Solve the inequality s-12 _> -1

Mathematics

1 answer:

My name is Ann [436]3 years ago

8 0

Answer:

s >= 11

Step-by-step explanation:

s-12 >= -1

Add 12 to both sides

s >= 11

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3: What is the factored form of this trinomial?

STALIN [3.7K]

X^2+3x+2
x^2+5x+6
x^2+4x+3

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3 years ago

An airplane flies to San Francisco from Los Angeles in 4 hours. It flies back in 3 hours. If the wind is blowing from the north

Sedaia [141]

Answer:

Airspeed in still air: 140 mph

Step-by-step explanation:

Let s represent the speed in still air. Recognize that the distance traveled is the same in either direction.

Also note that SF is north of LA.

Distance to SF from LA = Distance to LA from SF

(s-20)(mph)(4 hr) = (s+20)(mph)(3 hr)

Then:

4s - 80 = 3s + 60 => s = 60 + 80 + 140 (mph)

The airspeed of the plane was 140 mph in still air. With a tail wind, the plane is faster; with a headwind, slower.

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3 years ago

Jacob throws an acorn into the air. It lands in front of him. The acorn's path is

Burka [1]

Answer:

hits the ground at x = -0.732, and x = 2.732
only the positive solution is reasonable

Step-by-step explanation:

The acorn will hit the ground where the value of x is such that y=0. We can find these values of x by solving the quadratic using any of several means.

<h3>graphing</h3>

The attachment shows a graphing calculator solution to the equation

-3x^2 + 6x + 6 = 0

The values of x are -0.732 and 2.732. The negative value is the point where the acorn would have originated from if its parabolic path were extrapolated backward in time. Only the positive horizontal distance is a reasonable solution.

<h3>completing the square</h3>

We can also solve the equation algebraically. One of the simplest methods is "completing the square."

-3x^2 +6x +6 = 0

x^2 -2x = 2 . . . . . . . . divide by -3 and add 2

x^2 -2x +1 = 2 +1 . . . . add 1 to complete the square

(x -1)^2 = 3 . . . . . . . . written as a square

x -1 = ±√3 . . . . . . . take the square root

x = 1 ±√3 . . . . . . . add 1; where the acorn hits the ground

The numerical values of these solutions are approximately ...

x ≈ {-0.732, 2.732}

The solutions to the equation say the acorn hits the ground at a distance of -0.732 behind Jacob, and at a distance of 2.732 in front of Jacob. The "behind" distance represents and extrapolation of the acorn's path backward in time before Jacob threw it. Only the positive solution is reasonable.