If we are scaling up the surface area by a factor of 10 means that the two dimensions of area are each being increased by 10 times the original size. Therefore, the surface area is increased by a factor of 10 x 10, or by a factor of 100.
Answer: To know whether a radical expression is in simplest form or not you should put the numbers and letters inside the radical in terms of prime factors. Then, the radical expression is in the simplest form if all the numbers and letters inside the radical are prime factors with a power less than the index of the radical
Explanation:
Any prime factor raised to a power greater than the index of the root can be simplified and any factor raised to a power less than the index of the root cannot be simplified
For example simplify the following radical in its simplest form:
![\sqrt[5]{3645 a^8b^7c^3}](https://tex.z-dn.net/?f=%20%5Csqrt%5B5%5D%7B3645%20a%5E8b%5E7c%5E3%7D%20)
1) Factor 3645 in its prime factors: 3645 = 3^6 * 5
2) Since the powr of 3 is 6, and 6 can be divided by the index of the root, 5, you can simplify in this way:
- 6 ÷ 5 = 1 with reminder 1, so 3^1 leaves the radical and 3^1 stays in the radical
3) since the factor 5 has power 1 it can not leave the radical
4) the power of a is 8, then:
8 ÷ 5 = 1 with reminder 3 => a^1 leaves the radical and a^3 stays inside the radical.
5) the power of b is 7, then:
7 ÷ 5 = 1 with reminder 2 => b^1 leaves the radical and b^2 stays inside the radical
6) the power of c is 3. Since 3 is less than 5 (the index of the radical) c^3 stays inside the radical.
7) the expression simplified to its simplest form is
![3ab \sqrt[5]{3.5.a^3b^2c^3}](https://tex.z-dn.net/?f=3ab%20%5Csqrt%5B5%5D%7B3.5.a%5E3b%5E2c%5E3%7D%20)
And you know
it cannot be further simplified because all the numbers and letters inside the radical are prime factors with a power less than the index of the radical.
The inequality that represents the possible ways nina can eat 12 or more grams of protein is 2x + 3y ≥ 12
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more number and variables.
Let x be the number of cheese squares that she eats and y is the number of turkey slices that she eats. If nina can eat 12 or more grams of protein, hence:
2x + 3y ≥ 12
The inequality that represents the possible ways nina can eat 12 or more grams of protein is 2x + 3y ≥ 12
Find out more on equation at: brainly.com/question/2972832
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Did you mean this? <span>3^2x+1=3^x+5 => 3^(2x+1) = 3^(x+5)? If so, then 2x+1 is necessarily equal to x+5, so that 2x+1=x+5. Thus, x = 4 (answer).
Those parentheses are not optional; they must be part of your problem statement and solution.</span>
Rate of change is slope
So change in y/change in x
150/3=50