Angle 3 is equal to angle 5 because of vertical angles.
Answer:
The parabola is translated down 2 units.
Step-by-step explanation:
You have the parabola f(x) = 2x² – 5x + 3
To change this parabola to f(x) = 2x² - 5x + 1, you must have performed the following calculation:
f(x) = 2x² – 5x + 3 -2= 2x² - 5x + 1 <u><em>Expresion A</em></u>
The algebraic expression of the parabola that results from translating the parabola f (x) = ax² horizontally and vertically is g (x) = a(x - p)² + q, translating in the same way as the function.
- If p> 0 and q> 0, the parabola shifts p units to the right and q units up.
- If p> 0 and q <0, the parabola shifts p units to the right and q units down.
- If p <0 and q> 0, the parabola shifts p units to the left and q units up.
- If p <0 and q <0, the parabola shifts p units to the left and q units down.
In the expression A it can be observed then that q = -2 and is less than 0. So the displacement is down 2 units.
This can also be seen graphically, in the attached image, where the red parabola corresponds to the function f(x) = 2x² – 5x + 3 and the blue one to the parabola f(x) = 2x² – 5x + 1.
In conclusion, <u><em>the parabola is translated down 2 units.</em></u>
Basically, what is the least common multiplule
first factor
8=2*2*2
14=2*7
then group so you can find all factors
lcm=2*2*2*7=56
answer is is on day 56
Answer:
Step-by-step explanation:
By triangle sum theorem,
73°+ 39° + m∠1 = 180°
m∠1 = 180° - 102°
m∠1 = 78°
Since, m∠1 = m∠2 [Vertically opposite angles]
m∠2 = 78°
Sum of interior angles of a polygon = (n - 2)×180°
Where n = number of sides of the polygon
Sum of the interior angles of a quadrilateral = (4 - 2)×180°
= 360°
Therefore, 77° + m∠3 + 90° + m∠2 = 360°
77° + m∠3 + 90° + 78° = 360°
m∠3 = 360° - 245°
m∠3 = 115°
Answer:
3.6 feet
Step-by-step explanation:
The height of the rollercoaster in feet throughout the underground section is modeled by the equation :
....(1)
We need to find the height of the rollercoaster 6 feet horizontally through the underground section.
Put d = 6 feet in equation (1) as follows :
![h(6) = 0.15(6)^2 - 1.5(6)\\\\h=-3.6\ \text{feet}](https://tex.z-dn.net/?f=h%286%29%20%3D%200.15%286%29%5E2%20-%201.5%286%29%5C%5C%5C%5Ch%3D-3.6%5C%20%5Ctext%7Bfeet%7D)
or
h = 3.6 feet
So, the height of the rollercoaster 6 feet horizontal through the underground section is 3.6 feet.