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mafiozo [28]
3 years ago
6

The square of a number decreased by twice the number is equal to 28 more than the number. Find all possible values for the numbe

r
Mathematics
1 answer:
love history [14]3 years ago
3 0

Answer:

  -4 or 7

Step-by-step explanation:

Let x represent the number. Then the problem statement tells us ...

  x^2 -2x = 28+x

  x^2 -3x = 28 . . . . . subtract x

  x^2 -3x +2.25 = 30.25 . . . . add the square of half the x coefficient

  (x -1.5)^2 = 30.25 . . . . . . . . write the left side as a square

  x -1.5 = ±5.5 . . . . . . . . . . . . take the square root

  x = 1.5 ±5.5 = {-4, 7} . . . . . . . add 1.5

The number may be either -4 or 7.

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Geraldo has 3 fewer marbles then yan. Together, they have 21 marbles. Which represents this situation ?
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X = number of Yan's marbles.  x-3 = number of Geraldo's marbles

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6 0
3 years ago
The product of two numbers is 192. what is the minimum value of the sum of the first value plus twice the second value
VARVARA [1.3K]
Let x and y be the two positive numbers. -  Their product is 192: x *  y  =  192   equation 1

-  the sum of the first plus twice the second is a minimum:  x + 2y

<span>From the first equation, y =  192 / x. 
Substitute that into the second equation:
</span>
 x + 2y = x + 2(<span>192/x ) = x + 384/x

</span>f(x) is minimum when f'(x) = 0 and f"(x) > 0 

f(x)= <span>x + 384/x
</span>
f(x) = 1-384/x^2 

<span>1-384  / x^2 =  0 

x^2-384 = 0 

x^ 2= 354
 x = radical  354    = 18.8  here i'm confused why the number is decimal
???/ 
</span>

4 0
4 years ago
Are the graphs of the lines in the pair parallel? Explain. y=2\3x-17 4x-6y=-7
Papessa [141]
<span>y=2\3x-17and  4x-6y=-7 implies  - 6y= - 4x -7, and then y= (-4/-6)x +7/6 and so 
y=2/3x+7/6

but when we have y=ax+b and y=a'x+b', the two lines are parallels if a=a', in our case 2/3=2/3 the lines are parallel
                                   </span>
6 0
3 years ago
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