Study the work shown to find the exact solutions of this trigonometric equation.

Solve: 2 cosine (x) minus StartRoot 3 EndRoot = 0 for 0 less-than-or-equal-to x less-than-or-equal-to 2 pi. 2 cosine (x) minus StartRoot 3 EndRoot = 0. 2 cosine (x) = StartRoot 3 EndRoot. Cosine (x) = StartFraction StartRoot 3 EndRoot Over 2 EndFraction. Cosine Superscript negative 1 Baseline (StartFraction StartRoot 3 EndRoot Over 2 EndFraction) = x

Select all that are solutions of the equation over the specified domain.

Step-by-step explanation:

angle ABD = 180 - 116 = 64° (angles on a straight line are supplementary)

angle x = 2(64) = 128° (angle at centre = 2angle at circumference)

Topic: Circle properties

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9514 1404 393

Answer:

  "similar"

Step-by-step explanation:

Congruent polygons will have corresponding sides in the ratio 1:1, but they must also have identical corresponding angles. The description of figures with identical corresponding angles (along with proportional sides) is that they are "similar".

  Congruent polygons are similar polygons for which the ratio of the corresponding sides is 1:1.

Answer:

13.142

Step-by-step explanation:

The sum of the decimal numbers will be 13.142.

What is Decimal number?

A decimal number is a number that consists of a whole and a fractional part.

Given that;

The expression of the decimal numbers are,

⇒ 6.338 + 2.705 + 4.099

Now,

Since, The expression of the decimal numbers are,

⇒ 6.338 + 2.705 + 4.099

Add the numbers as;

 6.338

 2.705

+4.099

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

13.142

Thus, The sum of the decimal numbers will be 13.142.

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Answer: The cat is 4 years old, and the dog is 6 years old.

Step-by-step explanation:

We know that Buddy is 2 years old than Fluffy.

And 3 years ago, Buddy was 3 times older than Fluffy.

Let's define the variables:

B = age of Buddy

F = age of Fluffy.

The first statement can be written as:

B = F + 2

The second statement can be written as:

B - 3 = 3*(F - 3)

To solve this, we can replace the first equation into the second one, and solve that for F

B - 3 = 3*(F - 3)

(F + 2) - 3 = 3*F - 9

F - 1 = 3*F - 9

-1 + 9 = 3*F - F

8 = 2*F

8/2 = 4 = F

Fluffy is 4 years old, and with the first equation we can find the age of Buddy.

B = F + 2 = 4 + 2 = 6

Buddy is 6 years old

The required age of the dog buddy is 6 years old and the age of cat fluffy is 4 years old.

Given ,

James's dog buddy is 2 years older than Fluffy,

And the neighbor's cat Three Years ago, Buddy was three times older than fluffy.

Let ,

The age of buddy = B

The age of fluffy is = F

According to the question ,

Buddy, is 2 years older than Fluffy= Age of Buddy = Age of fluffy + 2 years older.

B = F +2

Again According to the question,

Three years ago age of Buddy = B - 3

Three years ago age of Fluffy = F - 3

Three years ago Buddy was three times older than fluffy = Three years ago age of Buddy = 3 × Three years ago Age of fluffy

B - 3 = 3 ( F - 3 )

Solving the equations,

B - 3 = 3 ( F - 3 )

Put the value of B from equation 1

F + 2 - 3 = 3 ( F -3 )

F - 1 = 3F - 9

F - 3F = - 9 +1

-2F = -8

2F = 8

[tex]F = \frac{8}{2}[/tex]

F = 4

The age of fluffy is 4 years old.

Then ,

The age of buddy

B = F + 2

B = 4 + 2

B = 6

The age of buddy is 6 years old.

The required age of the dog buddy is 6 years old and the age of cat fluffy is 4 years old.

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Answer:

[tex]p=39.4[/tex]°

Step-by-step explanation:

[tex]4a+4+75+p=180[/tex] (The sum of angles on a triangle is [tex]180[/tex]°)[tex]4a+p=180-4-75[/tex]

[tex]4a+p=101[/tex]

[tex]p+9a+2=180[/tex]  (Angles of a straight line sums to [tex]180[/tex]°)

[tex]p + 9a = 178[/tex]

Elimination can be used to find the value of one variable:

[tex]p+9a-(4a+p)=178-101[/tex]

[tex]5a = 77[/tex]

[tex]a=15.4[/tex]

Now, the value of [tex]p[/tex] can be found by using substitution:

[tex]4a+p = 101[/tex]

[tex]4(15.4)+p=101[/tex]

[tex]p = 101-61.6[/tex]

[tex]p = 39.4[/tex]

I hope this helps :)

Answer:

12 years

Step-by-step explanation:

Given that Mr. Hon purchases a new car every 4 years. Ms. Jasper purchases a new car every 6 years.

Assuming that they purchase new cars together after n years.

So, n must a multiple of 4 as well as multiple 6, i.e the number n is the lowest multiple (LCM) of 4 and 6.

As LCM od 4 and 6 is 12, so n=12.

Hence, after 12 years they will purchase news cars together.

Answer:

-8.4,-8,8,8.4

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

The number of candies can be divided among 2, 3, or 5 children so that is the same as saying: the number of candies must be divisible by 2, 3, and 5. In order for a number to be divisible by 5, it must end in 0 or 5 so we know the number of candies must end in 0 or 5. For a number to be divisible by 2, the number must end in an even number. 5 is not an even number so we know the number of candies must end in 0. If a number is divisible by 3, the digits added are divisible by 3. Go through each number(80, 90, 100) and see which one is divisible by 3. 90 is divisible by 2, 3, and 5.

Proof that 90 is divisible by 2, 3, and 5:

90 ÷ 2 = 45

90 ÷ 3 = 30

90 ÷ 5 = 18

The results are all whole numbers.

