A reflection and a glide are the same thing. <br> True or false?

Mary walks from corner D to corner E to corner F on a city block that measures 264 feet wide and 900 feet long. Kate walks diago

Kaylis [27]

Step-by-step explanation:

we have a rectangle, that is then cut in half diagonally into 2 right-angled triangles.

in our problem it does not matter which side is the larger and which is the shorter one, because the distance calculation for both cases involve one short and one long side. the sequence does not matter.

Mary walks one short and one large side to get to the opposite corner (from D to F) :

264 + 900 = 1,164 ft

Kate walks diagonally. and that diagonal is the Hypotenuse of the right-angled triangle with a short and a long side of the rectangle.

so, Pythagoras applies :

c² = a² + b²

with c being the Hypotenuse (the side opposite of the 90° angle), and a and b are the legs.

in our case that means

diagonal² = 264² + 900² = 69,696 + 810,000 =

= 879,696

diagonal = sqrt(879,696) = 937.9211054... ft ≈ 938 ft

so, Kate walked

1,164 - 938 = 226 ft

less than Mary.

4 0

1 year ago

Johan found that the equation –2|8 – x| – 6 = –12 had two possible solutions: x = 5 and x = –11. Which explains whether his solu

Effectus [21]

$-2|8-x|-6=-12 \ \ \ |\hbox{add 6} \\
-2|8-x|=-6 \ \ \ |\hbox{divide by (-2)} \\
|8-x|=3 \\
8-x=-3 \ \lor \ 8-x=3 \\
-x=-3-8 \ \lor \ -x=3-8 \\
-x=-11 \ \lor \ -x=-5 \\
x=11 \ \lor \ x=5 \\
\boxed{x=5 \hbox{ or } x=11}$

It should be x=11 instead of x=-11, so he is not correct because he made a sign error.

6 0

3 years ago

Read 2 more answers

The formula T= 2pi sqrt(L/32) relates the time, T, in seconds for a pendulum with the length, L, in feet, to make one full swing

tester [92]

The length of pendulum is 2.485 feet

<h3><u><em>Solution:</em></u></h3>

Given that,

The formula T= 2pi sqrt(L/32) relates the time, T, in seconds for a pendulum with the length, L, in feet, to make one full swing back and forth

<u><em>Therefore, the given formula is:</em></u>

$T=2\pi \sqrt{\frac{L}{32} }$

We have to find the length of pendulum that makes one full swing in 1.75 seconds

So the modify the given equation to find "L"

$T=2\pi \sqrt{\frac{L}{32} }\\\\ \sqrt{\frac{L}{32} }=\frac{T}{2 \pi}\\\\\text{Taking square root on both sides }\\\\\frac{L}{32} = \frac{T^2}{4 \pi^2}\\\\L = \frac{T^2}{4 \pi^2} \times 32\\\\L = \frac{T^2}{\pi^2 } \times 8$