Firefighters need to use a 60-foot ladder to save a child. She is 50 feet above street level. To the nearest tenth of a foot, how far from the bottom of the building must the
ladder be placed in order to reach the child exactly?

The ladder must be placed at a distance of 33.2 feet from the bottom of the building

Step-by-step explanation:

From what we have here, we are looking at a right angled triangle with the hypotenuse which is the length of the ladder

The height of the child is 50 feet from ground level

So we need to get the third side of the triangle

We can get this by considering the use of Pythagoras’ theorem

This will give us the length of the third side of the triangle

From Pythagoras’ the square of the hypotenuse is equal the sum of the squares of the two other sides

Let the unknown side be x

Thus;

60^2 = 50^2 + x^2

x^2 = 60^2 - 50^2

x^2 = (60-50)(60+50)

x^2 = (10)(110)

x^2 = 1100

x = square root of 1100

x = 33.166

To the nearest tenth, this is 33.2 feet

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true

1.3 million hoops i believe