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joja [24]
2 years ago
12

Simplify the radical expression.

Mathematics
1 answer:
tresset_1 [31]2 years ago
5 0

To simplify this fraction, multiply the entire fraction by the conjugate of the denominator. The conjugate of a square root and a number being added to it would be the number <em>subtracted </em>from the square root. In other words, the conjugate of \sqrt{a} + b would be\sqrt{a} - b.


Applying that information to our fraction shown here, the conjugate of the denominator would be \sqrt{3} - 4. We will multiply both the numerator and denominator of our original fraction by this expression to obtain our answer, as shown below.


\Big(\dfrac{1}{\sqrt{3} + 4}\Big)\Big(\dfrac{\sqrt{3} - 4}{\sqrt{3} - 4}\Big)

\dfrac{\sqrt{3} - 4}{3 - 16}

\dfrac{4 - \sqrt{3}}{13}


Our answer is \boxed{\dfrac{4 - \sqrt{3}}{13}}.


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pentagon [3]

Answer:

= x 3048

Step-by-step explanation:

6 0
2 years ago
Heather's school is switching from block scheduling to a more traditional schedule. She is trying to determine how the parents a
k0ka [10]
Had to look for the options for this question and here is my answer.
Based on the given scenario above regarding Heather school's scheduling, I can say that the question that would be the most appropriate for her to ask is "How do you feel about your child having to take summer school in order to graduate based on this traditional schedule?" Hope this helps.
8 0
3 years ago
What is the serving of coffee? 1 quart, 1 ml, or 1 c
ruslelena [56]
1 quart I think tbh idk but i think .
5 0
3 years ago
How do you do this question?
Alex Ar [27]

Step-by-step explanation:

(a) dP/dt = kP (1 − P/L)

L is the carrying capacity (20 billion = 20,000 million).

Since P₀ is small compared to L, we can approximate the initial rate as:

(dP/dt)₀ ≈ kP₀

Using the maximum birth rate and death rate, the initial growth rate is 40 mil/year − 20 mil/year = 20 mil/year.

20 = k (6,100)

k = 1/305

dP/dt = 1/305 P (1 − (P/20,000))

(b) P(t) = 20,000 / (1 + Ce^(-t/305))

6,100 = 20,000 / (1 + C)

C = 2.279

P(t) = 20,000 / (1 + 2.279e^(-t/305))

P(10) = 20,000 / (1 + 2.279e^(-10/305))

P(10) = 6240 million

P(10) = 6.24 billion

This is less than the actual population of 6.9 billion.

(c) P(100) = 20,000 / (1 + 2.279e^(-100/305))

P(100) = 7570 million = 7.57 billion

P(600) = 20,000 / (1 + 2.279e^(-600/305))

P(600) = 15170 million = 15.17 billion

7 0
2 years ago
What is 3/8<br> as an equivalent fraction with the LCM as the denominator?
tino4ka555 [31]

Answer:

3/8 = 9/24

Step-by-step explanation:

So here we have a basic multiplication problem and finding the LCM of 8 and 3. The first step in this problem is finding the LCM of 3/8. The LCM of 3 and 8 is 24. So yay! we have the bottom half of our answer!

Ex.-

The LCM of 8 and 3 is 24.

So now we have to find an equivalent fraction. Since we already know that 8 (the denominator in the original equation) can be multiplied by 3 to equal 24, we use 3 (the numerator in the original equation) and multiply it by itself to get an equivalent fraction.

Ex.-

8 x 3 = 24

3 x 3 = 9

Now that we have our numerator and denominator, all we have to do now is put them together to get our answer.

Ex.-

9/24 (answer) = 3/8 (original equation)

Hopefully I could help! :)

4 0
2 years ago
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