Answer:
or 
Step-by-step explanation:
<em>The question in English is</em>
Juan built a ramp that is 5 m long and 1 m high. How much is the distance (d) he travels when he climbs the ramp?
let
x -----> the length of the ramp
y ----> the height of the ramp
d ----> the distance Juan travels when he climbs the ramp
we know that
Applying the Pythagoras Theorem

we have


substitute the given values


-----> exact value
----> approximate value
X^2+6x+8=0
To write the above in the form of (x-p)^2=q we proceed as follows:
i] Re-write the expression:
x^2+6x=-8
ii] Calculate for the vale of c.
c=(b/2a)²
given that:
b=6, and a=1
thus
c=(6/2*1)^2=9
iii]
Add 9 on both sides of the equation from i
x^2+6x+9=-8+9
simplifying we get:
x^2+6x+9=1
factoring the LHS we get:
(x+3)(x+3)=1
(x+3)²=1
The above is in the form of:
(x-p)²=q
where:
p=3 and q=1
Answer:

Step-by-step explanation:
Let the number of acre of corn planted =x
Let the number of acre of soybeans planted =y
Seed costs for a farmer are $40 per acre for corn and $32 per acre for soybeans.
- Seed Cost for x acre of corn = $40x
- Seed Cost for y acre of soybeans = $32y
The farmer wants to spend no more than $5,000 on seed.
Therefore the linear inequality is:

Next, we graph the inequality

The graph is attached below.
Answer:

Step-by-step explanation:
300 degrees is in the fourth quadrant (it's between 270 and 360); sine is negative in the fourth quadrant.
Given we're in the fourth quadrant, the reference angle is 360 - 300 = 60 degrees
sin(60°) =
And since sine is negative, this value turns negative:
sin(300°) = 