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Tems11 [23]
3 years ago
5

Find the value of each variable, line l is tangent.

Mathematics
1 answer:
loris [4]3 years ago
4 0
This is the concept of geometry, we are required to find the values of angle a,b,c,d;
Given that the triangles are by line intersecting two parallel lines, therefore we can conclude that both triangles are similar;
thus;
angle b=40° ⇒alternate angles
angle b= angle c=40° ⇒base angles of isosceles triangles are equal;
angle d=180-(40+40)=180-80=100°
angle a=360-80=240°
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4 0
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4 0
3 years ago
Mohamed and Li Jing were asked to find an explicit formula for the sequence -5, -25, -125, -625,....
Nuetrik [128]

Answer:

Li Jing's formula i.e.  \boxed{g_n=-5\cdot \:5^{n-1}}  is right.

Step-by-step explanation:

Considering the sequence

-5,\:-25,\:-125,\:-625,...

A geometric sequence has a constant ratio r and is defined by

g_n=g_0\cdot r^{n-1}

\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{g_{n+1}}{g_n}

\frac{-25}{-5}=5,\:\quad \frac{-125}{-25}=5,\:\quad \frac{-625}{-125}=5

\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}

r=5

So, the sequence is geometric.

as

\mathrm{The\:first\:element\:of\:the\:sequence\:is}

g_1=-5

r=5

so

g_n=g_1\cdot r^{n-1}

\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:

g_n=-5\cdot \:5^{n-1}

Therefore, Li Jing's formula i.e.  \boxed{g_n=-5\cdot \:5^{n-1}}  is right.

8 0
3 years ago
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