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icang [17]
3 years ago
5

Create diagrams to represent the possible cases for common tangents between two circles. Your diagram can be created using multi

media sources or drawn by hand. They should not be copied and pasted from a website. Explain why your diagrams satisfy the given criteria.
No Common Tangents


Diagram:








Justification:

Mathematics
1 answer:
Anastaziya [24]3 years ago
3 0

I made mine from google drawings

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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
Donata bought 4 lemons and 4 plums at the local supermarket for a total of $ 21.60. Dan bought 11 lemons and 6 plums at the same
VashaNatasha [74]
  1. you must establish a equation system  with the information given , 4x numbers of limon , where x represent the cost of every lemon and 4y numbers of plums , where y represents the cost of plums
  2. now  the equation system is 1) 4x+ 4y = 21,60 and 2) 11x+ 6y = 40.29
  3. of the equation 1 you must obtain the value of x, 4x = 21.60+4y ⇒x=21.60/4+4y/4⇒x= 5.4+y
  4. now with the value of x , it is substitute in the equation 2)   11(5.4+y) + 6y = 40.29 , ⇒ 59.4 + 11y + 6y = 40.29 ⇒  17y = 40.29-59.4⇒ y = -19,11/7⇒ y = -2.73
  5. the value of y is substitute in the equation 1) x = 5.4 + ( -2,73)⇒ x= 2,67,  where ,the price of every lemon is $ 2,67
6 0
3 years ago
Carrie had 140 coins.She has 10 times as many coins as she had last month.How many coins did Carrie have last month?
Inessa [10]
Carrie had 14 coins last month
6 0
3 years ago
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Mr. Diaz is building a fence around his yard. For numbers 3a-3b, choose the values and term that correctly describe the shape of
Inga [223]
3a) The figure has 5 sides and 5 vertices

3b) None of the sides are congruent, so the figure is not are guitar polygon
3 0
3 years ago
Find a general solution of y" + 4y = 0.
klio [65]

Answer:

y(x)=C_{1}cos2x+C_{2}sin(2x)

Step-by-step explanation:

It is a linear homogeneous differential equation with constant coefficients:

y" + 4y = 0

Its characteristic equation:

r^2+4=0

r1=2i

r2=-2i

We use these roots in order to find the general solution:

y(x)=C_{1}cos2x+C_{2}sin(2x)

8 0
3 years ago
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