Keep in mind that, the directrix is "p" distance units away from the vertex, and the focus point is also "p" distance units from the vertex but in the opposite direction, so in short the vertex is half-way between both of them.
in this case the vertex is at the origin, and the directrix 5 units above it, so that means the parabola is vertical and opening downwards, like the one in the picture below, and the focus point is 5 units the other way.
Answer:
x = - 4
Step-by-step explanation:
Given
3 - 2 |0.5x + 1.5 | = 2 ( subtract 3 from both sides )
- 2 |0.5x + 1.5 | = - 1 ( divide both sides by - 2 )
|0.5x + 1.5 | = 0.5
The absolute value function always gives a positive value, however, the expression inside can be positive or negative, thus
0.5x + 1.5 = 0.5 ( subtract 1.5 from both sides )
0.5x = - 1 ( divide both sides by 0.5 )
x = - 2 ← solution Manuela obtained
OR
-(0.5x + 1.5) = 0.5 ← distribute parenthesis on left side by - 1
- 0.5x - 1.5 = 0.5 ( add 1.5 to both sides )
- 0.5x = 2 ( divide both sides by - 0.5 )
x = - 4 ← other solution to the equation
Answer:
A. 42, 120, 162
Step-by-step explanation:
27 x 6 = 162
or
42 + 120 = 162
Answer:
5 chickens, 20 goats
Step-by-step explanation:
We can set up two equations and use substitution
There are 25 total goats and chickens, so
Goats have 4 feet and chickens have two, so
By solving for G in the first equation,
We can now use substitution,
We have 5 chickens, so we have 20 goats.
Let's double check:
It checks out!
