Evaluate 12 x (4^-2/4^-4) A 1/4 B 3/4 C 16 D 192

The vertices of ∆ABC are A(2, 8), B(16, 2), and C(6, 2). what is the perimeter and area in square units

ad-work [718]

Check the picture below.

the triangle has that base and that height, recall that A = 1/2 bh.

now as for the perimeter, you can pretty much count the units off the grid for the segment CB, so let's just find the lengths of AC and AB,

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&A&(~ 2 &,& 8~) 
% (c,d)
&C&(~ 6 &,& 2~)
\end{array}~~~ 
% distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
AC=\sqrt{(6-2)^2+(2-8)^2}\implies AC=\sqrt{4^2+(-6)^2}
\\\\\\
AC=\sqrt{16+36}\implies AC=\sqrt{52}\implies AC=\sqrt{4\cdot 13}
\\\\\\
AC=\sqrt{2^2\cdot 13}\implies AC=2\sqrt{13}$

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&A&(~ 2 &,& 8~) 
% (c,d)
&B&(~ 16 &,& 2~)
\end{array}\\\\\\
AB=\sqrt{(16-2)^2+(2-8)^2}\implies AB=\sqrt{14^2+(-6)^2}
\\\\\\
AB=\sqrt{196+36}\implies AB=\sqrt{232}\implies AB=\sqrt{4\cdot 58}
\\\\\\
AB=\sqrt{2^2\cdot 58}\implies AB=2\sqrt{58}$

so, add AC + AB + CB, and that's the perimeter of the triangle.

8 0

3 years ago

A number cube is tossed and one card is randomly drawn. Find P(3, yellow) (BTW There are 5 cards 3 yellow 2 blue) The answer cho

adelina 88 [10]

I believe its 1/10 because there are 10 cards

5 0

3 years ago

Read 2 more answers

The total bill for a dinner party

melamori03 [73]

Answer:

Step-by-step explanation:

There were 9 other people there. First you would subtract how much marcus paid from the total (134.03-20.45=113.58). After that you just divide the remaining cost with 12.62 (113.58/12.62=9)

6 0

3 years ago

Read 2 more answers

Piano lessons cost $15. What expressions could be used to find the cost in dollars of 5 lessons

kirill115 [55]

Just write 15x5. Hope I helped

5 0

3 years ago

Suppose a basketball player has made 223223 out of 406406 free throws. If the player makes the next 22 free throws, I will pay y

makkiz [27]

Answer:

Expected value E = $0.45

Step-by-step explanation:

Expected value E = P×w - P'×l

Where;

P = probability of making the next 2 throw.

P = 223/406 × 223/406 = 0.3017

P' = probability of not making a throw.

P' = 1 - P = 1 - 0.3017

P' = 0.6983

w = expected win = $20

l = Expected loss = $8

Substituting the values;

E = 0.3017 × $20 - 0.6983 × $8

E = $0.4476

Expected value E = $0.45

5 0

3 years ago