Help please!!!! Thank you

Answer:

2√6/7

Step-by-step explanation:

The following data were obtained from the question:

Cos A =?

Hypothenus = 14

Adjacent = √96

Cos A = Adjacent /Hypothenus

Cos A = √96/14

Cos A = √(16 × 6)/14

Cos A = (√16 × √6)/14

Cos A = 4√6/14

Cos A = 2√6/7

Therefore, the value of Cos A is 2√6/7

Your question has been heard loud and clear.

tanθ+tan(60∘+θ)+tan(120∘+θ)

=tanθ+3–√+tanθ1−3–√tanθ+−3–√+tanθ1+3–√tanθ

[tanθ(1−3tan2θ)+(3–√+tanθ)(1+3–√tanθ)

=+(−3–√+tanθ)(1−3–√tanθ)1−3tan2θ

=9tanθ−3tan3θ1−3tan2θ=3tan3θ

Thank you.

Answer:  see proof below

Step-by-step explanation:

Use the following identities

tan (A + B) = (tan A + tan B)/(1 - tan A · tan B) -->  [tex]\dfrac{tanA+tanB}{1-tanA\cdot tanB}[/tex]

tan 60° = √3

tan 120° = -√3

tan 3A = (3tanA - tan³A)/(1 - 3 tan²A)  --> [tex]\dfrac{3tanA-tan^3A}{1-3tan^2A}[/tex]

Proof LHS → RHS

Given:                  tan Ф + tan(60° + Ф) + tan(120° + Ф)

Sum Difference: tan Ф + (tan 60° + tanФ)/(1-tan60°·tanФ) + (tan 120° + tanФ)/(1-tan120°·tanФ)

              (latex)    [tex]tan\theta+\dfrac{tan60^o+tan\theta}{1-tan60^o\cdot tan\theta}+\dfrac{tan120^o+tan\theta}{1-tan120^o\cdot tan\theta}[/tex]

Substitute:         tan Ф + (√3 + tanФ)/(1-√3·tanФ) + (-√3 + tanФ)/(1+√3°·tanФ)

               (latex)   [tex]tan\theta+\dfrac{\sqrt3+tan\theta}{1-\sqrt3 tan\theta}+\dfrac{-\sqrt3+tan\theta}{1+\sqrt3tan\theta}[/tex]

Common Denominator: [tan Ф(1-3tan²Ф)+8tanФ]\(1-3tan²Ф)

                (latex)   [tex]\dfrac{tan\theta(1-3tan^2\theta)+8\theta}{1-3tan^2\theta}[/tex]

Distribute:             (tan Ф - 3tan³Ф + 8Ф)\(1 - 3 tan²Ф)

               (latex)    [tex]\dfrac{tan\theta-3tan^3\theta+8\theta}{1-3tan^2\theta}[/tex]

Simplify:               (9Ф - 3tan³Ф)\(1 - 3 tan²Ф)

                          3(3Ф - tan³Ф)\(1 - 3 tan²Ф)

               (latex)   [tex]\dfrac{9\theta - 3tan^3\theta}{1-3tan^2\theta}[/tex]

                            [tex]\dfrac{3(3\theta - tan^3\theta)}{1-3tan^2\theta}[/tex]

Triple Angle Identity:   3 tan 3Ф

3 tan 3Ф = 3 tan 3Ф   [tex]\checkmark[/tex]

Answer:

18/25

Step-by-step explanation:

=54÷375÷3=18/25

=18/25

Answer

[tex] \boxed{\mathsf{3x(x + 3)}}[/tex]

Step by step explanation

[tex] \mathsf{3 {x}^{2} + 9x}[/tex]

Take 3x as common

⇒[tex] \mathsf{3x(x + 3)}[/tex]

Hope I helped!

Best regards!

Answer:

Step-by-step explanation:

Factor 3x out of 3x^2=3x(x)-9x=Factor 3x out of 9x=3x(x)+3x(-3)=factor 3x out of 3x(x)+3x(-3). =3x(x-3).

Answer:

The rate of the jet in still air is 852 miles per hour. The rate of the wind is 85 miles per hour.

