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drek231 [11]
3 years ago
9

In pentagon ABCDE, A = 87º, B = 1250, C = 63º, and E = 95º. Find

Mathematics
1 answer:
lesantik [10]3 years ago
6 0

Answer:

D = 170\º

Step-by-step explanation:

Given

Shape: Pentagon

A = 87\º

B = 125\º

C = 63\º

E = 95\º

Required

Find D

From the sum of angles in a Pentagon; we have that

A + B + C + D + E = 540

Substitute values for A, B, C and E

87\º + 125\º + 63\º + D + 95\º = 540\º

Collect Like Terms

87\º + 125\º + 63\º + 95\º + D = 540\º

370\º + D = 540\º

Collect Like Terms

D = 540\º - 370\º

D = 170\º

<em>Hence, from the list of given options, the correct answer is 170</em>

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Step-by-step explanation:

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3 years ago
Indicate the general rule for the arithmetic sequence with a3 = -12 and a8 = -37
Mandarinka [93]

Answer:

The general rule is a_n = -2 - 5(n-1)

Step-by-step explanation:

Arithmetic sequence:

In an arithmetic sequence, the difference between consecutive terms is always the same, and this difference is called common difference.

The general rule of an arithmetic sequence is given by:

a_{n} = a_1 + (n-1)d

In which a_1 is the first term and d is the common difference.

We can also find the nth term as a function of a term m, using:

a_n = a_m + (n-m)d

a3 = -12 and a8 = -37

First we find the common difference. So

a_n = a_m + (n-m)d

a_8 = a_3 + (8-3)d

-37 = -12 + 5d

5d = -25

d = -\frac{25}{5}

d = -5

So

a_n = a_1 - 5(n-1)

Finding the first term:

a_n = a_1 - 5(n-1)

Since a_3 = -12

a_n = a_1 - 5(n-1)

a_3 = a_1 - 5(3-1)

a_1 = a_3 + 10 = -12 + 10 = -2

So the general rule is:

a_n = a_1 - 5(n-1)

a_n = -2 - 5(n-1)

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The area of a rectangle is 48 cm² and the length of the rectangle is 8 cm longer than the width. What is the equation you would
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To solve for width, substitute the value of l in the first equation so that everything is in terms of w.

Final answer: 48= (8+w)*w
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B (2,1) is the answer
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