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Licemer1 [7]
3 years ago
10

Determine if the pair of triangles are similar or not.

Mathematics
1 answer:
dedylja [7]3 years ago
5 0

Answer: SAS

Step-by-step explanation:

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Help me solve this test :)
lakkis [162]

Answer:

D: (5 * 3)^3

D:  125 x 27

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
What is a quick and easy way to remember explicit and recursive formulas?
Oliga [24]
I always found derivation to be helpful in remembering. Since this question is tagged as at the middle school level, I assume you've only learned about arithmetic and geometric sequences.

First, remember what these names mean. An arithmetic sequence is a sequence in which consecutive terms are increased by a fixed amount; in other words, it is an additive sequence. If a_n is the nth term in the sequence, then the next term a_{n+1} is a fixed constant (the common difference d) added to the previous term. As a recursive formula, that's

a_{n+1}=a_n+d

This is the part that's probably easier for you to remember. The explicit formula is easily derived from this definition. Since a_{n+1}=a_n+d, this means that a_n=a_{n-1}+d, so you plug this into the recursive formula and end up with 

a_{n+1}=(a_{n-1}+d)+d=a_{n-1}+2d

You can continue in this pattern, since every term in the sequence follows this rule:

a_{n+1}=a_{n-1}+2d
a_{n+1}=(a_{n-2}+d)+2d
a_{n+1}=a_{n-2}+3d
a_{n+1}=(a_{n-3}+d)+3d
a_{n+1}=a_{n-3}+4d

and so on. You start to notice a pattern: the subscript of the earlier term in the sequence (on the right side) and the coefficient of the common difference always add up to n+1. You have, for example, (n-2)+3=n+1 in the third equation above.

Continuing this pattern, you can write the formula in terms of a known number in the sequence, typically the first one a_1. In order for the pattern mentioned above to hold, you would end up with

a_{n+1}=a_1+nd

or, shifting the index by one so that the formula gives the nth term explicitly,

a_n=a_1+(n-1)d

Now, geometric sequences behave similarly, but instead of changing additively, the terms of the sequence are scaled or changed multiplicatively. In other words, there is some fixed common ratio r between terms that scales the next term in the sequence relative to the previous one. As a recursive formula,

a_{n+1}=ra_n

Well, since a_n is just the term after a_{n-1} scaled by r, you can write

a_{n+1}=r(ra_{n-1})=r^2a_{n-1}

Doing this again and again, you'll see a similar pattern emerge:

a_{n+1}=r^2a_{n-1}
a_{n+1}=r^2(ra_{n-2})
a_{n+1}=r^3a_{n-2}
a_{n+1}=r^3(ra_{n-3})
a_{n+1}=r^4a_{n-3}

and so on. Notice that the subscript and the exponent of the common ratio both add up to n+1. For instance, in the third equation, 3+(n-2)=n+1. Extrapolating from this, you can write the explicit rule in terms of the first number in the sequence:

a_{n+1}=r^na_1

or, to give the formula for a_n explicitly,

a_n=r^{n-1}a_1
6 0
3 years ago
A square outdoor patio with side length x feet is surrounded by a brick walkway that is 4 feet wide. What is the area of the wal
Masja [62]

Answer:

Area of walkway = 16(x+4) ft^{2}

Step-by-step explanation:

Length of the sides of the square outdoor = x feet

Area of the square outdoor = length x length

                            = x * x

                            = x^{2} ft^{2}

The square outdoor is surrounded by 4 feet of walkway. So that,

length of the walkway = (x + 2(4))

                                     = (x + 8)

Area of walkway with outdoor = (x + 8)*(x + 8)

                                      = (x^{2} + 16x + 64) ft^{2}

Area of walkway = Area of walkway with outdoor - Area of the square outdoor

                            = ( x^{2} + 16x + 64) - x^{2}

                            = 16x + 64

Area of walkway = 16(x+4) ft^{2}

7 0
3 years ago
Please help me with the picture attached also, I am so confused
antoniya [11.8K]

Answer:

I can't see the picture?

Where is it???

Step-by-step explanation:

4 0
2 years ago
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Mary bought 176 flowers for 4 vases. How many flowers are needed for 7 vases?
Doss [256]

She planned to have 44 flowers per vase (176/4). 7 vases would mean 308 flowers.

3 0
2 years ago
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