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

Answer:

x = 6.5

Step-by-step explanation:

In order to solve this problem, you need to use trigonometry (sin, cosine, tangent).  

Sin = opposite/hypotenuse

Cosine = adjacent/hypotenuse

Tangent = opposite/adjacent

We need to use tangent in this case because 10 is the opposite side from the 57° angle, and x is right next to it, making it adjacent.  So, our equation would look like this:

tan (57)° = 10/x

Multiply both sides by x

x (tan (57)°) = 10

Divide both sides by tan (57)°

10 / tan (57)° = 6.49408 = 6.5

Step-by-step explanation:

We are given two angles measures and one side. Notice the given angle and the side that is opposite to that given angle is given. We need to find side x. But can we also find the angle opposite of the side we are trying to find. Yes we can

Remeber that triangles interior angles add up to 180.

Remeber that triangles interior angles add up to 180.One angle measure 90 and the other measure is 57 so

[tex]90 + 57 + x = 180[/tex]

[tex]x = 33[/tex]

So the angle opposite of the side we are trying to find is 33.

Since we know two angles and two sides that are opposite of those two angles respectively, we can use what is called Law of Sines

[tex] \frac{b}{ \sin(b) } = \frac{c}{ \sin(c) } [/tex]

where the numerator are the side measures, and the denominator are the angle measures.

Plug in the respectively values. Angle 57 is opposite of 10 and Angle 33 is opposite of x.

[tex] \frac{10}{ \sin(57) } = \frac{x}{ \sin(33) } [/tex]

Multiply both sides by sin 33 to isolate x.

We get

[tex]x = 6.494[/tex]

Round if needed

In other words, apply law of sines when you have two angles and two sides that are opposite of those angles respectively.

Answer:

√73

Step-by-step explanation:

a^2+b^2=c^2

8^2+3^2=c^2

64+9=c^2

√73 =√c^2

√73 =c

Answer:

Below.

Step-by-step explanation:

396,242,002

Answer:

[tex]a)x < - \frac{2}{5} [/tex]

[tex]b)4 < - 2[/tex]

Step-by-step explanation:

[tex]a)2x + \frac{1}{2} x + 2 < 1[/tex]

[tex] = 4x + x + 4 < 2[/tex]

[tex] = 5x + 4 < 2[/tex]

[tex] = 5x < 2 - 4[/tex]

[tex] = 5x < - 2[/tex]

[tex] = x < - \frac{2}{5} [/tex]

[tex] = x < - 0.4 \times ∈( - \infty . - \frac{2}{5} )[/tex]

[tex]b) \frac{1}{x} + 4 < \frac{1}{x} - 2[/tex]

[tex] = \frac{1}{x} + 4 < \frac{1}{x} - 2.x≠0[/tex]

[tex] = 4 < - 2[/tex]

= X ∈ ∅

Answer:

x = 5

y = 3

(5,3)

Step-by-step explanation:

use substitution...

4x -3(2x-7) = 11

-2x + 21 = 11

x = 5

y = 3

Answer: 14-degree decrease

Step-by-step explanation:

because it is getting colder and we know this because anytime temperature goes from positive to negative it becomes mad cold.

Anyways subtracting 14 from our initial temp at 8 degrees celsius brings us to a brisk -6 celsius

Answer:

[tex]2^{-4 n}\times3^{-2 n} + 3^{-2 n}\times4^{-n}[/tex]

Step-by-step explanation:

Assuming you meant [tex]\frac{6^{2n}+1*9^n*4^{2n}}{18^n*2^n*12^{2n}}[/tex], the answer is [tex]2^{-4 n}\times3^{-2 n} + 3^{-2 n}\times4^{-n}[/tex].

Answer:

x>-4 x≤-8

Step-by-step explanation:

Answer:

y - 4 = 1/3 (x - 3)

Step-by-step explanation:

Answer:

cos 0 = 1

.................

Answer:

6-2=1414

Step-by-step explanation:

6-2=1414

now

sub 6 from 2

4=1414

now divide 1414 by 4

1414÷4

[tex]1414 \div 4[/tex]

you will get the answer

Step-by-step explanation:

[tex] \frac{6}{14} - \frac{2}{14} \\ have \: same \: denomenator \: so \: we \\ \: can \: substract \: it \: directly \\ \frac{6 - 2}{14} \\ = \frac{4}{14} = \frac{2}{7} \\ thank \: you[/tex]

Step-by-step explanation:

cannot be written as a fraction so its irrational

Answer:

A, D, E, F

Step-by-step explanation:

0.32 is bigger than 0.058; smaller than 0.492 and 0.41, but also bigger than 0.28, 0.10 and 0.30

Answer:

Step-by-step explanation:

35

Answer:

y = (3/5)*x

Step-by-step explanation:

First, we can use the slope-intercept form of a line, or y=mx+b

To find the slope, m, we can find

(y₂-y₁)/(x₂-x₁). Denoting (0,0) as (x₁,y₁) and (5,3) as (x₂, y₂) (it is perfectly okay to have (0,0) as (x₂, y₂) and (5,3) as (x₁,y₁) as well), we have

(y₂-y₁)/(x₂-x₁) = (3-0)/(5-0) = 3/5

Therefore, our equation is

y = (3/5)x + b

To solve for b, we can plug any value of (x,y) from the line, e.g. (0,0), and solve from there, resulting in

y = mx + b

0 = (3/5)*0 + b

0 = b

Our equation is therefore

y = (3/5)*x + 0

= (3/5)*x

Answer:

76

Step-by-step explanation:

How many numbers are between 256 and 789 are divisible by 7 ?

