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goblinko [34]
3 years ago
5

Use an algebraic equation to find the measures of the two angles described below. Begin by letting x represent the degree measur

e of the angle's complement
The measure of the angle is 36 degrees greater than its complement
What is the measure of the complement?
X
Mathematics
1 answer:
KiRa [710]3 years ago
8 0

Using complementary angles concept, it is found that the measure of the complement is of 27º.

-------------------------

  • If two angles are complementary, their <u>measures add to 90º</u>, and thus, the complement of an angle x is given by 90 - x.
  • The measure of an <u>angle is 36 degrees greater than it's complement</u>, thus, the measure of the angle is given found using the following equation:

x = 90 - x + 36

2x = 126

x = \frac{126}{2}

x = 63

The complement is: 90 - x = 90 - 63 = 27.

The measure of the complement is of 27º.

A similar problem is given at brainly.com/question/11161460

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3 years ago
Select all the expressions that are equivalent to (2)^n+³
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Answer:

The expressions which equivalent to  (2)^{n+3} are:

4(2)^{n+1}  ⇒ B

8(2)^{n} ⇒ C

Step-by-step explanation:

Let us revise some rules of exponent

  • a^{m} × a^{m}  = a^{m+n}
  • (a^{m})^{n} = a^{m*n}

Now let us find the equivalent expressions of  (2)^{n+3}

A.

∵ 4 = 2 × 2

∴ 4 =  2^{2}

∴  (4)^{n+2} =  (2^{2})^{n+2}

- By using the second rule above multiply 2 and (n + 2)

∵ 2(n + 2) = 2n + 4

∴  (4)^{n+2} =  (2)^{2n+4}  

B.

∵ 4 = 2 × 2

∴ 4 =  2²

∴  4(2)^{n+1} = 2² ×  (2)^{n+1}

- By using the first rule rule add the exponents of 2

∵ 2 + n + 1 = n + 3

∴   4(2)^{n+1} =  (2)^{n+3}

C.

∵ 8 = 2 × 2 × 2

∴ 8 =  2³

∴  8(2)^{n} = 2³ ×  (2)^{n}

- By using the first rule rule add the exponents of 2

∵ 3 + n = n + 3

∴  8(2)^{n} =  (2)^{n+3}

D.

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∴ 16 = 2^{4}

∴  16(2)^{n} = 2^{4}  ×  (2)^{n}

- By using the first rule rule add the exponents of 2

∵ 4 + n = n + 4

∴  16(2)^{n} =  (2)^{n+4}

E.

(2)^{2n+3} is in its simplest form

The expressions which equivalent to  (2)^{n+3} are:

4(2)^{n+1}  ⇒ B

8(2)^{n} ⇒ C

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