(sinx + cosx)(1 − sinx cosx) ≡ sin3x + cos3x

Answer:

(6, -1)

Step-by-step explanation:

4x = 24

x = 6

2(6) + 7y = 5

12 + 7y = 5

7y = -7

y = -1

Answer: Choice C

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Explanation:

Recall that the form

[tex]z = r*\left[\cos\left(\theta\right)+i*\sin\left(\theta\right)\right][/tex]

can be abbreviated to

[tex]z = r*\text{cis}(\theta)[/tex]

The "cis" stands for the first letters of "cosine i sine" in that order.

The original fairly messy quotient can be shortened down to

[tex]\frac{90\text{cis}(\pi/4)}{2\text{cis}(\pi/12)}[/tex]

We have 90cis(pi/4) all over 2cis(pi/12) as one big fraction.

-------------------------------

Now we'll use this rule to divide two complex numbers

[tex]z_1 = r_1*\text{cis}(\theta_1)\\\\z_2 = r_2*\text{cis}(\theta_2)\\\\\frac{z_1}{z_2} = \frac{r_1}{r_2}*\text{cis}(\theta_1-\theta_2)\\\\[/tex]

As you can see, we divide the r1 and r2 values to form the final coefficient out front. The theta angles are subtracted to form the new argument.

-------------------------------

Let's apply that idea to what your teacher gave you

[tex]z_1 = 90*\text{cis}(\pi/4)\\\\z_2 = 2*\text{cis}(\pi/12)\\\\\frac{z_1}{z_2} = \frac{90}{2}*\text{cis}(\pi/4 - \pi/12)\\\\\frac{z_1}{z_2} = 45\text{cis}(3\pi/12 - \pi/12)\\\\\frac{z_1}{z_2} = 45\text{cis}(2\pi/12)\\\\\frac{z_1}{z_2} = 45\text{cis}(\pi/6)\\\\[/tex]

That last step then converts directly to the expression shown in choice C.

Answer:

1738 kilometers

Step-by-step explanation:

Answer:

y= 10/3 + x/3

Step-by-step explanation:

not sure how to explain this

The value of y for the given equation is y = [tex]\frac{x}{3}[/tex] + [tex]\frac{10}{3}[/tex].

A linear equation is an equation where the maximum power of the variable is one. A linear equation may contain more than one variables. However, the highest power of any variable must be one.

Here, a linear equation is given that contains two variables x and y.

Therefore, 6y - 2x = 20

⇒ 6y = 2x + 20

⇒ y = (2x + 20)/6

⇒ y = [tex]\frac{2x}{6}[/tex] + [tex]\frac{20}{6}[/tex]  

⇒ y = [tex]\frac{x}{3}[/tex] + [tex]\frac{10}{3}[/tex]

Hence, the value of y is   [tex](\frac{x}{3}+\frac{10}{3})[/tex]

Learn more about a linear equation here: https://brainly.com/question/21835898

#Tag #SPJ2

Answer:

B' (3, 1 )

Step-by-step explanation:

Given

A (- 1, 3 ) → A' (- 3, 7 )

x- coordinate goes from - 1 → - 3 , that is - 2

y- coordinate goes from 3 → 7 , that is + 4

Translation rule is (x, y ) → (x - 2, y + 4 ) , then

B (5, - 3 ) → B' (5 - 2, - 3 + 4 ) → B' (3, - 1 )

Answer:

5

Step-by-step explanation:

By process of elimination, we can say for sure that C and D are not the right answers because as x- the numbers on the top- increases, y- the numbers on the bottom- increases. This means that the slope is not negative, because the slope is the rate of change and it does not have a negative rate of change.

The equation for slope is y2-y1 / x2-x1. Meaning, y is on top and x is on bottom. This creates a fraction. So let's take 0 and 1 for X, the first and second values, and 3 and 8 for y, the first and second values. We swap them, because the second y value comes first, so we have 8 - 3 for the top, the numerator. Then we have 1 - 0 for the bottom, the denominator. Solving 8 - 3 and 1 - 0, we have 5/1. 5/1 simplifies to 5, and thus 5 is your slope.

