how to isolate the variable in the equation -2/3n + 7 = 15 lesson 6-2

Answer:

1. The distance of the ship from the base of the lighthouse is approximately 1.24 miles

2. a)The horizontal distance the plane must start descending is approximately  190.81 km

b) The angle the plane's path will make with the horizontal is approximately 18.835°

3. The depth of the submarine is approximately 107.51 m

Step-by-step explanation:

The

1. From the question, we have;

The height of the observer above the water = 80 ft.

The angle of depression of the ship from the observer, θ = 0.7°

Let the position of the observer be 'O', let the location of the ship be 'S', let the point directly above the ship at the level of the observer be 'H', we have;

[tex]tan(\theta) = \dfrac{Opposite \ leg \ length}{Adjacent \ leg \ length} = \dfrac{HS}{OH}[/tex]

[tex]The \ horizontal \ distance \ of \ the \ ship, OH = \dfrac{HS}{tan(\theta) }[/tex]

HS = The height of the observer = 80 ft.

Therefore, we get;

[tex]The \ horizontal \ distance \ of \ the \ ship, OH = \dfrac{80 \, ft.}{tan(0.7^{\circ}) } \approx 6,547.763 \ ft.[/tex]

The distance of the ship from the base of the lighthouse ≈ 6,547.763 ft. ≈ 1.24 miles

2. The elevation of the plane, h = 10 km

The angle of the planes path with the ground, θ = 3°

Similar to question (1) above, the horizontal distance the plane must start descending, d = t/(tan(θ))

∴ d = 10 km/(tan(3°)) ≈ 190.81 km

The horizontal distance the plane must start descending, d = 190.81 km

b) If the pilot start descending 300 km from the airport, the angle the plane's path will make with the horizontal, θ, will be given as follows;

From trigonometry, we have;

[tex]tan(\theta) = \dfrac{Opposite \ leg \ length}{Adjacent \ leg \ length}[/tex]

Where the opposite leg length = The elevation of the plane = 10 km

The adjacent leg length = The horizontal distance from the airport = 300 km

[tex]\therefore tan(\theta) = \dfrac{10 \, km}{300 \, km} = \dfrac{1}{3}[/tex]

[tex]\theta = arctan\left(\dfrac{1}{3} \right ) \approx 18.835^{\circ}[/tex]

The angle the plane's path will make with the horizontal, θ ≈ 18.835°

3. The angle at which the submarine makes the deep dive, θ = 21°

The distance the submarine travels along the inclined downward path, R = 300 m

By trigonometric ratios, we have;

The depth, of the submarine, 'd' is given as follows;

[tex]si(\theta)= \dfrac{Opposite \ leg \ length}{Hypotenuse \ length} = \dfrac{d}{R}[/tex]

∴ d = R × sin(θ)

d = 300 m × sin(21°) ≈ 107.51 m

The depth of the submarine ≈ 107.51 m

Answer:

x = 16

m<R = 34°

Step-by-step explanation:

▪︎Its an isoceles triangle, so the two opposite angles are equal. m<S = <T.

▪︎So, you write them equal to each other and solve the linear equation to find x.

▪︎Substitute the x value into any of the angles and multiply by 2, (as they are equal) to find the sum, which is 146°.

▪︎Sum of all angles in a triangle is 180°,so

146° + m< R =180°

▪︎than minus 146° from 180°.

▪︎And you will have your answer.

Answer:

15 I think. not fully shore though

Step-by-step explanation:

Multiply 3x4. then 18-12=6. lastly add 9

Answer:

15

it is given that. k= 4

so, putting the value of k. in

given equation = 18 - (3*4 ) + 9

18 - 12 + 9 = 15

hope it helps

Answer:

13

Step-by-step explanation:

Answer:

c=13

Step-by-step explanation:

Hey There!

c+11=24

When looking at this problem you want to get the variable on one side (c) and the constant on the other ( any whole number)

as you can see we need to get rid of the 11 on the left side

to do that we subtract 11 but whatever you do to one side you have to do to the other side

11-11 cancels out

24-11=13

so we can conclude that

c=13

Answer:

360 square meters.

Step-by-step explanation:

You can split the polygon into three rectangles. Then you just have to figure out the area of each rectangle and add them together. The first rectangle has length of 12 and height of 10 so area of 120. The second rectangle has length of 32 and height of 6 so area of 192. The third rectangle has length of 8 and height of 6 so are of 48. 120 + 192 + 48 = 360

Answer:

12m^2+14m

Step-by-step explanation:

The "^means exponet" Hope I made your day

:)

Answer:

139 e7

Step-by-step explanation:

I'm not good at scientific notation but I think I'm getting better....

Answer:

1.39 x 10^9

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given function:

The complete video games can be expressed as positive integers or whole numbers, so the domain is whole numbers.

