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ki77a [65]
3 years ago
10

Prove that x²+6x+18 is always greater than

Mathematics
1 answer:
Annette [7]3 years ago
3 0
One way to solve this would be to graph both y=x^2+6x+18 and y=2 - 1/x.  If the graph of the polynomial is always higher up (above) the graph of y=2-1/x, that alone is sufficient cause to state that the poly is always greater than 2-1/x.

You could also do this algebraically:  write the inequality

x^2+6x+18 > 2 -1/x.  This can be rewritten as x^2+6x+18-2+1/x > 0, or
                                                                         x^2+6x+16+1/x > 0

Try x=-3.  Then 9-18+16-1/3 = 6 2/3, which is greater than 0.

Or you could graph x^2+6x+16+1/x by hand or on a calculator.  Is the graph always above the x-axis?  If so,  <span>x²+6x+18 is always greater than 2-1/x.

</span>
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Select steps that could be used to solve the equation 1 + 3x = -x + 4.
Tema [17]

For this case we have the following equation:

1 + 3x = -x + 4

We must solve the equation by following the steps below:

We subtract 1 from both sides of the equation:

3x = -x + 4-1

On the right side of the equation we have that different signs are subtracted and the sign of the major is placed:

3x = -x + 3

We add x to both sides of the equation:

3x + x = 3\\4x = 3

We divide between 4 on both sides of the equation:

x = \frac {3} {4}

Thus, the correct option is option B

Answer:

x = \frac {3} {4}

Option B

6 0
4 years ago
Read 2 more answers
HELP !! ASAP !!
Sedaia [141]

Answer:

The roots are;

x = (2 + i)/5 or (2-i)/5

where the term i is the complex number representing the square root of -1

Step-by-step explanation:

Here, we want to use the completing the square method to solve the quadratic equation;

f(x) = -5x^2 + 4x -1

Set the function to zero

0 = -5x^2 + 4x - 1

So;

-5x^2 + 4x = 1

divide through by the coefficient of x which is -5

x^2 - 4/5x = -1/5

We now take half of the coefficient of x and square it

= -2/5^2 = 4/25

add it to both sides

x^2 - 4x/5 + 4/25= -1/5 + 4/25

(x- 2/5)^2 = -1/5 + 4/25

(x - 2/5)^2 = -1/25

Take the square root of both sides

x - 2/5 = √( -1/25

x - 2/5 = +i/5 or -i/5

x = 2/5 + i/5 or 2/5 - i/5

7 0
3 years ago
<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7B5%7D%5E%7B%20-%202%7D%20%20%5Ctimes%209%7D%20%7B%20%7B2%7D%5E%7B4%7D%20%20%
Illusion [34]

Answer:

36(5)^-2.

Step-by-step explanation:

5^-2 * 9

= 9(5)^-2

2^4 * 4 ^ -3

= 2^4 + (2^2)^-3

= 2^4 * 2^-6

= 2^-2

So the answer is

9(5^)-2 / 2^-2

= 9(5)^-2 * 2^2

= 4*9(5)^-2

= 36(5)^-2.

7 0
3 years ago
WILL GIVE BRAINLIEST if you show the steps
skelet666 [1.2K]

Answer:

i really dont know how to do this

Step-by-step explanation:

3 0
3 years ago
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3. Evaluate the expression (-10) - (-4)
STatiana [176]

Answer:

-6

Step-by-step explanation:

(-10) - (-4)

-10 +4 (because negative multiply by negative is positive)

= -6 (because -10+4 means different signs means you subtract and get the sign of the bigger number)

7 0
4 years ago
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