Answer:

[tex]169[/tex]

Step-by-step explanation:

[tex]13 \times 13 \times 1[/tex]

[tex] = 13 \times 13[/tex]

[tex] = 169[/tex]

Answer:

-12

Step-by-step explanation:

3q-6=x q=-2

(3(-2))-6

-6-6=x

-12=x

Answer:

1-a) 78+x+16+x+24=180°

118+2x=180

2x=62

so x=31

Step-by-step explanation:

thats a

Answer:

1a) x = 31

1b) x = 12

2) angle A = 60 degrees

3) x = 40 degrees

Step-by-step explanation:

Answer:

your friend has 6 more marbles

Step-by-step explanation:

7×2=14

10×2=20

20-14=6

Answer:

6

Step-by-step explanation:

First you multiply 7 by 2 because there is 2 marbles in each bag and there is 7 bags so that is 14 marbles

Then you multiple 2 by 10 because there is 10 bags with 2 marbles each which is 20.

20-14=6

Can I get brainliest?

Answer:

5<6 so tbh I have no idea what this is I just need point

Dilation is the transformation that changes the size of a shape.

4 is a positive number so the shape will increase in size.

So after dilating every side by 4:

0,1

-0.5,0

1,0

We get

0,4

-2,0

4,0

Answer:

We know that x is 2

Whilst y is 3

this can be changed due to it’s ratio

So in this code x+y=10

2+3=10

We can do it this way.

2+3=5 (add the ratios)

10/5=2 (Divide the sum by the number needed)

2*2=4 (multiply the quotient for each ratio)

3*2=6 (multiply the quotient for each ratio)

x is 4

y is 6

Answer:

See below:

Step-by-step explanation:

Hello! My name is Galaxy and I will be helping you today. I hope you are having a nice day!!

We can solve this problem in two steps, Comprehension and Solving

I'll start off with comprehension.

Comprehension

We know that ratios are basically fractions as they both show comparison, so we can make x:y into [tex]\frac{x}{y}[/tex].

We also have another equation, making this problem a system of equations.

Now that we know what to do, we can begin solving!

Solving

We can solve this by first getting our two equations.

[tex]\frac{x}{y}=\frac{2}{3}[/tex]

We can simplify the 2nd equation so that we know what one variable is.

[tex]x+y=10\\x=10-y[/tex]

We can now input our second equation into the first equation.

[tex]\frac{10-y}{y}=\frac{2}{3}\\3(10-y)=2y\\30-3y=2y\\30=5y\\y=6[/tex]

If y is six, then we can use the second equation to solve for x.

[tex]x+6=10\\x=4[/tex]

We know that x is 4 and y is 6.

We can now check our answers.

1st Equation

[tex]\frac{4}{6}=\frac{2}{3}?\\[/tex]

[tex]\frac{2}{3}=\frac{2}{3}[/tex]

2nd Equation

[tex]4+6=10?\\10=10[/tex]

We've proven our answers to be right, therefore, x is 4 and y is 6.

Answer:

there should be 14, 45 pound boxes

Step-by-step explanation:

1000-190= 810

810/45=14 boxes

Answer:

c I think that is the answer

Step-by-step explanation:

a_2=2a_4+2

a=_2+4_2

a=0

Answer:

She lives in the Southern Hemisphere.

Step-by-step explanation:

Answer:

= 7.25

Conversion a mixed number 4 3/

4

to a improper fraction: 4 3/4 = 4 3/

4

= 4 · 4 + 3/

4

= 16 + 3/

4

= 19/

4

To find a new numerator:

a) Multiply the whole number 4 by the denominator 4. Whole number 4 equally 4 * 4/

4

= 16/

4

b) Add the answer from previous step 16 to the numerator 3. New numerator is 16 + 3 = 19

c) Write a previous answer (new numerator 19) over the denominator 4.

Four and three quarters is nineteen quarters

Conversion a mixed number 2 1/

2

to a improper fraction: 2 1/2 = 2 1/

2

= 2 · 2 + 1/

2

= 4 + 1/

2

= 5/

2

To find a new numerator:

a) Multiply the whole number 2 by the denominator 2. Whole number 2 equally 2 * 2/

2

= 4/

2

b) Add the answer from previous step 4 to the numerator 1. New numerator is 4 + 1 = 5

c) Write a previous answer (new numerator 5) over the denominator 2.

