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3 years ago

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Find each measurement indicated.

1 answer:

nekit [7.7K]3 years ago

6 0

Answer:

D) 24

explanation:

Sana makatulong

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Perform the indicated operations. Write the answer in standard form, a+bi.<br> 5-3i / -2-9i

Vsevolod [243]

$\huge \boxed{\mathfrak{Answer} \downarrow}$

$\large \bf\frac { 5 - 3 i } { - 2 - 9 i } \\$

Multiply both numerator and denominator of $\sf \frac{5-3i}{-2-9i} \\$ by the complex conjugate of the denominator, -2+9i.

$\large \bf \: Re(\frac{\left(5-3i\right)\left(-2+9i\right)}{\left(-2-9i\right)\left(-2+9i\right)}) \\$

Multiplication can be transformed into difference of squares using the rule: $\sf\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$ .

$\large \bf \: Re(\frac{\left(5-3i\right)\left(-2+9i\right)}{\left(-2\right)^{2}-9^{2}i^{2}}) \\$

By definition, i² is -1. Calculate the denominator.

$\large \bf \: Re(\frac{\left(5-3i\right)\left(-2+9i\right)}{85}) \\$

Multiply complex numbers 5-3i and -2+9i in the same way as you multiply binomials.

$\large \bf \: Re(\frac{5\left(-2\right)+5\times \left(9i\right)-3i\left(-2\right)-3\times 9i^{2}}{85}) \\$

Do the multiplications in $\sf5\left(-2\right)+5\times \left(9i\right)-3i\left(-2\right)-3\times 9\left(-1\right)$ .

$\large \bf \: Re(\frac{-10+45i+6i+27}{85}) \\$

Combine the real and imaginary parts in -10+45i+6i+27.

$\large \bf \: Re(\frac{-10+27+\left(45+6\right)i}{85}) \\$

Do the additions in $\sf-10+27+\left(45+6\right)i$ .

$\large \bf Re(\frac{17+51i}{85}) \\$

Divide 17+51i by 85 to get $\sf\frac{1}{5}+\frac{3}{5}i \\$ .

$\large \bf \: Re(\frac{1}{5}+\frac{3}{5}i) \\$

The real part of $\sf \frac{1}{5}+\frac{3}{5}i \\$ is $\sf \frac{1}{5} \\$ .

$\large \boxed{\bf\frac{1}{5} = 0.2} \\$

3 0

3 years ago

Complete the equation of the line through (1,4)(1,4)left parenthesis, 1, comma, 4, right parenthesis and (2,2)(2,2)left parenthe

Ivahew [28]

Answer:

$y = -2x + 6$

Step-by-step explanation:

Given

$(x_1,y_1) = (1,4)$

$(x_2,y_2) = (2,2)$

Required

Determine the line equation

First, we calculate the slope (m) using

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{2-4}{2-1}\\$

$m = \frac{-2}{1}$

$m = -2$

The equation is then calculated using:

$y - y_1 = m(x - x_1)$

$y - 4 = -2(x - 1)$

Open bracket

$y - 4 = -2x + 2$

$y = -2x + 2 + 4$

$y = -2x + 6$

5 0

3 years ago

Read 2 more answers

The measure of two supplementary angles are x+10 and 2x-5. Find the values of x and then find the angles

astra-53 [7]

Answer:

68 1/3, 111 2/3

Step-by-step explanation:

The sum of two supplementary angles is 180°, so ...

(x +10) +(2x -5) = 180

3x +5 = 180 . . . . . collect terms

x +5/3 = 60 . . . . . divide by 3

x = 58 1/3 . . . . . . . subtract 5/3

The first angle is ...

x +10 = 58 1/3 +10 = 68 1/3

The second angle is ...

2x -5 = 2(58 1/3) -5 = 116 2/3 -5 = 111 2/3

The angles measure 68 1/3 and 111 2/3.

6 0

3 years ago

Mr. Smith had 34 of a peach pie left over. He split the leftover pie among his 3 co-workers.

viktelen [127]

Answer:

11.333 infinity

Step-by-step explanation:

when you divide 34 by 3 you then get 11.3 infinity which would also be a repeating decimal

8 0

3 years ago

I need help finding which angles are supplementary to eachother

Novay_Z [31]

Answer:

ICJ and ECI

hope this helped

8 0

2 years ago