Step-by-step explanation:

Let suppose that jet travels uniformly, that is, at constant speed, the expressions for its travels against the wind and with the wind are, respectively:

Against the wind

[tex]v -u = \frac{\Delta x_{1}}{\Delta t_{1}}[/tex]

With the wind

[tex]v +u = \frac{\Delta x_{2}}{\Delta t_{2}}[/tex]

Where:

[tex]v[/tex] - Speed of the jet in still air, measured in miles per hour.

[tex]u[/tex] - Speed of wind, measured in miles per hour.

[tex]\Delta x_{1}[/tex], [tex]\Delta x_{2}[/tex] - Distances travelled by jet against the wind and with the wind, measured in miles.

[tex]\Delta t_{1}[/tex], [tex]\Delta t_{2}[/tex] - Times against the wind and with the wind, measured in hours.

By adding both expressions:

[tex]2\cdot v = \frac{\Delta x_{1}}{\Delta t_{1}}+\frac{\Delta x_{2}}{\Delta t_{2}}[/tex]

[tex]v = \frac{1}{2}\cdot \left(\frac{\Delta x_{1}}{\Delta t_{1}} + \frac{\Delta x_{2}}{\Delta t_{2}} \right)[/tex]

Given that [tex]\Delta x_{1} = 2301\,mi[/tex], [tex]\Delta t_{1} = 3\,h[/tex], [tex]\Delta x_{2} = 2811\,mi[/tex] and [tex]\Delta t_{2} = 3\,h[/tex], the speed of the jet is:

[tex]v = \frac{1}{2}\cdot \left(\frac{2301\,mi}{3\,h}+\frac{2811\,mi}{3\,h} \right)[/tex]

[tex]v = 852\,\frac{mi}{h}[/tex]

The rate of the jet in still air is 852 miles per hour.

Lastly, the rate of the wind is:

[tex]u = \frac{\Delta x_{2}}{\Delta t_{2}}-v[/tex]

[tex]u = \frac{2811\,mi}{3\,h}-852\,\frac{mi}{h}[/tex]

[tex]u = 85\,\frac{mi}{h}[/tex]

The rate of the wind is 85 miles per hour.

Answer:

2.8125

Step-by-step explanation:

Answer:

C. and D.

Step-by-step explanation:

A. and B. are not within in the range of 3-10 centimeters per day.

Step-by-step explanation:

 This problem expects us to model the equation for the total cost of the services of the plumber given the conditions stated.

Say the fixed amount charged for coming to your house is $10

say the fix amount charged per is $3

and the time spent to do the job is X

Hence the scenario can be modeled as

[tex]Y= 3x+10[/tex]

the equation is similar to the equation of a straight line

[tex]Y= mx+c[/tex]

Answer:

-13.5v-21.6

Step-by-step explanation:

Distribute Rule: a(b+c) = ab+ac

2.7(-5v-8)

= 2.7*(-5v) + 2.7(-8)

= -13.5v-21.6

Answer: A. 1120 in³

Step-by-step explanation:

the formula for the volume of the pyramid: [tex]V=\frac{1}{3} lwh[/tex]

l (length)=16

w (width)=14

h (height)=15

     [tex]V=\frac{1}{3} lwh[/tex]

     [tex]V=\frac{1}{3} (16)(14)(15)[/tex]

     [tex]V=\frac{1}{3} 3360[/tex]

     [tex]V=1120[/tex]

Answer:

The answer is option A.

Step-by-step explanation:

Hey there!!

Given,

Length (l)= 16 in.

breadth (b)= 14 in.

height (h)= 15 in.

we have,

[tex]v. of \: pramid = \frac{1}{3} \times a \: of \: base \times height[/tex]

or, volume = {1/3 × (16×14)×15} cubic inch.

by simplifying it we get,

The volume is 1120 cubic inch.

Hope it helps..

Answer:

Hey there!

1.35 km/s would equal 3020 miles per hour.

Let me know if this helps :)

Answer:

50.2 miles/h.

Step-by-step explanation:

Turn km to miles:

1 km = 0.621 miles

1.35 km = ?