Two and one half is five halfs

Add: 19/

4

+ 5/

2

= 19/

4

+ 5 · 2/

2 · 2

= 19/

4

+ 10/

4

= 19 + 10/

4

= 29/

4

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(4, 2) = 4. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 2 = 8. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - nineteen quarters plus five halfs = twenty-nine quarters.

Step-by-step explanation:

Answer:

you can write it in exact form which is 9/4 or decimal form which is 2.25 or mixed number form 2 1/4

Step-by-step explanation:

Step-by-step explanation:

a. 17 + 6/10 = (17 x 10) / (1 x 10) + 6/10 = 170/10 + 6/10 = 176/10 = 17,6

b. 45 + 6/100 = (45 x 100) / (1 x 100) + 6/100 = 4 500/100 + 6/100 = 4 506/100 = 45,06

c. 3 + 5/10 + 2/100

= (3 x 100) / (1 x 100) + (5 x 10) / (10 x 10) + 2/100

= 300/100 + 50/100 + 2/100

= 352/100 = 3,52

d. 6 + 7/10 + 8/100 + 9/1 000

= (6 x 1 000) / (1 x 1 000) + (7 x 100) / (10 x 100) + (8 x 10) / (100 x 10) + 9/1 000

= 6 000/1 000 + 700/1 000 + 80/1 000 + 9/1 000

= 6 789/1 000 = 6,789

e. 11 + 6/10 + 8/1 000

= (11 x 1 000) / (1 x 1 000) + (6 x 100) / (10 x 100) + 8/1 000

= 11 000/1 000 + 600/1 000 + 8/1 000

= 11 608/1 000 = 11,608

f. 84 + 1/100 + 3/10

= (84 x 100) / (1 x 100) + 1/100 + (3 x 10) / (10 x 10)

= 8 400/100 + 1/100 + 30/100

= 8 431/100 = 84,31.

Hope this helps!!

Answer:

I am not certified because I also struggle with these but-

it might be

A. t = -5h-4

Step-by-step explanation:

For the answer A in the paragraph it states that the temperature was 4 degrees BELOW 0 meaning we shall put as -4° and each HOUR it keep going down 5 degrees so I would suppose it would be answer A.

Answer:

The sales tax is $3.5

The total cost is $53.5

Step-by-step explanation:

To find the sales tax, you have to find the 7 percent of 50 dollars. In decimal form, 7% is 0.07. So you just have to multiply 0.07 to 50.

50 x 0.07 = 3.5

That's why $3.5 is the sales tax.

In order to get the total cost including sales tax. You just have to add $50 to the sales tax which is $3.5.

$50 + $3.5 = $53.5

Answer:

Yes, because in 1 game you scored 12 points you didn't score multiple points in multiple games.

Answer:

205

Step-by-step explanation:

helicopter=65m

tap of the cliff=

the boy=350m

210=

that makes the answer 205

Answer:

205 meters

Step-by-step explanation:

The cliff is 350m, and the rescue helicopter is 65m above the top of the cliff.

This means that the helicopter is 415 meters above the bottom of the cliff.

The boy is 210m above the bottom of the cliff.

So, you have to subtract 210 from 415 to get 205.

Therefore, you have to lower the rescue 205m to reach the boy.

Answer:

4.6

Step-by-step explanation:

23/5=4.6

Answer:

1 and 3/20 total, 15/20 of the fish are yellow tangs which would also be 75%.

Step-by-step explanation:

2/5 and 3/4 need to be converted into a fraction with a similar denominator. 5x4= 20, so 20 is our denominator.

To find the numerator, we need to multiply 2 by 4, which equals 8, and 3 by 5 which equals 15.

8/20 + 15/20 = 23/20 or 1 3/20

Answer:

7 buckets.

Step-by-step explanation:

17.5 / 2.5 = 7

Answer:

7

Step-by-step explanation:

17.5/2.5=7

true

Step-by-step explanation:

Answer:

3x-3

Step-by-step explanation:

So false if you Multiply