Yes, they can be added and simplified further. 2√3 + 5√3 = 7√3 .
Take √3 as common factor:
2√3 + 5√3
(2 + 5)√3
7√3
The two irrational numbers sums to form another irrational number 7√3 . In decimals that is 12.12435...
20 : 5
Divide a common factor between these two numbers to simplify
Divide 5
20 / 5 = 4
5 / 5 = 1
The ratio simplified would be 4 : 1
Answer:
axis of symmtery: x = 3 or h = 3
Step-by-step explanation:
The vertex (h, k) of a parabola is the point wherein the graph intersects the axis of symmetry—the imaginary straight line that bisects a parabola into two symmetrical parts, where <em>x</em> =<em> h</em>.
- In the standard form of quadratic equation, y = ax² + bx + c, the equation of the axis of symmetry is:
.
- In the vertex form of the quadratic equation, y = a(x - h)² + k, the equation of the axis of symmetry is:
.
Regardless of whether the quadratic equation is in standard or vertex form, the x-coordinate (h) of the vertex determines the axis of symmtetry, hence<em>, </em><em>x = h. </em><em> </em>
Therefore, given that the vertex of a parabola is at point (3, 5), then it means that the axis of symmetry occurs at x = 3 or h = 3.
Answer:
| a - b | < length of third side < a + b
Step-by-step explanation:
Visualize the two given sides of the triangle (let's call then a and b), joined at the vertex of the triangle, and forming an angle. We can join the other free end of these two segments, with another segment whose length would vary according to how tiny or large the angle is. We can spread the aperture of the angle they form as much as we can just below (not reaching this angle measure, because in such case, there will be no triangle of tangible area. In such case, the length of the joining segment will be limited by the addition of the two sides:
length of third side < a + b
In the case the aperture of the angle formed by the two given sides is diminished as much as possible to still form a measurable triangle, the angle has to be just larger than zero, and in such case, the segment joining the other to ends of a and b would be just larger than the absolute value of the difference between a and b:
length third side > | a - b|
These are the two extreme cases, and the length of the third side must be within these limits.
