Answer:
x ∈ [-2, 7]
Step-by-step explanation:
The given equation ...
x^2 -5x -4 ≤ 10
can be rewritten as ...
x^2 -5x -14 ≤ 0
and factored as ...
(x +2)(x -7) ≤ 0
Clearly, the "or equal to" condition will be met when x=-2 and x=7. For values of x between these numbers, one factor is negative and the other is positive. Hence the product will be negative. So, numbers in that interval are the solution set.
x ∈ [-2, 7]
Answer:
a = 6
Step-by-step explanation:
Given information:
Slope = 6
Coordinates: (-9, 0) and (-8, a)
Slope formula = y2 - y1 / x2 - x1
Substitute the given values into the formula.
6 = a - 0 / -8 - (-9)
6 = a - 0 / 1
6 = a - 0
a = 6
hope this helps!! p.s. i really need brainliest :)
D is the correct formula that the model represents. Black represents negative values, while white represents positive.
Answer:
v_top = 2400 mi/hr
v_w = 400 mi/h
Step-by-step explanation:
Given:
- Total distance D = 4800 mi
- Headwind journey time taken t_up= 3 hr
- Tailwind journey time taken t_down = 2 hr
Find:
Find the top speed of Luke's snow speeder and the speed of the wind.
Solution:
- The speed of Luke v_l is in stationary frame is given by:
v_l = v_w + v_l/w
Where,
v_w: Wind speed
v_l/w: Luke speed relative to wind.
- The top speed is attained on his returned journey with tail wind. We will use distance time relationship to calculate as follows:
v_top = D / t_down
v_top = 4800 / 2
v_top = v_down = 2400 mi/hr
- Similarly his speed on his journey up with head wind was v_up:
v_up = D / t_up
v_up = 4800 / 3
v_up = 1600 mi/hr
- Now use the frame relations to find the wind speed v_w:
v_down = v_w + v_l/w
v_up = -v_w + v_l/w
- Solve equations simultaneously:
2400 = v_w + v_l/w
1600 = -v_w + v_l/w
4000 = 2*v_l/w
v_l/w = 2000 mi/h
v_w = 400 mi/h
<span>The incenter is equidistant from all three triangle sides.
So, PJ = PK = PL.
PJ = 4x -8
PL = x + 7
Therefore,
</span>4x -8 = <span>x + 7
3x = 15
x = 5
So, PJ = 12
PL = 12 and
PK = 12
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