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miss Akunina [59]
3 years ago
14

The denominator of a fraction is two more than the numerator. If both numerator and denominator are decreased by six, the simpli

fied result is 1718
17


18


. Find the original fraction. (Do NOT simplify.)
Mathematics
1 answer:
ira [324]3 years ago
4 0

Answer:

\dfrac{40}{42}

Step-by-step explanation:

Let the numerator of the fraction=x

Since the denominator of a fraction is two more than the numerator.

Denominator=x+2

The fraction is therefore:

\dfrac{x}{x+2}

If both numerator and denominator are decreased by six, the fraction becomes:

\dfrac{x-6}{x+2-6}

The simplified result is \dfrac{17}{18}

Therefore:

\dfrac{x-6}{x+2-6}=\dfrac{17}{18}\\$Next, we solve for x\\Cross multiply\\18(x-6)=17(x+2-6)\\18(x-6)=17(x-4)\\Expand the bracket\\18x-108=17x-68\\Collect like terms\\18x-17x=-68+108\\x=40

Substituting x=40 into the initial fraction

\dfrac{x}{x+2}=\dfrac{40}{40+2}=\dfrac{40}{42}

Therefore, the original fraction is \dfrac{40}{42}

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Ramos went to a pizza shop and spent half of his money on lunch. If Ramos had $4.50 left after lunch, how much money did he have
blondinia [14]

The Answer is $9.00 because if you just add 4.50 to 4.50 it is $9:00.

7 0
3 years ago
The sum of the areas of two circles is 80 pi
katovenus [111]
The area of a circle is A = πr^2. We let A1 And A2 the areas of the circles and r1 and r2 the radius of each, respectivley.

A1 + A2 = 80π
Substitute the formula for the area,
π(r1)^2 + π (r2)^2 = 80π

From the statement, we know that r2=2(r1).

<span>π(r1)^2 + π (2 x r1)^2 = 80π
</span>We can cancel π, we will have

5 x (r1)^2 = 80
Thus,

r1 = 4 and r2 = 8
5 0
3 years ago
2<img src="https://tex.z-dn.net/?f=%5Cpi" id="TexFormula1" title="\pi" alt="\pi" align="absmiddle" class="latex-formula"> x 24 s
Simora [160]

Answer: 48\pi

Step-by-step explanation:

(2 \times 24)\pi=48\pi

7 0
2 years ago
Answer this question please; number 5... show all work thank you
My name is Ann [436]

Answer:

rate of the plane in still air is 33 miles per hour and the rate of the wind is 11 miles per hour

Step-by-step explanation:

We will make a table of the trip there and back using the formula distance = rate x time

                 d              =            r       x       t

there

back

The distance there and back is 264 miles, so we can split that in half and put each half under d:

               d            =         r        x        t

there    132

back     132

It tells us that the trip there is with the wind and the trip back is against the wind:

           

              d           =        r         x        t

there     132        =    (r + w)

back      132       =     (r - w)

Finally, the trip there took 3 hours and the trip back took 6:

           

             d         =        r        *        t

there    132     =    (r + w)     *       3

back     132     =    (r - w)      *       6

There's the table.  Using the distance formula we have 2 equations that result from that info:

132 = 3(r + w)        and        132 = 6(r - w)

We are looking to solve for both r and w.  We have 2 equations with 2 unknowns, so we will solve the first equation for r, sub that value for r into the second equation to solve for w:

132 = 3r + 3w and

132 - 3w = 3r so

44 - w = r.  Subbing that into the second equation:

132 = 6(44 - w) - 6w and

132 = 264 - 6w - 6w and

-132 = -12w so

w = 11

Subbing w in to solve for r:

132 = 3r + 3(11) and

132 = 3r + 33 so

99 = 3r and

r = 33

7 0
3 years ago
Find the perimeter of the window to the nearest hundredth.<br><br> also how do you do it?
k0ka [10]

  • <em>I am assuming the picture is of a stained glass window in the shape of a semicircle</em>.

Answer: 7.71 feet.

Step-by-step explanation: <em>The formula for finding the circumference of a circle is \frac{1}{2} π × d + d.</em>

The diameter is 3 feet. Substitute this into the equation:

\frac{1}{2} π × 3 + 3.

Solve -

3.14 × 3 = 9.42

\frac{1}{2} of 9.42 = 4.71

4.71+3 = 7.71

Round -

The answer is already rounded.

Hope this helped!~

6 0
3 years ago
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