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3 years ago

Which equation can you solve to find the potential solutions to the equation log2x + log2(x – 6) = 4?

2 answers:

8 0

$\text{The domain:}\\x \ \textgreater \ 0\ \wedge\ x-6 \ \textgreater \ 0\\x \ \textgreater \ 0\ \wedge\ x \ \textgreater \ 6\\\\D:x\in(6;\ \infty)\\\\\log_2x+\log_2(x-6)=4\\\\\log_2[x(x-6)]=\log_22^4\iff x^2-6x=16\\\\x^2-2\cdot x\cdot3=16\ \ \ \ |+3^2\\\\\underbrace{x^2-2\cdot x\cdot3+3^2}_{(a-b)^2=a^2-2ab+b^2}=16+3^2\\\\(x-3)^2=25\to x+3=\pm\sqrt{25}\\\\x-3=-5\ \vee\ x-3=5\ \ \ \ |+3\\\\x=-2\notin D\ \vee\ x=8\in D\\\\Answer:\ x=8$

$\text{Used:}\\\\\log_ab+\log_ac=\log_a(b\cdot c)\\\\\log_ab=c\iff a^c=b$

Karolina [17]3 years ago

8 0

Answer:

The answer is C on engenuity

Step-by-step explanation:

x2 – 6x – 16 = 0

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erica [24]

Answer:

The answer should be C

Step-by-step explanation:

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3 years ago

To find 5, Beau found 22 = 4 and 32 = 9. He said that since 5 is between 4 and 9, 5 is between 2 and 3. Beau thinks a good estim

shusha [124]

Complete question

To find $\sqrt{5}$ , Beau found $2^2 = 4$ and $3^2 = 9$ . He said that since 5 is between 4 and 9, $\sqrt{5}$ , is between 2 and 3. Beau thinks a good estimate for $\sqrt{5}$ , is $\frac{2 + 3}{2} = 2.5$ Is his estimate high or low? How do you know?

Answer:

The estimation is high because 5 is very close to 4 so $\sqrt{5}$ will also be very close to $\sqrt{4}$ which is lower than the estimate

In order to get a good estimate

The first step is to choose a number between 2 and 3 let say 2.8 , 2,85 , 2.9 and the square them

i.e

$2.1^2 = 4.41$

$2.2^2 = 4.84$

$2.3^2 = 5.29$

From here we can see that $\sqrt{5}$ lies between 2.2 and 2.3 but is closer to 2.2

So a good estimate for $\sqrt{5}$ is 2.2

Step-by-step explanation:

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3 years ago

Divide square root 9^2 by square root 18y^2

Klio2033 [76]

I got y^2/2

My Solution:

√9^2/18 · y^2

= 1/2 y^2

Multiply Fractions: a · (b/c) = (a · b)/c

1·y^2/2

=y^2/2

Hope I helped,
Faith xx

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3 years ago

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anastassius [24]

Let A= the sky is red at night
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4 years ago

Select the correct answer. Which point lies on a circle with a radius of 5 units and center at P(6, 1)? A. Q(1, 11) B. R(2, 4) C

jasenka [17]

Answer:

T(9,-2)

Step-by-step explanation:

The circle has radius 5 units and center P(6,1).

The equation of this circle is

$(x-6)^2+(y-1)^2=5^2$