The triangle will remains in the first quadrant in all the above condition and the size of triangle is also same because only position of the triangle changes.
Further explanation:
Given:
Triangle is located in the first Quadrant.
To find:
(a) The Quadrant in which the triangle is located after series of transformation at given condition.
(b) The size of triangle after the series of transformation at given condition.
Calculation:
1. Transformation is .
As per the above transformation the coordinate of the triangle is shifted horizontally by
unit and the
coordinate is shifted vertically upwards by
units.
The triangle will remain in the first quadrant.
2. Rotated clockwise.
The triangle will be in the first quadrant and the size of triangle is also not change. Due to rotation the orientation of the triangle will change.
3. Transformation is .
As per the above transformation the coordinate of the triangle is shifted horizontally by
units and the
coordinate is shifted vertically downwards by
units.
The triangle will remains in the first quadrant.
Therefore, the triangle will remains in the first quadrant in all the above condition and the size of triangle is also same because only position of the triangle changes.
Learn more:
1. A problem on triangle brainly.com/question/7437053
2. A problem on transformation of triangle brainly.com/question/2992432
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Function
Keywords: Equations, Triangle, Transformation, Translate, first quadrant, size, x coordinate, y coordinate, shifted position, rotate clockwise, series of transformation, shifting, quadrant.
Answer:
Mixed number = 2
Improper fraction =
Step-by-step explanation:
These are the answers because:
1) The mixed number is 2 because there are two whole circles that are filled in, and the third circle is
shaded in. Therefore, the mixed number is 2
2) The improper fraction is because there 2 whole circles that are filled in which is
, and then
+
is
Hope this helps!
Answer:
match
Step-by-step explanation:
9514 1404 393
Answer:
m ≥ -√5
Step-by-step explanation:
If g(x) = f(|x|) for x∈i, then g(x) = f(x) for x∈ℝ: x ≥ 0.
f'(x) is 5th-degree, so f(x) is 6th-degree, meaning it is generally U-shaped. Since we're only concerned with x ≥ 0, we want to make sure f'(x) has no real zeros of odd multiplicity such that x > 0. The given factors of f'(x) make it have real zeros at x = -3 and x = -1.
For the last factor, (x² +2mx +5) to have no positive real zeros of odd multiplicity, we must have m ≥ 0 or the discriminant ≤ 0. The discriminant is ...
d = b² -4ac = (2m)² -4(1)(5) = 4m² -20 . . . . . discriminant of the last factor
d ≤ 0 . . . . . . . . . . the condition for no real zeros
4m² -20 ≤ 0
m² -5 ≤ 0 . . . . . . divide by 4
m² ≤ 5 . . . . . . . . .add 5
|m| ≤ √5 . . . . . . . take the square root
This tells us there will be a positive real zero of multiplicity 2 in f'(x) when m = -√5, and there will be no positive real zeros for -√5 < m < 0
There will be no odd-multiplicity positive real zeros in the derivative function f'(x) as long as m ≥ -√5. This means the slope of f(x) is non-negative for x ≥ 0, hence f(|x|) has its only minimum at x=0.
_____
<em>Additional comment</em>
The multiplicity of the zeros of f'(x) is important because the derivative will only change sign where the multiplicity is odd. When the discriminant of (x²+2mx+5) is zero, the associated positive real zero will have multiplicity 2, hence f'(x) will not change sign there.
