I could use some help w/ explanation please

Hello there!

Formulas

[tex] \displaystyle \large{ \sin (2 \theta) = 2 \sin \theta \cos \theta} \\ \displaystyle \large{ \cos (2 \theta) = \begin{cases} 2 { \cos}^{2} \theta - 1 \\ 1 - 2 { \sin}^{2} \theta \\ { \cos}^{2} \theta - { \sin}^{2} \theta \end{cases}}[/tex]

First, we have to find cos(theta). We know that the theta lies in Q3 which is negative for both sin and cos. To find cos, you can use the identity or Pythagoras.

Recall

[tex] \displaystyle \large \tt{ \sin \theta = \frac{opposite}{hypotenuse} } \\ \displaystyle \large \tt{ \cos \theta = \frac{adjacent}{hypotenuse} }[/tex]

Finding cos, I will use Pythagoras.

Recall Pythagorean

[tex] \displaystyle \large{ {a}^{2} + {b}^{2} = {c}^{2} }[/tex]

From sin = -1/6

[tex] \displaystyle \large{ {1}^{2} + {b}^{2} = {6}^{2} } \\ \displaystyle \large{1 + {b}^{2} = 36 } \\ \displaystyle \large{ {b}^{2} = 36 - 1 } \\ \displaystyle \large{ {b}^{2} = 35 } \\ \displaystyle \large{ {b} = \sqrt{35} }[/tex]

b is our adjacent. Hence,

[tex] \displaystyle \large{ \cos \theta = \frac{ \sqrt{35} }{6} }[/tex]

Since theta is in Q3, cos < 0 or in negative.

[tex] \displaystyle \large{ \cos \theta = - \frac{ \sqrt{35} }{6} }[/tex]

Finding sin(2theta)

[tex] \displaystyle \large{ \sin \theta = - \frac{ 1 }{6} }[/tex]

Hence,

[tex] \displaystyle \large{ \sin 2 \theta = 2( - \frac{ 1 }{6} )( - \frac{ \sqrt{35} }{6}) } \\ \displaystyle \large{ \sin 2 \theta = ( - \frac{ 1 }{3} )( - \frac{ \sqrt{35} }{6}) } \\ \displaystyle \large{ \sin 2 \theta = \frac{ \sqrt{35} }{18} }[/tex]

Recall

Finding cos(2theta)

The cos of 2theta has multiple formulas. All of them are same and also identity to each others.

I will be using the first one as it only involves cos, not sin.

[tex] \displaystyle \large{ \cos \theta = - \frac{ \sqrt{35} }{6} }[/tex]

Therefore,

[tex] \displaystyle \large{ \cos2 \theta = 2 { ( - \frac{ \sqrt{35} }{6} )}^{2} - 1 } \\ \displaystyle \large{ \cos2 \theta = 2 (\frac{ 35}{36}) - 1 } \\ \displaystyle \large{ \cos2 \theta = \frac{ 35}{18} - 1 } \\ \displaystyle \large{ \cos2 \theta = \frac{ 35}{18} - \frac{18}{18} \longrightarrow \boxed{\frac{17}{18} }}[/tex]

Answer

The last choice.

Let me know if you have any questions!

9514 1404 393

Answer:

  r = 2

Step-by-step explanation:

"A varies inversely with r cubed" means the relation is of the form ...

  A = k/r³

We can find the value of k as ...

  k = Ar³ = 72·5³ = 9000 . . . . . . . multiply the above relation by r³

And we can solve this for r to get ...

  r³ = 9000/A . . . . . . divide by A

  r = ∛(9000/A) . . . . . take the cube root

So, for A = 1125, we have ...

  r = ∛(9000/1125) = ∛8

  r = 2

what help you want

can u tell

[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]

[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]

[tex] \huge \boxed{\mathfrak{{2}^{3} }}[/tex]

The range of the function is [560, ∞]

The cost of the new phone = $500

The cost of month plan = $60

The average monthly cost of the cell phone is calculated as:

[tex]C(t) = 500 + 60t \\\\[/tex]

where:

t is the number of months of owing the phone

The range of the function is calculated as follows;

t ≥ 1

when t = 1

C(1) = 500 + 60(1) = $560

t can be any positive integer.

