Distance to travel = 20 m.
Let us determine the time, t, that each participant took to complete 20 m.
Barbara:
Average speed = (3 m)/(2 s) = 1.5 m/s
t = 20/1.5 = 13.3 s
Mark:
t = 5 s
Carlos:
y = x + 1
where
y = 20 m
x = time, t
Therefore
t =x = y - 1 = 20 - 1 = 19 s
Summary:
Barbara: 13.3 s
Mark: 5 s
Carlos: 19 s
Answer:
The winner is Mark
The rate of change is (amount of the change) / (time it took to change) .
Amount of the change = (3 - 1) = 2 .
Rate of change = (2) / (time it took to change from 1 to 3) .
Answer:
D. 10 < x < 43
Step-by-step explanation:
4x+8 must be greater than 48, but less than 180.
48 < 4x + 8 < 180
40 < 4x < 172
10 < x < 43
Answer:
A. Right angle -- if you multiply the slopes of 2 intersecting lines and you "-1" then the lines are perpendicular - in this case the line in quadrant 3 has a slope of "1" and the line in quadrant 4 has a slope of "-1", hence their product is "-1" and the angles formed at the intersection of the lines are right angles.
Step-by-step explanation:
The ladder, the wall and the floor form together a triangle rectangle, where the ladder is the hypotenuse of the triangle and the floor and wall are the cathetus. We know from Pythagoreas theorem that the square of the hypotenuse is equal to the sum of the two cathetus squared added, so we can write an equation with the data we have:
hyp^2 = cath1^2 + cath2^2
<span>hyp^2 = wall^2 + floor^2
</span>so we have the hypotenuse value, the floor value and the unknown is the wall height:
(22)^2 = wall^2 + (7)^2
484 = wall^2 + 49
wall^2 = 484 - 49 = 435
wall = √435
wall = 20.9
therefore the ladder touches the wall 20.9 feet above the ground
