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4 years ago

Which of the following correctly completes the the square for the equation below? x^2+18x=0

2 answers:

Nookie1986 [14]4 years ago

4 0

X² +18x = 0

To complete the square we are going to use formula a² +2ab +b² = (a+b)²

x² +2*9*x = 0
x² +2*9x+9² = 9²
(x+9)² = 9²
√(x+9)² = +/-√9²
x+9 = 9, or x+9 = -9
x=0, or x= - 18

The equation could be solved different way
x² +18x = 0
x(x+18) = 0
x=0 or x+18=0
x=0 or x=-18

My name is Ann [436]4 years ago

3 0

We know that a perfect square has the form
(x+y)^2 = x^2+2xy+y^2
If we substitute the numbers in the given equation, we have
(x+y)^2 = x^2+2xy+y^2 = x^2+2x(9) + y^2
By comparison of the coefficients of the term xy, we have y=9, hence we need y^2=9^2=81 to complete the square.

The completed square would be
(x+9)^2-81=0 (which expands back to x^2+18x=0)

However, if the objective is to solve the equation, I would solve it by factoring, i.e.
x^2+18x=0 => x(x+18)=0 => x=0 or x=-18

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jekas [21]

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5 0

4 years ago

Given the exponential equation 3x = 243, what is the logarithmic form of the equation in base 10?

weeeeeb [17]

The answer is $x= \frac{log_{10} (243 )}{log_{10} (3 )}$

$3^{x} =243$
Logarithm both sides of the equation:
$log_{10} (3^{x} ) = log_{10} (243 )$
Since: $log (a^{b}) = b*log(a)$ , then: $log_{10} (3^{x} ) =x*log_{10} (3 )$
Back to our equation:
$log_{10} (3^{x} ) = log_{10} (243 ) \\ 
x*log_{10} (3 ) = log_{10} (243 ) \\ 
x= \frac{log_{10} (243 )}{log_{10} (3 )}$

6 0

3 years ago

A Park ranger tags 100 animals. Use a proportion to estimate the total population for each sample.

7nadin3 [17]

Answer:

It is given that A Park ranger tags 100 animals.

This means the proportion of animals tagged= $\dfrac{100}{x}$

where 'x' represents the total population of animals.

We have to find total number of animals in each parts.

23 out of 100 animals are tagged.

That means the proportion of animals tagged= $\dfrac{23}{100}$

Now we know that the proportion must be equal.

$\dfrac{23}{100}=\dfrac{100}{x}$

⇒ $x=\dfrac{100\times 100}{23}=434.783$

which is approximately equal to 435.

Hence, the total population =435.

8 out of 116 animals are tagged

That means the proportion of animals tagged= $\dfrac{8}{116}$

Now we know that the proportion must be equal.

$\dfrac{8}{116}=\dfrac{100}{x}$

$x=\dfrac{100\times 116}{8}\\\\x=\dfrac{11600}{8}=1450$

which is approximately equal to 1450

Hence, the total population =1450.

5 out of 63 animals are tagged

That means the proportion of animals tagged= $\dfrac{5}{63}$

Now we know that the proportion must be equal.

$\dfrac{5}{63}=\dfrac{100}{x}$

$x=1260$

Hence, the total population =1260.

4 out of 83 animals are tagged

That means the proportion of animals tagged= $\dfrac{4}{83}$

Now we know that the proportion must be equal.

$\dfrac{4}{83}=\dfrac{100}{x}$

$x=\dfrac{100\times 83}{4}\\\\x=2075$

Hence, the total population =2075.

3 out 121 animals are tagged

That means the proportion of animals tagged= $\dfrac{3}{121}$

Now we know that the proportion must be equal.

$\dfrac{3}{121}=\dfrac{100}{x}$

$x=\dfrac{100\times 121}{3}\\\\x=4033.33$

Hence, the total population =4033.

83 out of 125 animals are tagged

That means the proportion of animals tagged= $\dfrac{83}{125}$

Now we know that the proportion must be equal.

$\dfrac{83}{125}=\dfrac{100}{x}$

$x=\dfrac{100\times 125}{83}\\\\x=150.6024$

Hence, the total population =151.

7 out 165 animals are tagged

That means the proportion of animals tagged= $\dfrac{7}{165}$

Now we know that the proportion must be equal.

$\dfrac{7}{165}=\dfrac{100}{x}$

$x=\dfrac{100\times 165}{7}\\\\x=2357.143$

Hence, the total population =2357.

7 0

3 years ago

√8x^2 divided by √2x

Ghella [55]

Question: Simplify $\frac{\sqrt{8x^2}}{\sqrt{2x}}$ .

First off, you <em>never</em> want square roots on the bottom of a fraction, so let's multiply both sides by $\sqrt{2x}$ to get rid of it. All we have to do from there is simplify!

$\frac{\sqrt{8x^2}}{\sqrt{2x}}*\frac{\sqrt{2x}}{\sqrt{2x}}=\frac{\sqrt{8x^2}*\sqrt{2x}}{2x}}=\frac{\sqrt{16x^3}}{2x}=\frac{4x\sqrt{x}}{2x}=\boxed{2\sqrt{x}}$

7 0

3 years ago

Read 2 more answers

What is the product of (n -8)(n + 2)?

xenn [34]

Answer:

n2-6n-16

Step-by-step explanation:

n(n+2)-8(n+2)

n2+2n-8n-16=

n2-6n-16

6 0

3 years ago