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Bess [88]
3 years ago
14

The pentagons JKLMN and PQRST are similar. Find the length x of PQ????? Help plssss

Mathematics
1 answer:
wariber [46]3 years ago
4 0

Answer:

4.5

Step-by-step explanation:

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A series contains 18 numbers and has a sum of 4,185. The last number of the series is 275. What is the first number?
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If the series is made up of numbers in an arithmetic progression, you have

\displaystyle\sum_{n=1}^{18}a_n=\sum_{n=1}^{18}(a_1+(n-1)d)=18a_1+153d=4185

where a_1 is the first term and d is the common difference between terms.

Since the last term in the series is a_{18}=275, you have

a_{18}=a_1+(18-1)d\implies a_1+17d=275

Solve the system

\begin{cases}18a_1+153d=4185\\a_1+17d=275\end{cases}

and you'll find that the first term is a_1=190 (with d=5).
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Step-by-step explanation:

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The height of a wooden pole, h, is equal to 15 feet. Ataut wire is stretched from a point on the ground to the top of the pole.
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The question is incomplete. Here is the complete question:

The height of a wooden pole, h, is equal to 15 feet. A taut wire is stretched from a point on the ground to the top of the pole. The  distance from the base of the pole to this point on the ground, b. is equal to 8 feet. What is the length of the wire?

Answer:

Length of wire = 17 feet

Step-by-step explanation:

Given:

The height of the wooden pole is, h=15\ ft

The distance from the base of the pole to this point on the ground is, b=8\ ft

Let the length of the wire be 'l'.

Now, consider the triangle formed by the pole, the base, and the wire. The length of the wire is the slant length and hence the hypotenuse of the triangle.

Using Pythagorean theorem, we can find the hypotenuse.

(Hypotenuse)^2=(height)^2+(base)^2\\l^2=h^2+b^2

Plug in the given values and solve for 'l'. This gives,

l^2=15^2+8^2\\\\l^2=225+64\\\\l^2=289\\\\l=\sqrt{289}\\\\l=\pm17

As length can never be negative, we ignore the negative result.

Therefore, the length of the wire is 17 feet.

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3 years ago
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