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Anna71 [15]
3 years ago
7

Complete the square for each expression. Then factor the Trinomial x^2+8x

Mathematics
1 answer:
Goryan [66]3 years ago
8 0

The value of x is x=0 or x=-8

Step-by-step explanation:

The expression is x^{2} +8x=0

To complete the square, the equation is of the form ax^{2} +bx+c=0

The constant term c can be determined using, c=\left(\frac{\frac{b}{a}}{2}\right)^{2}

\begin{aligned}c &=\left(\frac{8}{2}\right)^{2} \\&=\left(\frac{8}{2}\right)^{2} \\c &=4^{2} \\c &=16\end{aligned}

Rewriting the expression x^{2} +8x=0 and factoring the trinomial, we have,

\begin{array}{r}{x^{2}+8 x+16=16} \\{(x+4)^{2}=16}\end{array}

Taking square root on both sides, we get,

\begin{aligned}&x+4=\sqrt{16}\\&x+4=\pm 4\end{aligned}

Either,

\begin{array}{r}{x+4=4} \\{x=0}\end{array}  or \begin{array}{r}{x+4=-4} \\{x=-8}\end{array}

Thus, the value of x is  x=0 or x=-8

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Answer:

= 298/11

Step-by-step explanation:

3x + 5y = 2 | ×2 |

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6x + 10y = 4

6x - 12y = 60

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22y = -56

y = -56/22

y = -28/11

3x + 5y = 2 | ×4 |

2x - 4y = 20 | ×5 |

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22x = 108

x = 108/22

x = 54/11

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= 5(54/11) - (-28/11)

= 270/11 + 28/11

= 298/11

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2 years ago
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A and B are postive integers such that 1/a + 1/b +1/ab = 1. Find ab
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have:

\frac{1}{a}+\frac{1}{b}+\frac{1}{ab}=1\\\\=>\frac{b}{ab}+\frac{a}{ab}+\frac{1}{ab}=1\\\\\frac{a+b+1}{ab}=1

=> a + b + 1 = ab

⇔ a + b + 1 - ab = 0

⇔ b - 1 - a(b - 1) + 2 = 0

⇔ (b - 1)(1 - a) = -2

because a and b are postive integers => (b - 1) and (1 - a) also are integers

=> (b - 1) ∈ {-1; 1; 2; -2;}

(1 -a) ∈  {-1; 1; 2; -2;}

because (b -1).(1-a) = -2 => we have the table:

b - 1        -1             1              2             -2

1 - a         2            -2            -1              1

a              -1            3             2              0

b              0            2             3              -1

a.b            0           6             6               0

because a and b  are postive integers

=> (a;b) = (3;2) or (a;b) = (2;3)

=> ab = 6

Step-by-step explanation:

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Answer:

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Hence lake will never be free of pesticide.

5 0
3 years ago
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