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posledela
3 years ago
15

What is the 87th term of the arithmetic sequence of 12,0,-12

Mathematics
1 answer:
den301095 [7]3 years ago
7 0

Step-by-step explanation:

12,0,-12

a1 = 12 \\ a2 = 0 \\ d = a2 - a1 \\ d = 0 - 12 =  - 12 \\ an = a1 + (n - 1) \times d \\  \\ a87 = 12 + (87 - 1) \times ( - 12)  \\ a87 = 12  - 1032

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What is the sum of the interior angles of the polygon shown below?
Yanka [14]

Answer:

540 degrees

Step-by-step explanation:

The formula to find the sum of interior angles in any polygon is the following:

S=180(n-2)

Where (n) represents the number of sides in the polygon. In this case, the polygon has (5) sides, therefore substitute (5) in place of (n) and solve;

S=180(n-2)\\\\S=180(5-2)\\\\S=180(3)\\\\S=540

4 0
3 years ago
The diagram represents the shape and dimensions of Kayla's garden. A special fertilizer is used for the vegetable garden. Each b
Serjik [45]

Answer:

B. 18 bags

Step-by-step explanation:

First you need to determine the area of the vegetable garden. The vegetable garden is a rectangle with the following dimensions:

L = 24 ft

W = 9 ft

The Formula for the area of a rectangle is:

A = L\times W

So let's solve it:

A = L\timesW\\A = 24 ft\times9ft\\A= 216ft^{2}

With that, we can figure out how many bags of fertilizer would be needed by dividing the area of the vegetable garden by how much one bag of fertilizer covers:

\dfrac{214ft^2}{12ft^2/bag}=18\;bags

3 0
3 years ago
Read 2 more answers
Tutorial Exercise A boat leaves a dock at 2:00 PM and travels due south at a speed of 20 km/h. Another boat has been heading due
ANTONII [103]

Answer:

Both the boats will closet together at 2:21:36 pm.

Step-by-step explanation:

Given that - At 2 pm boat 1 leaves dock and heads south and boat 2 heads east towards the dock. Assume the dock is at origin (0,0).

Speed of boat 1 is 20 km/h so the position of boat 1 at any time (0,-20t),

        Formula :   d=v*t

at 2 pm boat 2 was 15 km due west of the dock because it took the boat 1 hour to reach there at 15 km/h, so the position of boat 2 at that time was (-15,0)

the position of boat 2 is changing towards east, so the position of boat 2 at any time (-15+15t,0)

      Formula : D=\sqrt{(x2-x1)^2+(y2-y1)^2}

⇒                     D = \sqrt{20^2t^2+15(t-1)^2}

Now let           F(t) = D^2(t)

                ∵    F'(t) = 800t + 450(t-1) =  1250t -450\\F'(t) =0

⇒                     t= 450/1250

⇒                     t= .36 hours

⇒                       = 21 min 36 sec

Since F"(t)=0,

∴ This time gives us a minimum.

Thus, The two boats will closet together at 2:21:36 pm.

3 0
3 years ago
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Dee spent $20.90 i think
4 0
3 years ago
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Find the volume of the prism.
leonid [27]

Answer:

Step-by-step explanation:

Volume = L × W × H

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6 0
3 years ago
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