[tex] \: \: \: \: \: \: \: \: \: \: 4y - 2(3y - 5) \\ \\ = > 4y- 6y + 10 \\ \\ = > \green{\boxed{ - 2y + 10}}[/tex]

Answer:

iam sorry but furries are good lg!!!

Furry can have two definitions. A furry is either an anthrophomorphic animal which has human characteristics or a person that shows interest in furries. If you draw other people's fursona, i don't think that makes you a furry tbh. If you show interest and if you have your own fursona and you're passionate about it, however, then yeah you're pretty much a furry. Being a furry isn't bad honestly, it's just a hobby. I'm a furry myself and i honestly love this fandom. I met a lot of great people!

Answer:

x=6.25

Step-by-step explanation:

What you do is add up all the angles equal to 180 because a triangle always adds up to 180 degrees and you are given all angles.

Answer:

x = 25/4

General Formulas and Concepts:

Pre-Algebra

Geometry

Step-by-step explanation:

Step 1: Set up equation

(22x + 1)° + (6x - 17)° + (4x - 4)° = 180°

Step 2: Solve for x

Answer:

I think its the green one

Step-by-step explanation:

if you get it wrong sorry

Answer:

Goodnight!!! :)

Step-by-step explanation:

Answer:

nothing

Step-by-step explanation:

a product of 2 positive numbers always shows a positive value if we add them

Answer:

60

Step-by-step explanation:

Hope this helped!

Answer:

60

Step-by-step explanation:

Answer:

Q and W are similar but not congruent.

Step-by-step explanation:

Answer:

0.51

Step-by-step explanation:

okay I'm not good at explaining this but I'm going to try my best

put 0.15 on top of 0.36 like this

1

0.15

0.36

_____

0.51

5+6=11

3+2=5 I said 2 because 5+6=11 so you had to carry your 1

then you would just bring your 0 down cause everybody know 0+0=0 lol!

Answer:

x = number of students in the van = 14

y = number of students in the bus = 37

Step-by-step explanation:

Let

x = number of students in the van

y = number of students in the bus

14x + 2y = 270 (1)

9x + 9y = 459 (2)

Multiply (1) by 9 and (2) by 2

126x + 18y = 2,430 (3)

18x + 18y = 918 (4)

Subtract (4) from (3)

126x - 18x = 2,430 - 918

108x = 1,512

x = 1,512 / 108

= 14

x = 14 students in each van

Substitute x = 14 into (1)

14x + 2y = 270

14(14) + 2y = 270

196 + 2y = 270

2y = 270 - 196

2y = 74

y = 74/2

= 37

y = 37 students in each bus

x = number of students in the van = 14

y = number of students in the bus = 37

Answer:

3:5 or 3/5 is equal to 30:50 or30/50

so the answer is 50 chocolate cones

Answer:

x=8

Step-by-step explanation:

Each of the angles in a rectangle equal 90, so you would set 10x+10 equal to 90.

10x+10=90

10x=80

x=8

Answer:

Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6. Thus, the equation of the line is y = ½x + 6.

Answer:

See below.

Step-by-step explanation:

This question makes no sense.

Here is the question. Pay attention to the words in boldface.

"In order to write the equation of the line passing through the point (-2, 2) that is parallel to the line y = 2x + 3 , the next step is to find the y-intercept of the perpendicular line. What is the y-intercept of the perpendicular line through point (-2, 2)?"

Is the question asking for the parallel line or the perpendicular line?

Answer:

8,748

Step-by-step explanation:

f(x) = [tex]12(3)^{x}[/tex]

f(6) = [tex]12(3)^{6}[/tex] = 12 × 9³ = 12 × 729 = 8,748

Answer: C

Step-by-step explanation:

Supplementary angles add up to 180

x + 83 = 180

x= 97

Answer:

Thus, the dimensions of the metal plate are 10 dm and 8 dm.

Step-by-step explanation:

For a quadratic equation:

[tex]x^2+bx+c=0[/tex]

The sum of the roots is -b and the product is c. Note the leading coefficient is 1.

We know the perimeter of the rectangular metal plate is 36 dm and its area is 80 dm^2. Being L and W its dimensions, then:

P=2(L+W)=36

A=L.W=80

Note both formulas are closely related to the roots of the quadratic equation, we only need to adjust the data for the perimeter to be exactly the sum of L+W and not double of it.

Thus we use the semi perimeter instead as P/2=L+W=18

The quadratic equation is, then:

[tex]x^2-18x+80=0[/tex]

Factoring by finding two numbers that add up to 18 and have a product of 80:

[tex](x-10)(x-8)=0[/tex]

The solutions to the equation are:

x=10, x=8

Thus, the dimensions of the metal plate are 10 dm and 8 dm.

Answer:

I think it's 11

Step-by-step explanation:

11 times 3 is 33 minus 8 is 25 and 25 is greater than 22

Answer:

h > 10

Step-by-step explanation:

3h-8>22

1. Separate the coefficient and variable.

Separate 3h, we'll save that for later.

2. Use inverse operations and apply it to both sides of the equation.

In this case, it is subtraction, so we will add 8 to both sides of the equation.

3h - 8 > 22

    + 8   + 8

That gives us 3h > 30, because the 8 and 8 cancels out.

3. Use inverse operations. (3h and 30.)

In this case, it is multiplication, so we will divide 3 from both sides of the equation.

3/3 > 30/3

30 divided by 3 is 10, therefore, the answer is h > 10

(Since we did not divide 30 with a negative number, the sign stays the same, and it is not switched.)

Step-by-step explanation:

hii, im good and ur the best. thank uuuu oncemore..

Answer:

Each song is 2.3 minutes long

Step-by-step explanation:

55/24=2.3