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zmey [24]
2 years ago
9

What is the solution to 2x2+8x=x2-16?

Mathematics
2 answers:
natita [175]2 years ago
6 0

Answer:

x = -4

Step-by-step explanation:

=> 2x²+8x = x²-16

=> 2x²- x² + 8x + 16 = 0

=> x² + 8x + 16 = 0

<u><em>Using mid-term break formula</em></u>

=> x² + 4x + 4x + 16 = 0

=> x(x+4)+4(x+4) = 0

=> (x+4)(x+4) = 0

=> (x+4)² = 0

<em>Taking square root on both sides</em>

=> x+4 = 0

=> x = -4

Semmy [17]2 years ago
3 0

Answer:

x = -4

Step-by-step explanation:

1. (2x2 +  8x) -  (x2 - 16)  = 0

2. Factoring  x2+8x+16  

The first term is,  x2  its coefficient is  1 .

The middle term is,  +8x  its coefficient is  8 .

The last term, "the constant", is  +16  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 16 = 16  

Step-2 : Find two factors of  16  whose sum equals the coefficient of the middle term, which is   8 .

     -16    +    -1    =    -17  

     -8    +    -2    =    -10  

     -4    +    -4    =    -8  

     -2    +    -8    =    -10  

     -1    +    -16    =    -17  

     1    +    16    =    17  

     2    +    8    =    10  

     4    +    4    =    8    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  4  and  4  

                    x2 + 4x + 4x + 16

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x+4)

             Add up the last 2 terms, pulling out common factors :

                   4 • (x+4)

Step-5 : Add up the four terms of step 4 :

                   (x+4)  •  (x+4)

            Which is the desired factorization

Multiply  (x+4)  by  (x+4)  

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (x+4)  and the exponents are :

         1 , as  (x+4)  is the same number as  (x+4)1  

and   1 , as  (x+4)  is the same number as  (x+4)1  

The product is therefore,  (x+4)(1+1) = (x+4)2

(x + 4)2  = 0

3.

Solve  :    (x+4)2 = 0  

 (x+4) 2 represents, in effect, a product of 2 terms which is equal to zero

For the product to be zero, at least one of these terms must be zero. Since all these terms are equal to each other, it actually means :   x+4  = 0

Subtract  4  from both sides of the equation :  

                     x = -4

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slamgirl [31]

Answer:

  1. 108 cm^2
  2. 211.2 cm^2
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Step-by-step explanation:

In each case, you can use the given formula to find the surface area. The area of the triangular base (B) is ...

  A = 1/2bh

where b is the base of the triangle, and h is the height of the triangle perpendicular to that base.

You will notice that B is multiplied by 2 in the area formula, because there is a triangular base at either end of the prism. That means we can save some work by not multiplying by 1/2, and then by 2.

__

For figures 1, 3, 4, the triangle is a right triangle, so the base and height make up two of the three sides of it. The perimeter is finished by adding the length of the hypotenuse. That sum is then multiplied by the "height" of the prism (distance between bases) to find the lateral area as part of the area formula (Ph).

In figure 3, the triangle is equilateral, so the perimeter is not the sum of the base and height and a third side. In the attached spreadsheet, we have used a value "rest of perimeter" to make the sum be the right value for use in computing the value of Ph. For figure 3, that is 6+6-5.2=6.8. Then the sum 6 +5.2 +6.8 is 18, the proper perimeter for that figure.

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The idea here is to let a spreadsheet do the tedious work of applying the same formula to different sets of numbers. The areas are ...

  1. 108 cm^2
  2. 211.2 cm^2
  3. 308.8 mm^2
  4. 560 yd^2

__

By way of example, we can "show work" for problem 1:

1. S = Ph +2B

  S = (4 +3 +5)(8) +2(1/2)(4)(3) = 12(8) +12 = 96 +12 = 108 . . . cm^2

4 0
2 years ago
Read 2 more answers
Factor this x^3 + 27
masya89 [10]
(x+3)(x^2-3x+9)

this gets the x^3 while the 3x cancels out and 3*9=27

hope this helps although i didn't explain very well :)
8 0
2 years ago
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e-lub [12.9K]
The number is (2√3) / 3

To find the missing number, convert what it says in words to an equation:
15 {x}^{2}  = 20x
Divide both sides by 15:
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Take the square root:
x =  \sqrt{ \frac{4}{3} }  \\  \\ x =  \frac{2}{ \sqrt{3} }  \\  \\ x =  \frac{2 \sqrt{3} }{3}
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