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KatRina [158]
3 years ago
14

The sum of two complementary angles is 90°. For one pair of complementary angles, the measure of the first angle is 15 less than

twice the measure of the second angle. Write a system of equations that can be used to determine the measure of the first angle, a, and the measure of the second angle, b.
Mathematics
2 answers:
steposvetlana [31]3 years ago
4 0

let 2nd angle = x

 then 1st angle = 2x-15

 then you have 90 = x + 2x-15

2x +x = 3x

 so now 90 = 3x-15

add 15 to each side

105=3x

x = 105/3 = 35

1st angle = 35 degrees

 2nd angle = 2(35) - 15 = 70-15 = 65


ludmilkaskok [199]3 years ago
4 0

Answer:

Measure of first angle = 65° and Measure of second angle = 35°

Step-by-step explanation:

Let measure of first angle be a and measure of second angle be b

Now, the measure of the first angle is 15 less than twice the measure of the second angle

⇒ a + 15 = 2b

⇒ a = 2b - 15

Now, sum of two complementary angles is 90

⇒ a + b = 90

⇒ 2b - 15 + b = 90

⇒ 3b - 15 = 90

⇒ 3b = 105

⇒ b = 35

And a = 65

Therefore, Measure of first angle = 65° and Measure of second angle = 35°

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Oksanka [162]

⇨ The value of this <u>simplified expression</u> = -4096/1 or -4096.

<h3>   </h3>
  • To solve this expression, just multiply the power base by how many times indicate the exponent, and then divide the numerator and denominator of the fraction by the same number.

Power or potentiation is a multiplication in equal factors, where there are <em>terms responsible</em> for obtaining the final result. An potency is given by \large \sf a^{n}. The terms of a power are:

<h3>     </h3>
  • Base
  • Exponent
  • equal factors
  • power
<h3>         </h3>

✏️ <u>Resolution/Answer</u>:

\\ \large \sf \dfrac{-4^{6} \cdot 4^{2}}{4^{4}}=\\\\

  • Multiply the powers of the numbers at numerator of the fraction, with the base <em>being multiplied by how many times</em> to indicate the exponent.

\\\large \sf \dfrac{-4^{6} \cdot 4^{2}}{4^{4}}=

\large \sf \dfrac{-4\cdot4\cdot4\cdot4\cdot4\cdot4\cdot 4^{2}}{4^{4}}=

\large \sf \dfrac{-4\cdot4\cdot4\cdot4\cdot16\cdot 4^{2}}{4^{4}}=

\large \sf \dfrac{-4\cdot4\cdot16\cdot16\cdot 4^{2}}{4^{4}}=

\large \sf \dfrac{-16\cdot16\cdot16\cdot 4^{2}}{4^{4}}=

\large \sf \dfrac{-16\cdot16\cdot16\cdot 4\cdot4}{4^{4}}=

\large \sf \dfrac{-16\cdot16\cdot16\cdot 16}{4^{4}}=\\\\

  • <em>Multiply </em>the power at denominator of the fraction:

\\\large \sf \dfrac{-16\cdot16\cdot16\cdot 16}{4^{4}}=

\large \sf \dfrac{-16\cdot16\cdot16\cdot 16}{4\cdot4}=

\large \sf \dfrac{-16\cdot16\cdot16\cdot 16}{16}=\\\\

  • <em>Multiply </em>the numerator numbers together:

\\\large \sf \dfrac{-16\cdot16\cdot16\cdot 16}{16}=

\large \sf \dfrac{-16\cdot16\cdot 256     }{16}=

\large \sf \dfrac{-256\cdot 256     }{16}=

\large \sf \dfrac{- 65536  }{16}=\\\\

  • Simplify the fraction by number 16:

\\\large \sf \dfrac{- 65536  }{16}=

\large \sf \dfrac{- 65536  \div16}{16\div16}=

{\orange{\boxed{\boxed{\pink {\large \displaystyle \sf { \frac{-4096}{1}  \ or \ -4096 }}}}}} \\\\\\

  • So this expression in its simplified form = -4096/1 or -4096.

{\orange{\boxed{\boxed{\pink {\large \displaystyle \sf { \frac{-4096}{1}  \ or \ -4096 }}}}}}\\\\

                                 ★ Hope this helps! ❤️

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