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nika2105 [10]
3 years ago
12

Which of the following pairs of circles have/as a common external tangent select all that apply

Mathematics
1 answer:
iragen [17]3 years ago
3 0

Answer:

i need a picture cuz i dont see any external that apply

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Determine formula of the nth term 2, 6, 12 20 30,42​
nalin [4]

Check the forward differences of the sequence.

If \{a_n\} = \{2,6,12,20,30,42,\ldots\}, then let \{b_n\} be the sequence of first-order differences of \{a_n\}. That is, for n ≥ 1,

b_n = a_{n+1} - a_n

so that \{b_n\} = \{4, 6, 8, 10, 12, \ldots\}.

Let \{c_n\} be the sequence of differences of \{b_n\},

c_n = b_{n+1} - b_n

and we see that this is a constant sequence, \{c_n\} = \{2, 2, 2, 2, \ldots\}. In other words, \{b_n\} is an arithmetic sequence with common difference between terms of 2. That is,

2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2

and we can solve for b_n in terms of b_1=4:

b_{n+1} = b_n + 2

b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2

b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2

and so on down to

b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)

We solve for a_n in the same way.

2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)

Then

a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)

a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))

a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))

and so on down to

a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2

\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}

6 0
2 years ago
#17-1: Simplify this complex fraction. 1/3 / 6/9
Gnesinka [82]

\huge{\boxed{\frac{1}{2}}}

To divide by a fraction, you multiply by its reciprocal, which you find by flipping the numerator and the denominator. \frac{1}{3} \div \frac{6}{9} = \frac{1}{3} * \frac{9}{6}

Multiply the numerators and the denominators separately. \frac{1}{3} * \frac{9}{6} = \frac{1*9}{3*6} = \frac{9}{18}

Simplify by dividing both sides of the equation by 9. \frac{9 \div 9}{18 \div 9} = \boxed{\frac{1}{2}}

3 0
3 years ago
Read 2 more answers
-2x < -6
Soloha48 [4]

Answer:

x > 3

Step-by-step explanation:

This is based on the concept 'when a negative number is multiplied to both sides of the inequality, the sign gets reversed. For example, x > - 2 when it is multiplied by - 1, it becomes - x < 2.'

*only when the number is -ve.

Similarly, in this question, multiply both sides by - 1.

2x > 6

x > 6/2

x > 3

For more : take - 5 > - 2, as you know

Note that 5 is actually greater than 2. To make this true we change signs

8 0
3 years ago
In the diagram AB is parallel to CD. Calculate the value of A ?
olga55 [171]

The image of the diagram is missing, so i have attached it.

Answer:

a = 30°

Step-by-step explanation:

From the diagram attached, we can see that the 2 angles a and 5a are interior supplementary angles.

The sum of interior supplementary angles is 180°

Thus;

5a + a = 180

6a = 180

a = 180/6

a = 30°

4 0
3 years ago
Solve absolute value equation [3x+5]-3
ehidna [41]
Its 2. because yea you know whats going on
7 0
3 years ago
Read 2 more answers
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