Generalizing, we could look for a procedure that, given two integers A and B, with B>A , and a module M, tells us how many integers x, with A<=x<=B , are divisible by M.

a) let n1 be the lowest integer >=A such that n1 is divisible by M.

If n1>B , than not even n1 has the required properties and the output of the procedure is 0; otherwise, go to the next step.

n1 will be the first number of the sequence of numbers divisible by M.

b) let n2 be the highest integer <=B such that n2 is divisible by M.

Notice that it’s not possibile that n2<A , as you alway have the possibility n2=n1 .

n2 w

A simple way to think about this is by calculating the largest multiple of 7 less than 256 (let’s call it y) and the smallest multiple of 7 greater than 789 (let’s call it x). The answer is then all the multiples of 7 in between these two numbers, which can be represented by:

x−y7−1

Let’s do it:

252 is the largest number less than 256 divisible by 7. y = 252

791 is the smallest number greater than 789 that’s divisible by 7.

Thus, our answer is 113-36–1 = 76.

Note: we subtract 1 or else we would include the number on the top end of the range (in this case, 791).

Hope it helped you!!

Pls mark me the brainliest :)

Answer:

the middle one is correct

Step-by-step explanation:

the first one is incorrect because the way negative numbers are ordered is incorrect it should be "-3, -2, -1"

the middle one is correct because the pattern is consistent and the order of the numbers are correct

the third one is incorrect because the pattern doesn't match "-15" isn't counting by twos 15 isn't an even number

hope I helped ❤

Explanation:

The first number line is incorrect because the -1, -2, -3 should be reversed to get -3, -2, -1. It's reversed because the negatives are a mirror image of the positive counterpart.

The second number line is correct. Each number shown is separated with a gap size of 20. This gap size stays the same throughout the number line.

The third number line is incorrect. The gap from -15 to -12 is 3 units, while the gap from -12 to -10 is 2 units. We see that the gap size isn't the same through the entire number line.

So to summarize: the gap size must be the same and the numbers must be written in the correct order.

Answer:

30, +11, 11, -1

Step-by-step explanation:

-10 + 30 = 10, 40 - 30= 10

-3 + 11 = 8

5 + (1.5 x 4) = 11

5 - (1.5 x 4) = -1

Answer: I THINK fraction

Step-by-step explanation:

1/4 = fraction

Answer:

166.25

Step-by-step explanation:

12 1 /4 + 154

166 1/4

665/4 , 166.25

Hey there!

12 1/4 + 11.14

= 49/4 + 11.14

= 12.25 + 11.14

= 23.39 or 23 39/100

Answer: 23.39 or 23 39/100

Good luck on your assignment and enjoy your enjoy your day!

~Amphitrite1040:)

Step-by-step explanation:

3m is the answer.

hope it helps

Answer:

3 meters

Step-by-step explanation:

The train starts at (0, 0) and ends at (6, 3). So the train travels in 6 seconds (6 - 0) 3 meters (3 - 0).

Answer:

-1/3

Step-by-step explanation:

The formula for slope is [ y2-y1/x2-x1 ].

-3-(-1)/5-(-1)

-2/6

-1/3

Best of Luck!

Answer:

C 6 loaves with flour left over

Step-by-step explanation:

Take the amount of flour and divide by the amount of flour per loaf

9/2 ÷ 2/3

Copy dot flip

9/2 * 3/2

27/4

Change to a mixed number

4 goes into 27 6 times with 3 left over

6 3/4

Answer:

He can make 6 loafs and he would have 1/6 cups of flour left

Step-by-step explanation:

Answer:

Its minus 70 every time

Step-by-step explanation:

n=32

Answer:

it will take 36 months to completely pay the loan

Step-by-step explanation:

see that if the number of months paid is 1 and the amount owed is 2450 and that on number of months paid is 2 and then the amount owed is 2380

every month we have to substract 70

so we can make a pattern

0 months = 2520

1 month = 2450 that is 2520 - 70

2 months =  2380 that is 2520 - (2 × 70)

3 months = 2310 that is 2520 - (3 × 70)

.....

then it continues till n months

so

n months = 2520 - (n ×70)

n months = 2520 - (36 × 70)

36 months = 2520 - 2520

Histograms are used to graph the frequency of data, where the length of the bar represents the frequency.

The number of students that drank the recommended amount of water are 125

Given that

[tex]Recommended = 40\ or\ more[/tex]

The number of students who drank the recommended amount are students whose frequency (i.e. length of bars) is 40 or more

From the histogram (see attachment), only 2 bars are above the frequency of 40.

And the number of students in these bars are: 50 and 75

[tex]Total =50 + 75[/tex]

[tex]Total =125[/tex]

Hence, the number of students that drank the recommended amount of water are 125

Read more about histograms at:

https://brainly.com/question/14421716

Answer:

A (the firs one)

Step-by-step explanation:

Intersecting at (-3, 3)

Answer:

Lisa spent $35.50

Step-by-step explanation:

$20.50 + $8.75 + $6.25 = 35.5

In terms of money, it is $35.50

Answer:

[tex]thank \: you[/tex]