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laiz [17]
3 years ago
12

In the figure, lines a, b, and c are parallel and m24 = 48

Mathematics
1 answer:
Debora [2.8K]3 years ago
8 0

Answer:

m<1 = 48°

m<2 = 132°

m<3 = 132°

m<5 = 48°

Step-by-step explanation:

Given:

m<4 = 48°

Required:

m<1, m<2, m<3, and m<5

Solution:

m<1 = m<4 (alternate exterior angles are congruent)

m<1 = 48° (substitution)

m<2 = 180° - (m<1) (linear pair theorem)

m<2 = 180° - 48° (substitution)

m<2 = 132°

m<3 = m<2 (alternate interior angles are congruent)

m<3 = 132° (substitution)

m<5 = m<4 (corresponding angles are congruent)

m<5 = 48° (substitution)

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3 years ago
Rationalize the denominator of $\frac{5}{2+\sqrt{6}}$. The answer can be written as $\frac{A\sqrt{B}+C}{D}$, where $A$, $B$, $C$
horrorfan [7]

Answer:

A +B+C+D  = 3 is the correct answer.

Step-by-step explanation:

Given:

$\frac{5}{2+\sqrt{6}}$

To find:

A+B+C+D = ? if given term is written as following:

$\frac{A\sqrt{B}+C}{D}$

<u>Solution:</u>

We can see that the resulting expression does not contain anything under \sqrt (square root) so we need to rationalize the denominator to remove the square root from denominator.

The rule to rationalize is:

Any term having square root term in the denominator, multiply and divide with the expression by changing the sign of square root term of the denominator.

Applying this rule to rationalize the given expression:

\dfrac{5}{2+\sqrt{6}} \times \dfrac{2-\sqrt6}{2-\sqrt6}\\\Rightarrow \dfrac{5 \times (2-\sqrt6)}{(2+\sqrt{6}) \times (2-\sqrt6)} \\\Rightarrow \dfrac{10-5\sqrt6}{2^2-(\sqrt6)^2}\ \ \ \ \   (\because \bold{(a+b)(a-b)=a^2-b^2})\\\Rightarrow \dfrac{10-5\sqrt6}{4-6}\\\Rightarrow \dfrac{10-5\sqrt6}{-2}\\\Rightarrow \dfrac{-5\sqrt6+10}{-2}\\\Rightarrow \dfrac{5\sqrt6-10}{2}

Comparing the above expression with:

$\frac{A\sqrt{B}+C}{D}$

A = 5, B = 6 (Not divisible by square of any prime)

C = -10

D = 2 (positive)

GCD of A, C and D is 1.

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4 years ago
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Usimov [2.4K]
4d+6+2d can be reduced to 6d+6

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TEA [102]

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Phoenix [80]

Answer:

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