During his vacation, Dalyn rents a small boat from a rental service that charges a flat fee of $50 plus $20 per hour (including taxes). The total charge comes to $150 . Which equation can be used to calculate the number of hours, x, that Dalyn rents the boat?

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

0.006

0.1 × 0.06 =

= 1/10 × 6/100

= 6/1000

= 0.006

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: The answer is 12.57 because the formula is The area of a circle is pi times the radius squared (A = π r²). Hope this helps.

Step-by-step explanation:

Answer:

adult cost £7, child cost £2

Step-by-step explanation:

let a represent an adult and c a child , then

2a + 3c = 20 → (1)

a + 4c = 15 → (2)

Multiplying (2) by - 2 and adding to (1) will eliminate a

- 2a - 8c = - 30 → (3)

Add (1) and (3) term by term to eliminate a, that is

- 5c = - 10 ( divide both sides by - 5 )

c = 2

Substitute c = 2 into either of the 2 equations and evaluate for a

Substituting into (2)

a + 4(2) = 15

a + 8 = 15 ( subtract 8 from both sides )

a = 7

The cost of an adult ticket is £7 and a child ticket is £2

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:

D) conmutativa

Step-by-step explanation:

Propiedad conmutativa: Cuando se suman o multiplican dos números, la suma o el producto es el mismo independientemente del orden en que

los números se suman o multiplican.

Se da como:

a + b = b + a

a × b = b × a

Propiedad distributiva: La suma de dos números por un tercer número es igual  a la suma de cada número sumado por el tercer número. Se da como:

a × (b + c) = (a × b) + (a × c)

Propiedad asociativa:  Se da como:

a + (b + c) = (a + b) + c

a × (b × c) = (a × b) × c

Propiedad  inverso aditivo:  Se da como

a + (-a) = 0

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:

38.89%

Step-by-step explanation:

the whole p8e chart is 360° as a perfect circle would be,

so : 360° - ( 66° + 144° ) = 360° - 210° = 140°

140° of the pie chart was cast in favor of candidat C.

(140° ÷ 360°) × 100 = 38.89%

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

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

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:

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:

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:

The correct option is;

Shirt Express charges less per shirt. For the cost to be the same 74 shirts must be ordered

Step-by-step explanation:

1) The given table for Shirt Express can be used to find the equation of the total cost of each made by Shirt Express as follows;

The rate of change of the function m is given as follows;

[tex]m = \dfrac{y_2 - y_1 }{x_2 - x_1}[/tex]

Therefore, we have;

m = (438 - 353)/(50 - 40) = 8.5

Te equation in slope and intercept form is then y - 438 = 8.5(x - 50)

From which we have;

y = 8.5·x - 8.5×50 + 438 = 8.5·x + 13

y = 8.5·x + 13

Therefore, Shirt Express initially charges 13 per shirt which is less than the 50 Shirt Custom charges

2)  the cost to be the same, we equate both shirts equations to get;

8.5·x + 13 = 8·x + 50

0.5·x = 50 - 13 = 37

x = 37/0.5 = 74 shirts

Therefore, for the cost to be the same 78 shirts must be ordered

[tex]\frac{w+14}{4w+6} = \frac{3}{4}[/tex]

So do cross multiplication.

4×(w+14)=4w+56

3×(4w+6)=12w+18

4w+56=12w+18

Carry the 4w to the right side, and the 18 to the left

56-18=12w-4w

38=8w

w=4 3/4

Sorry if this is not what you were asking for.

♡  But anyways, I Hope this helped! ♡

❀ 0ranges ❀

Answer:

Step-by-step explanation:

[tex] \sf{ \frac{w + 14}{4w + 6} = \frac{3}{4} }[/tex]

Apply cross product property

⇒[tex] \sf{4(w + 14) = 3(4w + 6) }[/tex]

Distribute 4 through the parentheses

Similarly, Distribute 3 through the parentheses

⇒[tex] \sf{4w + 56 = 12w + 18}[/tex]

Move variable to left hand side and change it's sign

Move constant to right hand side and change it's sign

⇒[tex] \sf{4w - 12w = 18 - 56}[/tex]

Collect like terms

⇒[tex] \sf{ - 8w = 18 - 56}[/tex]

Calculate

⇒[tex] \sf{ - 8w = - 38}[/tex]

Divide both sides of the equation by -8

⇒[tex] \sf{ \frac{ - 8w}{ - 8} = \frac{ - 38}{ - 8} }[/tex]

Calculate

⇒[tex] \sf{w = 4.75}[/tex]

Hope I helped!

Best regards!!

Answer:

6.0435*10²⁴

Step-by-step explanation:

Moon:  7.35*10²²

Earth: 5.97*10²⁴

7.35*10²² = 0.0735*10²⁴

then:

0.0735*10²⁴ + 5.97*10²⁴ = (0.0735 + 5.97)*10²⁴

=  6.0435 *10²⁴

Answer: 6,130,000

Step-by-step explanation:

No work needed

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:

  1 in : 8 ft  or  1 : 96

Step-by-step explanation:

The scale is the ratio of model dimensions to actual dimensions:

  19 in : 152 ft = 1 in : 8 ft = 1 in : 96 in = 1 : 96

__

The scale can be expressed in mixed units as 1 in : 8 ft, or it can be expressed as the pure ratio 1 : 96.

Answer:

3n+16

Step-by-step explanation:

three times: (3) a number n +16

(3)n+16 or 3xn+16

3n+16

Answer:

Step-by-step explanation:

Plug in the value of y & z in the expression

[tex]\frac{3}{2}y-3+\frac{5}{3}z=\frac{3}{2}*6-3+\frac{5}{3}*3\\\\\\=3*2 - 3 + 5 *1\\\\\\= 6 - 3 + 5\\\\\\= 3 + 5\\\\\\= 8[/tex]

Answer: 11

Step-by-step explanation:

If y=6 and z=3 then your problem will look like this : 3/2(6) - 3 + 5/3(3)

Put both 6 and 3 over 1 to turn them into a fraction and then multiply

3/2 multiplied by 6/1 is 18/2 which reduces to 9

5/3 multiplied by 3/1 is 15/3 which reduces to 5

Then your problem will look like this : 9 - 3 + 5

Follow order of operations and add and subtract from left to right

9 - 3 is 6 and 6 + 5 is 11

So your answer is 11

Answer:

50

Step-by-step explanation:

180 - (65 + 65)

= 180 - 130

= 50

Answer:

C. and D.

Step-by-step explanation:

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

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).