1.35 × 0.621 = 0.838 miles/s

0.838 miles = 1 second

? = 1 hour

1 hour = 60 minutes

60 × 0.838

= 50.28 miles/h

Hope this is helpful.

Answer:

B. Start at -7 on the number line and move 11 to the right.

Step-by-step explanation:

Given:

We can add or remove only positive numbers on the number line to get it  correct, so we need to open the parenthesis. When evaluated we get:

-7- (-11) = - 7 + 11 = 4

Correct interpretation of of this expression is:

Correct choice is:

Answer:

The boutique charges $64 for a wallet, and $25 for a belt.

Step-by-step explanation:

We can write two equations using the information we are given. The we solve the system of equations to find the prices.

Let w = price of 1 wallet.

Let b = price of 1 belt.

"Last month, the company sold 25 wallets and 62 belts, for a total of $3,150."

25w + 62b = 3150

"This month, they sold 78 wallets and 19 belts, for a total of $5,467."

78w + 19b = 5467

We now have the following system of 2 equations in 2 unknowns.

25w + 62b = 3150

78w + 19b = 5467

We will use the substitution method.

Solve the first equation for w.

25w + 62b = 3150

25w = -62b + 3150

w = -62/25 b + 126

Now substitute w with -62/25 b + 126 in the second equation, and solve for b.

78w + 19b = 5467

78(-62/25 b + 126) + 19b = 5467

-4836/25 b + 9828 + 19b = 5467

-4836/25 b + 19b = -4361

Multiply both sides by 25.

-4836b + 475b = -109,025

4361b = 109,025

b = 25

Now we substitute 25 for b in the first original equation and solve for w.

25w + 62b = 3150

25w + 62(25) = 3150

25w + 1550 = 3150

25w = 1600

w = 64

Answer: The boutique charges $64 for a wallet, and $25 for a belt.

Answer:

50

Step-by-step explanation:

180 - (65 + 65)

= 180 - 130

= 50

Answer:

no solution

Step-by-step explanation:

if you do 3*6= 18 and 3+14 is 17 so 18=17 is not true therefore it has no solution

Answer:

3n+16

Step-by-step explanation:

three times: (3) a number n +16

(3)n+16 or 3xn+16

3n+16

Answer:

The distance between campsite and checkpoint is: 4.47 miles

Step-by-step explanation:

Given that the coordinates :

Campsite at (-8,-6) and

Next checkpoint at (-4,-4).

To find:

Distance between campsite and checkpoint = ?

Solution:

Let point A be the campsite i.e. A(-8, -6)

Let point B be the next checkpoint i.e. B(-4, -4)

We have to find the distance AB.

We can use Distance formula  to find the distance between two points on xy coordinate plane:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]x_1 = -8\\y_1 = -6\\x_2 = -4\\y_2 = -4[/tex]

[tex]AB = \sqrt{(-4-(-8))^2+(-4-(-6))^2}\\\Rightarrow AB = \sqrt{4^2+2^2}\\\Rightarrow AB = \sqrt{16+4}\\\Rightarrow AB = \sqrt{20}\\\Rightarrow \bold{AB=4.47}[/tex]

So, the distance between campsite and checkpoint is: 4.47 miles

Answer:

The answer is below

Step-by-step explanation:

Let us assume the rate of printing in machine A is x per hour and the rate for machine B is y. Given that machine B prints at half the rate of machine A, therefore:

y = (1/2)x                       (1)

Also, both machine produces 200 newspaper printouts, and both operate at different times for a total of 4 hours. Therefore:

200/x + 200/y = 4       (2)

Put y = (1/2)x in equation:

[tex]\frac{200}{x}+\frac{200}{(\frac{1}{2} )x}=4\\ \\ \frac{200}{x}+\frac{400}{x}=4\\\\Multiply\ through\ by\ x:\\\\200+400=4x\\\\4x=600\\\\x=150[/tex]

Put x = 150 in equation y:

y=(1/2)150 = 75

Therefore the rate of machine A is 150 newspapers per hour while that of machine B is 75 newspapers per hour

Answer:

7

Step-by-step explanation:

variable = 84/12

             = 7

84 ÷ 12 = 7

Verification

12 × 7 = 84

Complete the space by dividing, 12 x 7 = 84: *

Answer:

8-9y

Step-by-step explanation:

(-3*3y)+(3*1)+5

=-9y+3+5

=8-9y

Answer:

− 9 y + 8

Step-by-step explanation:

Apply the distributive property.

