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Helga [31]
3 years ago
6

The numerator of a fraction (which is in its simplest form) is 5 less than the denominator. If the numerator is multiplied by 2,

and the denominator is increased by 16, then the fraction becomes smaller by 1/3 of it. Find the original fraction.
Mathematics
1 answer:
timama [110]3 years ago
3 0
N = d - 5

2n/(d + 16) = n/d - 1/3 n/d
2n/(d + 16) = 2/3 n/d Divide by 2n
1 / (d + 16) = 1/3 d
Here's the tricky part.
d + 16 = 3d the two denominators are equal. the numerators are both 1.
16 = 2d
d = 8
so the numerator is d - 5
n = 8 - 5
n = 3

Let's see if it checks out.
n = 3
d = 8

2*3 = 6
8 + 16 = 24
New fraction 6/24 = 1/4
(3/8 - 1/3 ) = 1/8
3/8 - 1/8 = 1/4 so it checks with the original conditions put on it.


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Factor the trinomial x^2 - 16x +63
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Factor the following:
x^2 - 16 x + 63
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3 0
3 years ago
\begin{aligned} &y=2x +1 \\\\ &x-y=-3 \end{aligned} ​ y=2x+1 x−y=−3 ​ Is (2,5)(2,5)left parenthesis, 2, comma, 5, right
trapecia [35]

Answer:

Yes

Step-by-step explanation:

Given the system of equations

\begin{aligned} &y=2x +1 \\\\ &x-y=-3 \end{aligned}

We want to determine if (2,5) is a solution of the system.

We can do this by substitution of the given point into the equations and see if it holds.

Given (x,y)=(2,5), x=2, y=5

<u>In the first equation</u>

y=2x+1

5=2(2)+1

5=5

Therefore, <u>the point (2,5) satisfies the first equation.</u>

<u>In the second equation</u>

x-y=2-5=-3

Since our result (-3) is equal to the Right Hand Side, <u>the point also satisfies the second equation.</u>

<u />

Therefore, (2,5) is a solution of the system.

7 0
3 years ago
Ryan owns three-eighths of a florist shop worth $76,000. What is the value of Ryan's shares of the business?
timofeeve [1]
3/8 of 76,000....." of " means multiply

3/8 * 76,000 = 228,000/8 = 28,500 <==
6 0
3 years ago
Yo is this correct? A group of students go out to lunch. If four have burritos and two have tacos, the bill will be $19.00. If t
frez [133]

Answer:

The price of the burrito is $3.5 and the price of the taco is $2.5.

Step-by-step explanation:

2x+5y=19.5

5x+2y=22.5

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

5(2x+5y)=5(19.5)

-2(5x+2y)=-2(22.5)

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

10x+25y=97.5

-10x-4y=-45

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

21y=52.5

y=52.5/21=2.5

2x+5(2.5)=19.5

2x+12.5=19.5

2x=19.5-12.5

2x=7

x=7/2=3.5

x=3.5, y=2.5

The price of the burrito is $3.5 and the price of the taco is $2.5.

4 0
2 years ago
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