$\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}$

$\stackrel{\textit{"z" inversely proportional to "t"}}{z=\cfrac{k}{t}}\qquad \textit{we also know that} \begin{cases} t=9\\ z=28 \end{cases} \\\\\\ 28=\cfrac{k}{9}\implies 252=k~\hfill \boxed{z=\cfrac{252}{t}} \\\\\\ \textit{when t = 12, what is "z"?}\qquad z=\cfrac{252}{12}\implies z=21 \\\\\\ \textit{when z = 36, what is "t"?}\qquad 36=\cfrac{252}{t}\implies t=\cfrac{252}{36}\implies t=7$

3 0

2 years ago

My neighbor is buying new carpet for her bedroom floor. The length of the bedroom is 16 feet. The area of the bedroom is 288 squ

Delicious77 [7]

Answer:

The width of my neighbor,'s room is 18 feet

Step-by-step explanation:

My neighbor is buying new carpet for her bedroom floor. The length of the bedroom is 16 feet. The room has the shape of a rectangle. Although it was not mentioned, we can tell from the area of the room given. If the room was a square,all the sides would have been equal. Since it's a rectangle having length and width of different sizes.

Area = length × width

Area = 288 square feet

Length = 16 feet

Width = 288/16 = 18 feet

The width of the room is longer than the length of the room

3 0

3 years ago

When Maria finished medical school, she owed $36,000 in student loans. She repaid of the total

Viktor [21]

Answer:

$24,000

Step-by-step explanation:

To find how much she owed, find 2/3 of 36,000, since she repaid 1/3

36000(2/3)

= 24,000

So, two years after graduating, Maria owed $24,000

7 0

3 years ago

A kite is a quadrilateral with two pairs of adjacent, congruent sides. The vertex angles are those angles in between the pairs o

umka21 [38]

Let the kite is the quadrilateral A B C D with the two pairs of adjacent congruent sides. (Please find the attached diagram also)

Now, its given in question, see from figure,

AB is congruent to AD

BC is congruent to DC

So, let us join the points A & C to form AC ; and points B and D to form BD.

So, AC is common side to triangles ABC and ADC.

So, Because AB ≈AD

BC ≈ DC

And, AC is common, therefore,

triangle ABC is congruent to triangle ADC

⇒∠ ABC ≈ ∠ADC

The above are the angle.

4 0

4 years ago

A cell phone company charges $40 per month plus a $35 activation fee.Write an expression for the total cost for m months.​

A cell phone company charges $40 per month plus a $35 activation fee.Write an expression for the total cost for m months.