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vova2212 [387]
3 years ago
7

How many dots will figure n have? Explain how you know this.

Mathematics
2 answers:
Firdavs [7]3 years ago
6 0
Up to the table everything is right at the exception of the n value (in the table).

How many dots... figure 10: You found it it's 49 (and not 9)

How many dots... figure 25: You found it it's 109 (and not 24). Expanding it gives : 13+24x4

How many dots... figure 100: You found it it's 409 (and not 99). Expanding it gives : 13+99x4

How many common difference are added to 13 for figure 100. It's easy you also found it, it's 99, the common difference being 4 so it's 99x4

Now let's calculate the number of dots in figure "n" which is:

a(n) = a₁ + (n-1)x4 (4 being the common difference and a₁ = 1st term)

explanation: lookup again at your table and compare the FIG # part with the EXPAND part:

FIG #           EXPAND (and notice the figures in the parenthesis)
---------         -----------
1                 13 + (0)x4    = 13  (for fig# 1 we have (0)
2                 13 + (1)x4    = 17  (for fig# 2 we have (1)
3                 13 + (2)x4  = 21    (for fig# 3 we have (2)
4                 13 + (3)x4  = 25    (for fig# 4 we have (3)
.                  ........................
.                 .........................
.                ........................
n               13 + (n-1)x4            (for fig#  we have (n-1)

As you notice the number in the parenthesis is always = fig # - 1

Hope that you understand this formula of an arithmetic progression with first term a = 13 and 4, the common difference. Note that n is the number of terms

LenKa [72]3 years ago
5 0
N = ((n-1) + 4) + 4, to my understanding. 
although your answers seem right written in the columns, but your method of applying numbers to equation seems incorrect in 'expand' column. for example, answer for 3 should be something like this...
3   21   17+4
4   25    21+4
hope it helps.
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I need help doing thsi
Naily [24]
True! Because T is the defining letter of the line, so it would be true!

Hope this helps!! :)
7 0
3 years ago
adams car can travel 450 miles on a full tank of gas. his gas tank can hold 15 gallons. kennys car can travel 416 miles on a ful
Elden [556K]
450/15 = 30 mpg -- Adam's
416/13 = 32 mpg -- Kenny's

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8 0
3 years ago
Solve for x.<br><br> 3/4x + y = e<br><br> Show work.
12345 [234]
To solve for x you need to get it by itself
start by subtracting y
3/4x=e-y
then divide by 3/4 or multiply by 4/3
so, x=(4(e-y))/3
distribute
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5 0
3 years ago
What is the sum of the numbers in the series? 15 + 11 + 7 + . . . + (–129)
babymother [125]
Using Gauss's method
Total number of terms = [15-(-129)]/4+1=36+1=37
Add
S=15+11+7+....-125-129
S=-129-125-...+7+11+15
--------------------------------
2S=-114-114-114...(37 times)
=>
sum=S=(1/2)*(-114)*37=-2109


Using AP, T(n)=15+11+7+....-129
T(n)=19-4n  => T(1)=15, T(37)=-129
S(n)=(1/2)(37)(T(1)+T(37)=(1/2)37(15-129)=2109
3 0
3 years ago
prove that the quadrilateral whose vertices are the points A(-1,1), B(-3,4), C(1,5) and D(3,2) is a parallelogram.
Vsevolod [243]

Answer:

Since \overrightarrow{AB} = \overrightarrow{DC} and \overrightarrow{AD} = \overrightarrow{BC}, then the quadrilateral ABCD is a parallelogram.

Step-by-step explanation:

First, we label each point of the quadrilateral with the help of a graphing tool. If the quadrilateral ABCD is a parallelogram, then \overrightarrow{AB} = \overrightarrow{DC} and \overrightarrow{AD} = \overrightarrow{BC}. If we know that A(x,y) =(-1, 1), B(x,y) =(-3,4), C(x,y) = (1,5) and D(x,y) = (3,2), then the measure of each vector is, respectively:

\overrightarrow{AB} = (-3,4)-(-1,1)

\overrightarrow{AB} = (-2, 3)

\overrightarrow{DC} = (1,5)-(3,2)

\overrightarrow{DC} = ( -2,3)

\overrightarrow{AD} = (3,2)-(-1,1)

\overrightarrow{AD} = (4, 1)

\overrightarrow{BC} = (1,5)-(-3,4)

\overrightarrow{BC} = (4, 1)

Since \overrightarrow{AB} = \overrightarrow{DC} and \overrightarrow{AD} = \overrightarrow{BC}, then the quadrilateral ABCD is a parallelogram.

7 0
3 years ago
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