Answer:
Step-by-step explanation:
In order to find the horizontal distance the ball travels, we need to know first how long it took to hit the ground. We will find that time in the y-dimension, and then use that time in the x-dimension, which is the dimension in question when we talk about horizontal distance. Here's what we know in the y-dimension:
a = -32 ft/s/s
v₀ = 0 (since the ball is being thrown straight out the window, the angle is 0 degrees, which translates to no upwards velocity at all)
Δx = -15 feet (negative because the ball lands 15 feet below the point from which it drops)
t = ?? sec.
The equation we will use is the one for displacement:
Δx = 
and filling in:
which simplifies down to
so
so
t = .968 sec (That is not the correct number of sig fig's but if I use the correct number, the answer doesn't come out to be one of the choices given. So I deviate from the rules a bit here out of necessity.)
Now we use that time in the x-dimension. Here's what we know in that dimension specifically:
a = 0 (acceleration in this dimension is always 0)
v₀ = 80 ft/sec
t = .968 sec
Δx = ?? feet
We use the equation for displacement again, and filling in what we know in this dimension:
Δx = 
and of course the portion of that after the plus sign goes to 0, leaving us with simply:
Δx = (80)(.968)
Δx = 77.46 feet
Given that △XYZ is mapped to △X'Y'Z' using the rules (x, y)→(x+5, y−3) followed by (x, y)→(−x, −y) .
We know that (x,y) => (x+h,y+k) type operation represents translation so rule (x, y)→(x+5, y−3) will cause translation.
We know that (x,y) => (-x,-y) type operation represents rotation about origin so rule (x, y)→(−x, −y) will cause rotation.
So combining both results and comparing with given choices. we find that only 1st choice "△XYZ is congruent to △X'Y'Z' because the rules represent a translation followed by a rotation, which is a sequence of rigid motions."
is correct.
Answer:
y = -4.
Step-by-step explanation:
The line with equation y = 4 is a horizontal line on the coordinate plane which passes through the y-axis at y = the point (0, 4).
The other line parallel to this must also be horizontal and , as it passes through the point (1 , -4), must also pass through the y-axis at ( 0, -4). The equation of this line is y = -4.
Answer:
B. -19/25
Step-by-step explanation:
You are looking for an answer that is greater than -4/5 (which is equal to -0.80) but less than -3/4 (which is equal to -0.75). So, you can easily convert the fractions to decimals by dividing.
-33/50 = -0.66, which is greater than -0.75, so it can be eliminated.
-19/25 = -0.76, which fits our parameters, so it is the answer.
-19/20 = -0.95, which is less than -0.80, so it can be eliminated.
-7/10 = -0.70, which is greater than -0.75, so it can be eliminated.
The table would fit because if he rolled the table in which sideways it would fit since its smaller than the door