The range of the function = [560, ∞]

Learn more here: https://brainly.com/question/14489958

Answer:

I think B. R: (60,560)

Step-by-step explanation:

Not 100% sure but tell me if im wrong

Although your question is vague a general answer within the concept of your of your question is provided. The correct answer to a numeric entry field will be automatically populated after the explanation is open ( i.e. True is the correct answer )

When you open up the explanations to a correct answer the entry field for the answer will automatically be populated with the correct answer, because by selecting/clicking on the explanation you will be granted access to the answer behind the explanation as well. also another way to access the correct answer is to  simply select the entry field

Learn more : https://brainly.com/question/18890785

Answer:

56,58,60

Step-by-step explanation:

x = 1st side of triangle

x+2 = 2nd side

x+4 = 3rd side

P = side1 + side 2 + side 3

174 = x+ x+2  + x+4

Combine like terms

174 = 3x+6

Subtract 6 from each side

174 -6 = 3x+6-6

168 = 3x

Divide by 3

168/3 = 3x/3

56 =x

1st side = 56

2nd side = 58

3rd side = 60

Answer:

option A is right answer

Part (a)

We have some unknown number x which is a placeholder for a positive whole number (eg: x = 4).

What's happening to x are these two things, in this exact order

We multiply first, then add. The order is important. We're following the order of operations PEMDAS here. If we knew what x was, then we'd go forward in the PEMDAS chain; however, we don't know what x is. So we go backwards in the chain to isolate x. This will undo every operation applied to x.

So,

C = 85x+60

C-60 = 85x

85x = C-60

x = (C-60)/85

In the second step, I subtracted 60 from both sides to undo the "plus 60" operation. Then in the last step, I divided both sides by 85 to undo the multiplication.

===============================================================

Part (b)

How many ski trips can we take if we spend $315? We simply plug in C = 315 into that equation we just found at the end of part (a).

Doing so gets us...

x = (C-60)/85

x = (315-60)/85

x = 255/85

x = 3

We can take 3 ski trips if we spent a total of $315

Repeat the same steps for C = 485

x = (C-60)/85

x = (485-60)/85

x = 425/85

x = 5

We can take 5 ski trips if we spent a total of $485

Note how plugging something like x = 5 into the original equation yields:

C = 85x+60

C = 85*5+60

C = 425+60

C = 485

Showing that x = 5 leads to C = 485. This helps confirm the second answer. I'll let you check the first answer.

Answer:

408

Step-by-step explanation:

1275 times .32=408.

Answer:

The answer would be $408

Answer:

16896

Step-by-step explanation:

3×1×11×512

=16896

Step-by-step explanation:

3×1×11×5×1×2=330

Answer:

true, negative, negative

Answer:

21 loads

Step-by-step explanation:

357/17=21

Step-by-step explanation:

A line perpendicular to a surface or to another line considered as a base.

If a female is chosen, then the probability that she is satisfied with the company's customer service is 0.24.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given that, A credit card company surveys 125 of its customers to ask about satisfaction with customer service. The results of the survey, divided by gender, are shown below.

                                     Males                           Females

Extremely Satisfied          25                              7

Satisfied                            21                              13

Neutral                              13                               16

Dissatisfied                        9                                14

Extremely Dissatisfied       2                                 5

Here, the total number of customers is 125. (N=125).

If a female is chosen, find the probability that she is satisfied with the company's customer service. Here, conditional probability is used.

[tex]P(satisfied|female) = \frac{P(satisfied and female)}{P(females)} \\Here\\P(satisfied|female) = \frac{n(satisfied and female)}{N} \\= \frac{13}{125} \\= 0.104\\P(female) = \frac{n(female)}{N} \\= \frac{55}{125} \\= 0.44\\Now, \\P(satisfied|female) = \frac{n(satisfied and female)}{P(female)} \\= \frac{0.104}{0.44}\\= 0.24[/tex]

Hence, if a female is chosen, then the probability that she is satisfied with the company's customer service is 0.24.

