Mathematics

Mathematics, 07.07.2019 12:50, kimberlynassar1962

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

answer

Answers: 2

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Answers

Answer

answered: Lolmickles968

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

Answer

answered: tyijiapostell

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.

Answer

answered: Guest

Idk what the answer is bc i don't get it

Answer

answered: Guest

x= 1

step-by-step explanation: convert 5\frac{11}{12}5

12

11

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

c

b

=

c

ac+b

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{5\times 12+11}{12}3.25+0.5x+1

3

1

+

6

5

x=

12

5×12+11

2 simplify 5\times 125×12 to 6060

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{60+11}{12}3.25+0.5x+1

3

1

+

6

5

x=

12

60+11

3 simplify 60+1160+11 to 7171

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{71}{12}3.25+0.5x+1

3

1

+

6

5

x=

12

71

4 simplify \frac{5}{6}x

6

5

x to \frac{5x}{6}

6

5x

3.25+0.5x+1\frac{1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+1

3

1

+

6

5x

=

12

71

5 convert 1\frac{1}{3}1

3

1

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

c

b

=

c

ac+b

3.25+0.5x+\frac{1\times 3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

3

1×3+1

+

6

5x

=

12

71

6 simplify 1\times 31×3 to 33

3.25+0.5x+\frac{3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

3

3+1

+

6

5x

=

12

71

7 simplify 3+13+1 to 44

3.25+0.5x+\frac{4}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

3

4

+

6

5x

=

12

71

8 simplify 3.25+0.5x+\frac{4}{3}+\frac{5x}{6}3.25+0.5x+

3

4

+

6

5x

to \frac{13.75}{3}+\frac{4x}{3}

3

13.75

+

3

4x

\frac{13.75}{3}+\frac{4x}{3}=\frac{71}{12}

3

13.75

+

3

4x

=

12

71

9 simplify \frac{13.75}{3}

3

13.75

to 4.5833334.583333

4.583333+\frac{4x}{3}=\frac{71}{12}4.583333+

3

4x

=

12

71

10 subtract 4.5833334.583333 from both sides

\frac{4x}{3}=\frac{71}{12}-4.583333

3

4x

=

12

71

−4.583333

11 simplify \frac{71}{12}-4.583333

12

71

−4.583333 to \frac{4}{3}

3

4

\frac{4x}{3}=\frac{4}{3}

3

4x

=

3

4

12 multiply both sides by 33

4x=\frac{4}{3}\times 34x=

3

4

×3

13 simplify \frac{4}{3}\times 3

3

4

×3 to \frac{12}{3}

3

12

4x=\frac{12}{3}4x=

3

12

14 simplify \frac{12}{3}

3

12

to 44

4x=44x=4

15 divide both sides by 44

x=1

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