5}\\

<h3>new value</h3>

Apparently, the new value of this fraction is 2/3. We can use this to find the value of x.

  \dfrac{x+2}{x+5}=\dfrac{2}{3}\\\\3(x+2)=2(x+5)\qquad\text{multiply by $3(x+5)$}\\\\3x+6=2x+10\qquad\text{eliminate parentheses}\\\\x=4\qquad\text{subtract $2x+6$}

The original fraction is ...

  4/(4+3) = 4/7

_____

<em>Alternate solution</em>

In the ratio 2/3, the numerator is twice the difference between the denominator and numerator. 2 = 2(3 -2)

The problem statement tells us the difference between the numerator and denominator is 3. That is not changed by adding the same number to each. This means the fraction equivalent to 2/3 is (2·3)/(3·3) = 6/9. Subtracting 2 from each of the numerator and denominator gives the original fraction:

  (6-2)/(9-2) = 4/7

You might be interested in
Which graph represents a proportional relationship? <br>​
Alina [70]

Answer:

If the relationship between two quantities is a proportional relationship, this relationship can be represented by the graph of a straight line through the origin with a slope equal to the unit rate. For each point (x, y) on the graph, ž is equal to k, where k is the unit rate. The point (1, k) is a point on the graph.

7 0
3 years ago
The blue segment below is a diameter of oo. What is the length of the radius
kumpel [21]
Im pretty sure it’s b
7 0
3 years ago
I beg someone help.
erastovalidia [21]

We will begin by working through Part (a): Simplify √18

To simplify a square root such as the one above, we must factor out perfect square numbers (this means we must find a number that multiplies to 18 and gives a whole number when we square root it). Using our knowledge that √9 is a perfect square, we should factor out a 9 from 18, as modeled below:

√18 = √(9*2)

We can separate this square root into two square roots multiplied together, as shown below:

√(9*2) = √9 * √2

Now, we should simplify √9, which equals 3, because 3 * 3 = 9.

√9 * √2 = 3 * √2 = 3√2

Therefore, √18 = 3√2.


Now, we can move on to the next problem: √6 * √15.

To begin this problem, we can multiply the square roots together, which means multiplying the numbers under the radical.

√6 * √15 = √(6*15) = √90

To simplify this, we use the same process as above:

√90 = √(10 * 9) = √9 * √10 = 3√10

Note: We know that this fully simplified because we cannot factor out another perfect square number from the number under the radical (10).

Therefore, your two answers are 3√2 and 3√10.

Hope this helps!

8 0
3 years ago
Read 2 more answers
4 2/3 - 2 1/3 plsss get me the answer​
posledela
The answer is 2 1/3, or 2.3 repeating.
3 0
3 years ago
Read 2 more answers
Help due soon will give brainliest
Bess [88]

Answer:

I believe the answer would be D) 12

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Other questions:
  • 3:008 3.825 3.09 3.18 greatest to least
    9·2 answers
  • What number has the same value as 50 tens
    12·2 answers
  • What is the ratio of 9 gallons to 21 quarts?(convert the measurements)
    5·1 answer
  • "TUUvui &lt;
    14·1 answer
  • Margot is studying the yield of bushels of wheat in comparison to the amount of rainfall, in inches, that occurs. She finds the
    11·2 answers
  • Paul runs 4.8 km every morning. How many feet are in 4.8 km, given that 1 mile = 1.609 km and 1 mile = 5,280 feet?
    12·2 answers
  • The bank charges 4 dollars a day for accounts under $100. Lisa's account had a balance of $15. What would the y-intercept be?
    7·1 answer
  • Select all the measurements that are equivalent to 2.4 meters.
    6·2 answers
  • Can you plase help me with this i have been posting this for a while Hello can you make me a animal mask like this my grade is l
    15·1 answer
  • X/-22=3 what is X Help
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!