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Rama09 [41]
3 years ago
15

find a number such that if you add 8 and divide the result by 4 you will get the same answer as if you subtracted 3 from the ori

ginal number and divided by 2
Mathematics
1 answer:
blagie [28]3 years ago
8 0

Answer:

14

Step-by-step explanation:

First condition

Let the number be x

\dfrac{x+ 8}{4} = \dfrac{x - 3}{2}       Cross multiply

2(x + 8) = 4*(x - 3)                             Remove the brackets

2x + 16 = 4x - 12                               Add 12 to both sides

2x + 16 + 12 = 4x - 12 + 12                Simplify

2x + 28 = 4x                                     Subtract 2x from both sides

2x - 2x + 28 = 4x - 2x                      Simplify

28 = 2x                                             Divide both sides by 2

28/2 = 2x/2                

x = 14

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7 0
3 years ago
Brainliest for the first solution
mr Goodwill [35]

Q1  Solution:

x = 3 or x = -1

Step-by-step explanation:

x²-2x-3 = 0

In order to solve the quadratic equation by factoring, we have to determine two numbers whose sum is -2 and their product -3. By trial and error the two numbers are found to be; -3 and 1. The next step is to split the middle term by substituting it with the above two numbers found;

x²+x-3x-3  =  0

x(x+1)-3(x+1)  = 0

(x-3)(x+1) = 0

Finally we apply the zero Product Property :

If ab = 0 then a  = 0 or b  = 0

This implies;

x-3= 0 or x+1 = 0

x = 3 or x = -1 are the solutions to x²-2x-3 = 0

Q2  Solution:

x  = -1/2 or x  =  3

Step-by-step explanation:

2x²-5x-3  =0

In order to solve the quadratic equation by factoring, we have to determine two numbers whose sum is -5 and their product 2(-3)=-6. By trial and error the two numbers are found to be; -6 and 1. The next step is to split the middle term by substituting it with the above two numbers found;

2x²-6x+x-3  = 0

2x(x-3)+1(x-3) = 0

(2x+1)(x-3) = 0

2x+1 = 0 or x-3 =  0

2x = -1 or x =  3

x  = -1/2 or x  =  3 are the solutions of the given quadratic equation.

Q3 Soution:

x = 4 or x = 3

Step-by-step explanation:

x²-7x = -12

x²-7x+12 = 0

In order to solve the quadratic equation by factoring, we have to determine two numbers whose sum is -7 and their product 12. By trial and error the two numbers are found to be; -4 and -3. The next step is to split the middle term by substituting it with the above two numbers found;

x²-4x-3x+12 = 0

x(x-4)-3(x-4)  = 0

(x-4)(x-3) = 0

x-4 = 0 or x-3 = 0

x = 4 or x = 3 are the solutions of the given quadratic equation.

Q4:

x = -2/3 or x = 6

Step-by-step explanation:

3x² = 16x+12

3x²-16x-12 = 0

In order to solve the quadratic equation by factoring, we have to determine two numbers whose sum is -16 and their product 3(-12)= -36. By trial and error the two numbers are found to be; -18 and 2. The next step is to split the middle term by substituting it with the above two numbers found;

3x²-18x+2x-12 = 0

3x(x-6)+2(x-6) = 0

(3x+2)(x-6) = 0

3x+2 = 0 or x-6 =0

3x = -2 or x = 6

x = -2/3 or x = 6 are the solutions of the given quadratic equation.

Q5:

x = 6 or x = -4

Step-by-step explanation:

x²-2x-24 = 0

In order to solve the quadratic equation by factoring, we have to determine two numbers whose sum is -2 and their product -24. By trial and error the two numbers are found to be; -6 and 4. The next step is to split the middle term by substituting it with the above two numbers found;

x²-6x+4x-24 = 0

x(x-6)+4(x-6) = 0

(x-6)(x+4) = 0

x-6 = 0 or x+4 = 0

x = 6 or x = -4 are the solutions to the given quadratic equation.

Q6:

x  = 4/3 or x  = -1

Step-by-step explanation:

3x² = x+4

3x²-x-4 = 0

In order to solve the quadratic equation by factoring, we have to determine two numbers whose sum is -1 and their product -12. By trial and error the two numbers are found to be; -4 and 3. The next step is to split the middle term by substituting it with the above two numbers found;

3x²-4x+3x-4 = 0

x(3x-4)+1(3x-4)  =0

(3x-4)(x+1) = 0

3x-4 =0 or x+1 =0

3x  = 4 or x = -1

x  = 4/3 or x  = -1 are the solutions to the given quadratic equation.

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Answer:

The probability of finding aleast one or more defective charmins = 0.40951

Step-by-step explanation:

The probability of not finding a defective charmin = 1

probability of finding defective charmain = 1-0.1 =0.9

The probability of not finding all five defective item =

Then,

probability of not finding all five defective item=0.59049

Thus,

The probability of finding atleast one or more defective chairmins = 1-0.59049

Therefore,

The probability of finding atleast one or more defective chairmins =0.40951

7 0
2 years ago
90 3/7 was a demical
LenKa [72]
90.42857143 or
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6 0
3 years ago
11 less than 7 times a number is 5 more than 6 times the number. find the number.
kolezko [41]

Let's translate the words into expressions:

11 less than 7 times a number is 7x-11

5 more than 6 times the number is 6x+5

So we have the equation

7x-11 = 6x+5

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3 years ago
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