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Alecsey [184]
3 years ago
11

Pentagons STUVW and XYZAB are similar with XY = 32 , YZ = 36 , ST = 4c + 2 and TU = 5c + 2 What is the length of TU

Mathematics
1 answer:
Vesna [10]3 years ago
8 0

Answer:

TU = 4.5units

Step-by-step explanation:

Since the pentagons are similar, hence the ratios of their similar sides will be equal to a constant.

Hence;

XY/ST = YZ/TU

Given the following

XY = 32

YZ = 36

ST = 4c + 2

TU = 5c + 2

Substitute into the expression as shown;

32/4c+2 = 36/5c+2

Cross multiply

36(4c+2) = 32(5c+2)

144c + 72 = 160c + 64

144c - 160c = 64 - 72

-16c = -8

c = -8/-16

c = 1/2

Recall that TU = 5c + 2

TU =5(1/2) + 2

TU = 2.5 + 2

TU = 4.5

Hence the length of TU is 4.5units

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What are the next three terms in the sequence 4, -1, -6, -11, ...?
Fynjy0 [20]

Answer:

In summary, "the next three terms" are {-16, -21, -26}

Step-by-step explanation:

Note that the common difference separating the terms of 4, -1, -6, -11, ... is -5.  Each new term is found by combining the previous term with -5.

Thus, the applicable formula is a(n) = 4-5(n-1).

We should test this.  Take the term -6 and determine whether or not this formula correctly predicts the next term:  -11:

a(4) = 4-5(4-1) = 4 - 5(3) = 4 - 15 = -11 (yes).

We have the first four terms and need the 5th, 6th and 7th terms.

The fifth term, a(5), is 4-5(5-1) = 4-20 = -16

The sixth term is a(6) = 4-5(6-1) = -21

The seventh term is a(7) = 4 -5(6) = -26

In summary, "the next three terms" are {-16, -21, -26}

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Mikes favorite peaches are $2.50 per pound at the local farmers market. She bought 13.5 pounds. how much did she spend?
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anygoal [31]

Answer:

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Step-by-step explanation:

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