For more references on probability, click;

https://brainly.com/question/30034780

#SPJ2

8x=15+9

8x÷8=24÷8

x=3

you are going to divide 8 by 8 which will cancel each other and you will left with x and divide 24by 8 which will give you 3

9514 1404 393

Answer:

  100 ft

Step-by-step explanation:

The centroid divides each median into parts in the ratio 2 : 1. The longest part is 2/(2+1) = 2/3 of the whole length of the median.

That is, AG = 2/3AC = (2/3)(150 ft) = 100 ft.

Answer:

highest temperature would be

-22 + 139 = 117°F

The statement "a system that consists of a linear equation and a quadratic equation can have zero, one, or two solutions" is true .

A linear equation is an algebraic equation of the form [tex]y= mx+b.[/tex]involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

We define a quadratic equation as an equation of degree 2, meaning that the highest exponent of this function is 2. The standard form of a quadratic is , [tex]y = ax^2 + bx + c[/tex]

where a, b, and c are numbers and a cannot be 0.  

According to the question

A system that consists of a linear equation and a quadratic equation can have zero, one, or two solutions.​

This statement is true as

if we see graphically  

A quadratic equation is a parabola and a linear equation is a straight line.

There could be 3 situations of intersection of line and parabola

1. straight line never crosses the parabola

i.e line passing above or below parabola without touching

it is called zero solution

2. where the straight line is a tangent to the parabola, 'touching' it at only one point.

i.e single point lies in both line and parabola

it is called one solution

3. the line cuts across the parabola, it will cut the parabola at 2 points

it is called two solution .

Hence, The statement " a system that consists of a linear equation and a quadratic equation can have zero, one, or two solutions "is true .

To know more about linear equation and quadratic equation here:

https://brainly.com/question/2263981

#SPJ2

Answer:   The intersections of the graphs of a system of equation correspond to the solutions of the system. Since we saw that a line can intersect a parabola zero, one, or two times, a linear-quadratic system can have zero, one, or two solutions.

Step-by-step explanation:PLATO

Answer:

[tex]3.1 \times {}^{ - 6} [/tex]

Step-by-step explanation:

[tex]3.1 \times 10 {}^{ - 6} [/tex]

Answer:

0.81

Step-by-step explanation:

Answer:

0.81818181818181....

Step-by-step explanation:

It is irrational

Answer:

10.5 percents

Step-by-step explanation:

1)100+30=130 percents;

2) 130/100*15=19.5percents of discount from the first price

3) 130-19.5=110.5 percents- new price from the initial price

4)110.5-100=10.5 percents - the percentage of profit

Answer:

C

Step-by-step explanation:

5 states per year = 5y

Already visited 10 states = +10

5y + 10 = 50

To find y

5y = 50 - 10

5y = 40

y = 40/5

y = 8 years

Answer:

x = -5

Step-by-step explanation:

-7x + 4 = 39

-7x (+ 4 - 4) = 39 - 4

-7x = 35

-7x/-7 = 35/-7

x = -5

Answer:

Step-by-step explanation:

The probability an R&B song will play is 0 because 20 - 3 = 17 and 17 - 12 = 5, leaving 5 - 5 to be 0.

Let's solve your equation step-by-step.

9x=10

Step 1: Divide both sides by 9.

9x / 9 = 10 /9

x = 10 / 9

Answer:

x = 10 / 9

Answer:

yes

Step-by-step explanation:

because -16 and -2 is a whole number. and it doesnt have neither fractions nor decimals.

hope this helps. have a good day

Answer:

the answer is 3-3n

Step-by-step explanation:

6-(n-1)x3

=3-3n

An equation for the nth term of the arithmetic sequence is aₙ=9-3n.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.

The given arithmetic sequence is 6,3,0,-3,...

Here, first term a=6 and common difference is 3-6=-3

Substitute a=6 and d=-3 in aₙ=a+(n-1)d, we get

aₙ=6+(n-1)(-3)

aₙ=6-3n+3

aₙ=9-3n

Therefore, an equation for the nth term of the arithmetic sequence is aₙ=9-3n.

To learn more about an arithmetic sequence visit:

https://brainly.com/question/10396151.

#SPJ2