9514 1404 393
Answer:
36°, 54°, 90°
Step-by-step explanation:
We have to assume that the given measures are <em>angle</em> ratios, not <em>side</em> ratios. Sides in the ratios 2:3:5 will not form a triangle.
For some multiplier x, the angle values will total 180°.
2x +3x +5x = 180
x = 180/(2+3+5) = 18
Then the angle measures are ...
2x° = 2·18° = 36°
3x° = 3·18° = 54°
5x° = 5·18° = 90°
The angle measures are 36°, 54°, and 90°.
By "y = −9x2 − 2x" I assume you meant <span>y = −9x^2 − 2x (the "^" symbol represents exponentiation).
Let's find the first derivative of y with respect to x: dy/dx = -18x - 2. This is equivalent to the slope of the tangent line to the (parabolic) curve. Now let this derivative (slope) = 0 and solve for the critical value: -18x - 2 = 0, or
-18x = 2. Solving for x, x = -2/18, or x = -1/9.
When x = -1/9, y = -9(-1/9)^2 - 2(-1/9). This simplifies to y = -9/9 + 2/9, or
y = -7/9.
The only point at which the tangent to the curve is horiz. is (-1/9,-7/9).</span>
Answer: Segment GD is parallel to segment HC.
Step-by-step explanation:
In ΔAHC
AG=GH (given)...........1
As BD is the median of ΔABC bisecting AC at D
∴AD=DC.........2
⇒
(from 1 and 2)
⇒segment GD is dividing the sides AH and AC in same ratio.
Therefore by the converse of Basic proportionality theorem,segment GD is parallel to segment HC.
Converse of basic probability theorem states that if a line divides any two sides of a triangle in the same ratio, then the line must be parallel to the third side.
Answer:
x ≈ 33.0
Step-by-step explanation:
The third angle in the triangle is
180° - 70° - 76° = 180° - 146° = 34°
Using the Sine rule in the triangle
=
( cross- multiply )
x × sin34° = 19 × sin76° ( divide both sides by sin34° )
x =
≈ 33.0 ( to the nearest tenth )