In order to easily picture out the operation involving fractions, let's write it in an algebraic equation. So, the above description is written as
20x⁶/15y⁵ × 5y²/6x⁴
The first thing to do is to simplify the easiest terms: the constants. Just multiply all the constants on the numerator and all the constants on the denominator independently. The simplified constant becomes
(20*5)/(15*6) = 10/9
So, the equation to be solved now is
10x⁶y²/9y⁵ x⁴
So, I also multiplied all the variables in the numerator and denominator independently, just like the constants. Then, you apply the laws of exponents. When you divide terms with exponents of the same value of the base, you subtract the exponent on the numerator minus the denominator. It goes like this:
10/9 * x⁶⁻⁴*y²⁻⁵ = 10/9*x²y⁻³
Now, when the exponent as written to the power of a negative exponent, just simply take its reciprocal to make it positive. So, the final answer is
10x²/9y³ or that is letter D.
Answer:
Step-by-step explanation:
Method #1
We can draw a <em>right triangle</em> on the graph upon where the points are located and use the Pythagorean Theorem:
* Whenever we talk about distance, we ONLY want the NON-NEGATIVE root.
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Method #2
We can use the Distance Formula:
![\sqrt{[-x_1 + x_2]^{2} + [-y_1 + y_2]^{2}} = D](https://tex.z-dn.net/?f=%5Csqrt%7B%5B-x_1%20%2B%20x_2%5D%5E%7B2%7D%20%2B%20%5B-y_1%20%2B%20y_2%5D%5E%7B2%7D%7D%20%3D%20D)
<em>N</em>[−3, 2] <em>M</em>[−6, 0]
![\sqrt{[3 - 6]^{2} + [0 + 2]^{2}} = D](https://tex.z-dn.net/?f=%5Csqrt%7B%5B3%20-%206%5D%5E%7B2%7D%20%2B%20%5B0%20%2B%202%5D%5E%7B2%7D%7D%20%3D%20D)
![\sqrt{[-3]^{2} + 2^{2}} = D](https://tex.z-dn.net/?f=%5Csqrt%7B%5B-3%5D%5E%7B2%7D%20%2B%202%5E%7B2%7D%7D%20%3D%20D)
* Whenever we talk about distance, we ONLY want the NON-NEGATIVE root.
** You see? It does not matter which method you choose, as long as you are doing the work correctly.
I am delighted to assist you anytime.
I believe the correct answer is 3:4
i might be incorrect, if i am i am very sorry. I hope this helps!
The population model is an exponential decay because it decreases
The exponential model of the population is P = 3000(0.64^1/7)^t
<h3>How to determine the function?</h3>
The population decreases by 0.36 every 7 years.
This means that the function is an exponential decay.
An exponential decay function is represented as:
P = a((1 - r)^1/n)^t
Where:
- a represents the initial value (3000)
- r represents the rate (0.36)
- n represents the number of years the population decreases (7)
- P and t are the variables
So, we have:
P = 3000((1 - 0.36)^1/7)^t
Evaluate the difference
P = 3000(0.64^1/7)^t
Hence, the exponential model of the population is P = 3000(0.64^1/7)^t
Read more about exponential functions at:
brainly.com/question/11464095
Answer:
The vertex forms an acute angle.
