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Genrish500 [490]
3 years ago
15

Find the slope of the given line in the following graph.

Mathematics
1 answer:
andre [41]3 years ago
3 0

Take one point from the cartesian plane.

I am taking:

  • (5,-5)
  • x= 5
  • y= -5

\large \sf \frac{y}{x}

\large \sf  \cancel\frac{ - 5}{5}

\sf \: m =  - 1

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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
All the sides of a hexagon become three times the original length. find the ratio of areas of the new and old hexagons.
Anastaziya [24]
To determine the ratio, we need to know the formula of the area of an hexagon in terms of the length of its sides. We cannot directly conclude that the ratio would be 3, the same as that of the ratio of the lengths of the side, since it may be that the relationship of the area and length is not equal. The area of a hexagon is calculated by the expression:

A = (3√3/2) a^2

So, we let a1 be the length of the original hexagon and a2 be the length of the new hexagon.

A2/A1 = (3√3/2) a2^2 / (3√3/2) a1^2
A2/A1 = (a2 / a1)^2 = 3^2 = 9

Therefore, the ratio of the areas of the new and old hexagon would be 9.
7 0
3 years ago
A box of chalk contains 10 pieces. how many pieces of chalk are in 40 boxes
Ivanshal [37]
10 x 40 = 400 so the answer is 400 pieces of chalk.
3 0
3 years ago
Read 2 more answers
Identify the variables in the following.<br> A) 4r- 3<br> B) x + 7
Doss [256]

A). 4r − 3

There are no like terms.

Answer:

= 4r − 3

B). x + 7

There are no like terms.

Answer:

= x + 7

4 0
3 years ago
Find the height of the figure below if the volume is 480.66 cm^3.
salantis [7]

V=\pi r^{2}h\\ 480.66=\pi  6^{2} h\\first, divide both sides by \pi:\\153=6^{2}h\\153=36h\\divide both sides by 36:\\4.25=h

4 0
3 years ago
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