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Lelechka [254]
3 years ago
11

The reciprocal of 5 less than a number is 4 times the reciprocal of twice the number. find the number.

Mathematics
1 answer:
ivolga24 [154]3 years ago
6 0
5 less than the number is x - 5
The reciprocal is 1/(x - 5)

This number is 1/(x - 5) = 4(1/(2x)) Cross multiply.
2x = 4*(x - 5) Remove the brackets.
2x = 4x - 20 Subtract 2x from both sides
0 = 4x - 2x - 20
0 = 2x - 20 Add 20 to both sides
20 = 2x Divide by 2
20/2 = x
10 = x
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3 years ago
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Solve the following equation, answer as a reduced, mixed number. Then place the correct number in the box provided. 4(7 - 3x) =
Luda [366]

Answer:  x = 0

<u>Step-by-step explanation:</u>

4(7 - 3x) = 7(4 - 2x)

28 - 12x = 28 - 14x        <em>distributed</em>

28 + 2x = 28                 <em>added 14x to both sides</em>

       2x = 0                    <em>subtracted 28 from both sides</em>

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3 0
3 years ago
Determine the vertex of the function f(x) = 3(x − 2)2 + 1.
anastassius [24]

The vertex point of the function f(x) = 3(x - 2)² + 1 is (2 , 1) ⇒ answer A

Step-by-step explanation:

Any quadratic function represented graphically by a parabola

1. If the coefficient of x² is positive, then the parabola open upward

  and its vertex is a minimum point

2. If the coefficient of x² is negative, then the parabola open

   downward and its vertex is a maximum point

3. The standard form of the quadratic function is: f(x) = ax² + bx + c

    where a, b , c are constants

4. The vertex form of the quadratic function is: f(x) = a(x - h)² + k,

     where h , k are the coordinates of its vertex point

∵ The function f(x) = 3(x - 2)² + 1

∵ The f(x) = a(x - h)² + k in the vertex form

∴ a = 3 , h = 2 , k = 1

∵ h , k are the coordinates of the vertex point

∴ The coordinates of the vertex point are (2 , 1)

The vertex point of the function f(x) = 3(x - 2)² + 1 is (2 , 1)

Learn more:

You can learn more about quadratic function in brainly.com/question/1357167

#LearnwithBrainly

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