The sum of the two <em>rational</em> equations is equal to (3 · n² + 5 · n - 10) / (3 · n³ - 6 · n²).
<h3>How to simplify the addition between two rational equations</h3>
In this question we must use <em>algebra</em> definitions and theorems to simplify the addition of two <em>rational</em> equations into a <em>single rational</em> equation. Now we proceed to show the procedure of solution in detail:
- (n + 5) / (n² + 3 · n - 10) + 5 / (3 · n²) Given
- (n + 5) / [(n + 5) · (n - 2)] + 5 / (3 · n²) x² - (r₁ + r₂) · x + r₁ · r₂ = (x - r₁) · (x - r₂)
- 1 / (n - 2) + 5 / (3 · n²) Associative and modulative property / Existence of the multiplicative inverse
- [3 · n² + 5 · (n - 2)] / [3 · n² · (n - 2)] Addition of fractions with different denominator
- (3 · n² + 5 · n - 10) / (3 · n³ - 6 · n²) Distributive property / Power properties / Result
To learn more on rational equations: brainly.com/question/20850120
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Answer:
4,243 cm^3
Step-by-step explanation:
In this question, we are asked to calculate the amount of gift wrap needed to cover the box.
This is indirectly telling us to calculate the volume of the triangular prism.
Mathematically, the area of a triangular prism is the area of the base multiplied. y the height.
Area of the base is 1/2 * 12 * 10.4 = 62.4 cm^2
The volume is thus 62.4 * 68 = 4,243.2 cm^3
Answer:
the angle of 3 is 50
Step-by-step explanation:
What you would do is add 90 to 40 which would get you 130. Then you will subtract 130 from 180 which gets you 50 for angle 1. Since angle 1 is across from angle 3, angle 3 will also be 50.
Answer:
<em>97.5 sq. ft.</em>
Step-by-step explanation:
Im presuming the question asks to find area of the shaded region.
First of all, the total figure is a rectangle. We can write an expression(in words) for the shaded area.
<em>Shaded Area = Area of Rectangle - Area of Small Triangle(White) - Area of Large Triangle(White)</em>
Now, we find respective areas.
Area of rectangle:
length * width = (5+10) * (12) = 15 * 12 = 180
Area of Small Triangle (white):
A = (1/2) * base * height = (1/2) * 5 * (12-3) = (1/2) * 5 * 9 = 22.5
Area of Large Triangle (white):
A = (1/2) * base * height = (1/2) * 10 * (12) = 60
Now, we find area of shaded region:
<em>Shaded Area = Area of Rectangle - Area of Small Triangle(White) - Area of Large Triangle(White)</em>
<em>Shaded Area = 180 - 22.5 - 60 = 97.5 sq. ft.</em>
The answer is going to be 4.5
