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3 years ago

What is the value of x?

Mathematics

1 answer:

viktelen [127]3 years ago

6 0

Answer:

x = 113

Step-by-step explanation:

The sum of the angles of a triangle are 180 degrees

37+54+ x-24 = 180

Combine like terms

67+x = 180

Subtract 67 from each side

67-67+x = 180-67

x =113

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3 years ago

Read 2 more answers

If (3-4i) (x+yi) = 1 + 0i. The value of x and y is

Black_prince [1.1K]

Step-by-step explanation:

$\textsf{\large{\underline{Solution}:}}$

<h3>Given That:</h3>

$\rm: \longmapsto (3 - 4i)(x + iy) = 1 + 0i$

$\rm: \longmapsto 3(x + iy) - 4i(x + iy)= 1 + 0i$

$\rm: \longmapsto 3x + 3iy - 4ix +4y= 1 + 0i$

On rearranging the terms, we get:

$\rm: \longmapsto (3x + 4y)+ (3y - 4x)i = 1 + 0i$

Comparing both sides, we get:

$\rm: \longmapsto 3x + 4y = 1 --- (i)$

$\rm: \longmapsto 3y - 4x = 0 --- (ii)$

Multiplying (i) by 4, we get:

$\rm: \longmapsto 12x + 16y = 4--- (iii)$

Multiplying (ii) by 3, we get:

$\rm: \longmapsto 9y - 12x = 0 --- (iv)$

Adding equations (iii) and (iv), we get:

$\rm: \longmapsto25y = 4$

$\rm: \longmapsto y =\dfrac{4}{25}$

From (ii), we get:

$\rm: \longmapsto 3y - 4x = 0$

$\rm: \longmapsto 3y = 4x$

$\rm: \longmapsto x = \dfrac{3}{4} y$

$\rm: \longmapsto x = \dfrac{3}{4} \times \dfrac{4}{25}$

$\rm: \longmapsto x = \dfrac{3}{25}$

Therefore:

$\rm: \longmapsto (x,y)= \bigg( \dfrac{3}{25}, \dfrac{4}{25} \bigg)$

★ Which is our required answer.

$\textsf{\large{\underline{More To Know}:}}$

$\rm1.\ i^{4n} = 1$

$\rm2. \ i^{4n+1} = i$

$\rm3.\ i^{4n+2} = -1$

$\rm4.\ i^{4n+3} = -i$

4 0

3 years ago