Question

If the ladder is 10 m long and 5 m from the base of the building, how high up the building will the ladder reach?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find out how high up the building the ladder will reach, we can use the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (the ladder in this case) is equal to the sum of the squares of the other two sides.

Let x represent the height up the building that the ladder reaches. We can set up the equation as follows:

10^2 = 5^2 + x^2
100 = 25 + x^2
x^2 = 75
x = √75
x ≈ 8.66 m

Therefore, the ladder will reach approximately 8.66 meters up the building.

Answer 2

Susie determined that the system of equations below has infinitely many solutions. The first line goes through the points (2, -13) and (-2, -1) The second line goes through the points (5, -22) and (-3, 2) is she coorect

Answer 3

[AI-generated answer — Bot GPT 3.5]

To determine if the system of equations has infinitely many solutions, we need to check if the two lines are parallel or coincident (i.e., they overlap and are the same line).

To check if the two lines are parallel, we need to compare the slopes of the lines. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula: slope = (y2 - y1) / (x2 - x1).

For the first line:
slope = (-1 - (-13)) / (-2 - 2)
slope = 12 / -4
slope = -3

For the second line:
slope = (2 - (-22)) / (-3 - 5)
slope = 24 / -8
slope = -3

Since both lines have the same slope of -3, they are parallel to each other. Therefore, the system of equations does not have infinitely many solutions. Susie is not correct.