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3 years ago

3-2i/1+4i include each step necessary in simplifying

Mathematics

1 answer:

Likurg_2 [28]3 years ago

8 0

Answer:

$\frac{3-2i}{1+4i}=\frac{11}{17}-\frac{10}{17}i$

Step-by-step explanation:

$\frac{3-2i}{1+4i}$ <-- Given

$\frac{3-2i}{1+4i}*\frac{1-4i}{1-4i}$ <-- Multiply by the conjugate of the denominator as a factor of 1

$\frac{(3-2i)(1-4i)}{(1+4i)(1-4i)}$

$\frac{(3)(1)+3(-4i)-2i(1)-2i(4i)}{(1)(1)+1(-4i)+4i(1)+4i(-4i)}$ <-- Use the Distributive Property and FOIL

$\frac{3-12i-2i-8i^2}{1-4i+4i-16i^2}$

$\frac{3-10i-8i^2}{1-16i^2}$

$\frac{3-10i-8(-1)}{1-16(-1)}$ <-- Rewrite $i^2$ as $-1$

$\frac{3-10i+8}{1+16}$

$\frac{11-10i}{17}$

$\frac{11}{17}-\frac{10}{17}i$ <-- Rewrite in $a\pm bi$ form

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Which of the following is a factor of both f(x)=x^2-4x-45 and g(x)=x^2-25

wolverine [178]

Answer:

-5

Step-by-step explanation:

x² - 4x - 45 = 0

(x - 9)(x + 5) = 0

x = 9 or -5

x² - 25 = 0

(x + 5)(x - 5) = 0

x = 5 or -5

-5 is a common factor between both of them

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2 years ago

Jan and two of her friends raised money by having a bake sale. They split the proceeds. If each person received $32.19, how much

Dimas [21]

You need to multiply the answer by how many people got that amount, Jan +her 2 friends would be 3 people so
32.19 x 3 = 96.57

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3 years ago

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7x^2=9+x what are the values of x Will give medal and points

DENIUS [597]

7x² = 9 + x Subtract x from both sides
7x² - x = 9 Subtract 9 from both sides
7x² - x - 9 = 0 Use the Quadratic Formula

a = 7 , b = -1 , c = -9

x = $\frac{-b \pm \sqrt{b^2 - 4ac} }{2a}$ Plug in the a, b, and c values
x = $\frac{- (-1) \pm \sqrt{(-1)^2 - 4(7)(-9)} }{2(7)}$ Cancel out the double negative
x = $\frac{1 \pm \sqrt{(-1)^2 - 4(7)(-9)} }{2(7)}$ Square -1
x = $\frac{1 \pm \sqrt{1 - 4(7)(-9)} }{2(7)}$ Multiply 7 and -9
x = $\frac{1 \pm \sqrt{1 - 4(-63} }{2(7)}$ Multiply -4 and -63
x = $\frac{1 \pm \sqrt{1 + 252} }{2(7)}$ Multiply 2 and 7
x = $\frac{1 \pm \sqrt{1 + 252} }{14}$ Add 1 and 252
x = $\frac{1 \pm \sqrt{253} }{14}$ Split up the $\pm$
x = $\left \{ {{ \frac{1 + \sqrt{253} }{14} } \atop { \frac{1 - \sqrt{253} }{14} }} \right.$
The approximate square root of 253 is 15.905973.
x ≈ $\left \{ { \frac{1 + 15.905973}{14} } \atop { \frac{1 - 15.905973}{14} }} \right$ Add and subtract
x ≈ $\left \{ {{ \frac{16.905973}{14} } \atop { \frac{14.905973}{14} }} \right.$ Divide
x ≈ $\left \{ {{1.2075} \atop {1.0647}} \right.$ Round to the nearest hundredth
x ≈ $\left \{ {{1.21} \atop {1.06}} \right.$

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3 years ago

Will mark Brainliest!! :)

Georgia [21]

Step-by-step explanation:

The system of equations for eq 1 which is 3x + y = 118 represents the Green High School which filled three buses(with a specific number of students identified as x) and a van(with a specific number of students identified as y) with a total of 118 students.

for eq 2; 4x + 2y = 164; represents Belle High School which filled four buses(with a specific number of students identified as x) and two vans(with a specific number of students identified as y) with a total of 164 students.

The solution represents the specific number of students in the buses and vans in eq1 and eq 2 with x being 36 students and y being 10 students.

substituting 36 for x and 10 for y in eq 1;

3(36) + 10 = 108 + 10 = 118 total students for Green High School

substituting 36 for x and 10 for y in eq2;

4(36) + 2(10) = 144 + 20 = 164 total students for Belle High school

6 0

2 years ago

What THREE integers have a sum of 300?

quester [9]

Answer:

Here we will use algebra to find three consecutive integers whose sum is 300. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 300. Therefore, you can write the equation as follows:

(X) + (X + 1) + (X + 2) = 300

To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:

X + X + 1 + X + 2 = 300

3X + 3 = 300

3X + 3 - 3 = 300 - 3

3X = 297

3X/3 = 297/3

X = 99

Which means that the first number is 99, the second number is 99 + 1 and the third number is 99 + 2. Therefore, three consecutive integers that add up to 300 are 99, 100, and 101.

99 + 100 + 101 = 300

We know our answer is correct because 99 + 100 + 101 equals 300 as displayed above.

Step-by-step explanation:

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3 years ago

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