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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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Rudiy27

The number:

5.634\times10^2

is going to be between the numbers 563 and 564; since 10 squared equals 100 and the decimal point will move to places to the right.

Therefore, the answer is D.

8 0
1 year ago
I’ll give points and brainalist for correct answer / explanation
PolarNik [594]

Answer:

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Step-by-step explanation:

3 0
3 years ago
What is the answer??????​
dusya [7]

Answer:

1) A 1 1/3    2) C  1 5/12

Step-by-step explanation:

1) 2/6+4/8+5/10

Reduce 4/8 with 4 and 5/10 with 5.

2/6+1/2+1/2

Reduce 2/6 with 2.

1/3+1/2+1/2

Add fractions with a common denominator.

1/3+2/2

Reduce 2/2 with 1

1/3+1

Write all numerators above the common denominator.

1+3/3

Calculate.

4/3 = 1 1/3

2) 2 3/4 - 1 1/3

Change to improper fractions.

11/4 - 4/3

Write all numerators above the common denominator.

33-16/12

Calculate.

17/12 = 1 5/12

Hope this helps :)

3 0
3 years ago
In ΔSTU, the measure of ∠U=90°, the measure of ∠S=31°, and TU = 77 feet. Find the length of US to the nearest tenth of a foot.
Anton [14]

Answer:

US = 128.15 ft

Step-by-step explanation:

tan 31° = 77/US

0.6009 = 77/US

0.6009US = 77

US = 128.15 ft

7 0
3 years ago
Read 2 more answers
An animal shelter spends $4.50 per day to care for each bird and $5.50 per day to care for each cat. Nathaniel noticed that the
Paraphin [41]

Answer:

The number of birds are 6 and number of cats are 21 at the shelter on Thursday .

Step-by-step explanation:

Let us assume that the number of bird be x .

Let us assume that the num ber of cat be y .

As given

An animal shelter spends $4.50 per day to care for each bird and $5.50 per day to care for each cat. Nathaniel noticed that the shelter spent $142.50 caring for birds and cats on Thursday.

4.50x + 5.50y = 142.50

Simplify the above

\frac{450x}{100} + \frac{550y}{100} = \frac{14250}{100}

450x + 550y = 14250

As given

Nathaniel found a record showing that there were a total of 27 birds and cats on Thursday.

x + y = 27

Two equations are

450x + 550y = 14250

x + y = 27

Multiply x + y = 27 by 450 and subtracted from 450x + 550y = 14250 .

450x - 450x + 550y - 450y = 14250 - 12150

100y = 2100

y = \frac{2100}{100}

y = 21

Putting  the value of  y in the equation x + y = 27 .

x + 21 = 27

x = 27 - 21

x = 6

Therefore the number of birds are 6 and number of cats are 21 at the shelter on Thursday .


7 0
3 years ago
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