3(−3y)+3⋅1+5

Multiply −3 by 3.

−9y+3⋅1+5

Multiply 3 by 1.

−9y+3+5

Add  3  and  5 .

− 9 y + 8

Answer:

Hey there!

The equation is x+2x+5+6x-17+3x+2, or 12x-10

12x-10=50

12x=60

x=5

Let me know if this helps :)

Answer:

12, Increase

Step-by-step explanation:

12 is by far the lowest in the set, and removing the number would raise the mean.

0.006

0.1 × 0.06 =

= 1/10 × 6/100

= 6/1000

= 0.006

Answer:

71°

142°

Step-by-step explanation:

[tex] \because QS \: is \: the \: bisector \: of \: \angle \: PQR\\

\therefore m\angle RQS =m\angle PQS\\

\because m\angle RQS = 71\degree...(given) \\

\huge \red{ \boxed{\therefore m\angle PQS = 71\degree}} \\ \because \: m\angle \: PQR = m\angle PQS + m\angle RQS \\ \because \: m\angle \: PQR = 71\degree + 71\degree \\ \huge \purple{ \boxed{\therefore \: m\angle \: PQR = 142\degree}}[/tex]

Answer:

11

Step-by-step explanation:

You're done! Therefore, the answer is 11.

Answer:

11

Step-by-step explanation:

I know this has already been answered but I need points, lol. i would add the step by step explanation but someone has already done so, so i dont feel the need to.

gothychan

Answer:

number between 12 and 14

Step-by-step explanation:

Start with given compound inequality, Add 4 to all sides ,combine terms on the left side ,combine terms on the right side, multiply all by 2, multiply ,so the number is between 12 and 14 which makes it possible to be 12,13,or 14

Answer:

150.72 units³

Step-by-step explanation:

volume = πr²h

= 3.14×4²×3

= 150.72

Answer:

[tex]y = \$335931.5 + \$110668.5x[/tex]

Step-by-step explanation:

Given

[tex]Salary\ in\ 2000 = \$446,600[/tex] (Median)

[tex]Salary\ in\ 2008 = \$1,331,948[/tex] (Median)

Required

Determine a Linear Equation

The above question illustrates an Arithmetic Progression (AP)

The nth term of an AP is

[tex]T_n = a + (n - 1) d[/tex]

In this case;

[tex]a = Salary\ in\ 2000 = \$446,600[/tex]

[tex]n = 2008 - 2000 + 1 = 9[/tex]

[tex]T_n = Salary\ in\ 2008 = \$1,331,948[/tex]

Substitute these in the given formula

[tex]\$1,331,948 = \$446,600 + (9 - 1) d[/tex]

[tex]\$1,331,948 = \$446,600 + 8d[/tex]

Collect Like Terms

[tex]\$1,331,948 - \$446,600 = 8d[/tex]

[tex]\$885348 = 8d[/tex]

Divide both sides by 8

[tex]d = \$110668.5[/tex]

The linear equation is generated as follows;

[tex]T_n = a + (n - 1) d[/tex]

In this case;

[tex]a = Salary\ in\ 2000 = \$446,600[/tex]

[tex]d = \$110668.5[/tex]

[tex]T_n = y[/tex]

[tex]n = x[/tex]

Substitute these in the given formula

[tex]y = \$446,600 + (x - 1) * \$110668.5[/tex]

Open bracket

[tex]y = \$446,600 + \$110668.5x - \$110668.5[/tex]

Collect Like Terms

[tex]y = \$446,600 - \$110668.5 + \$110668.5x[/tex]

[tex]y = \$335931.5 + \$110668.5x[/tex]

Hence, the linear equation is

[tex]y = \$335931.5 + \$110668.5x[/tex]