Correct choice is (4)

Answer:

Whole Number

Explanation:

Domain : The set of all the input values (i.e. the value of x ) in the function is called domain

The daily cost of production in a video game factory is calculated using c(x) = 400 + 25x

Cost expression : C(x) = 400 + 25x

Cost expression : C(x) = 400 + 25x

As x defines the number of complete video, since number of video cannot be negative.

1) Integers : integers are the numbers which can be positive, negative or zero, but cannot be a fraction

As, number of videos cannot be negative

so, x cannot be any integers

So, Integers is not the domain

2) Positive real numbers : Real numbers are the numbers which include both rational and irrational numbers.

As the x represent the complete number of video games, thus, x cannot be irrational

Hence, Positive real numbers is not the domain

3) Positive Rational Number : a number is expressed in the form of p/q then it is a rational number

The number of videos are in the complete number, so a fraction cannot be a complete number, thus, rational number cannot be a domain.

4) Whole Number : Whole numbers include natural numbers that begin from 1 onwards

As Numbers of videos are the complete number, and they are always positive, which is the defination of whole number, Domain is whole number

Answer:

katelyn

Step-by-step explanation:

you divide distance by time to get rate, and katelyn has a faster rate because 210/3 is more than 540/8

Answer:

Katelyn drove faster

t=d/s

s=d/t

d=s*t

Step-by-step explanation:

s=d/t is what we are using to find the speed

Katelyn- 210/3=70

Samantha-540/8=67.5

70>67.5

Katelyn drove faster

Answer:

56÷x+8

Step-by-step explanation:

Answer: u multiply them all together

Step-by-step explanation:nugggybi8ybggg8yiubgy8iibgu777777777b8u

Answer:

Step-by-step explanation:

8-(-3)= 8+3+33=42

Answer:

V = (14)(4)   V = 56cm³

Step-by-step explanation:

The Volume is Base times Height

We are given that the base is 7cm by 2cm.

That is 14 cm²  (The cubes each have volume of 1 cm³, so the volume of that bottom row is 14cm³, technically, but ignore that for now.)

To find the volume, multiply the base times the height.

V = 14cm² × 4cm

V = 56cm³

9514 1404 393

Answer:

  Vertex: (-1, 4)

  Maximum: f(-1) = 4

  Increasing: (-∞, -1)

  Decreasing: (-1, ∞)

Step-by-step explanation:

The equation can be written in vertex form by "completing the square."

First factor out the leading coefficient from the x-terms.

  f(x) = -(x² +2x) +3

Then add the square of half the x-coefficient inside parentheses. Add the opposite of that amount outside parentheses.

  f(x) = -(x² +2x +1) +3 +1

Write in vertex form.

  f(x) = -(x +1)² +4 . . . . . . . compare to a(x -h)² +k

You can see that the vertex is (h, k) = (-1, 4), and that the vertical scale factor 'a' is negative. This means the vertex is the maximum and the parabola opens downward.

The function will be increasing to the left of the maximum, decreasing to its right.

__

Vertex: (-1, 4)

Maximum: f(-1) = 4

Increasing: (-∞, -1)

Decreasing: (-1, ∞)

Graph: see attached

Answer:

The LCM of 315 and 450 is 3150. Hope this helps :)

Step-by-step explanation:

Answer:

Assuming what you meant was [tex]\frac{1}{2}x + 3 = -x +7[/tex], the answer would be x = 8

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

Work Shown:

1 ft = 12 inches

1 ft, 2 inches = 12 inches + 2 inches .... add 2 inches to both sides

1 ft 2 inches = 14 inches

Now we'll use the scale ratio to help find the answer

(2 inches)/(5 miles) = (14 inches)/(x miles)

2/5 = 14/x

2x = 5*14

2x = 70

x = 70/2

x = 35

The distance between the two locations is 35 miles.

Answer:

20 ounces of water

Step-by-step explanation:

Work backwards. David has 18 ounces, which is half of Charlie's. So, Charlie had 18•2=36 ounces. That was 3/5 of Barbara's water, so Barbara had 60 ounces. That is 3/4 of Amanda's water, so Amanda had 80 ounces. To find how much Amanda had left subtract 60 from 80 to get 20.

Answer:

Answer: (286/11) ÷ 2 = 13

Step-by-step explanation:

The quotient of 286 and 11 is given by the equation A = 26

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first number be represented as x

Now , the value of x = 286

Let the second number be represented as y

The value of y = 11

Let the quotient be represented as A

The value of A is given by the equation ,

A = x/y

Substituting the values in the equation , we get

A = 286/11

The value of A = 26

Therefore , the value of A is 26

Hence , the equation is A = 26

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Answer:

-3 is what I got

Step-by-step explanation:

Answer:

on the first one its 18 and the second one its 0 eighths

Step-by-step explanation:

i did it

The question was incomplete. The question should be like below :

Calculate 48×3/8 & choose which option is correct.

The options are :

1 ) 20

2 ) 18

3 ) 24

4 ) 16

The correct option is 2) 18

An expression is a mathematical sentence in which more than one number or variable is present with one or more mathematical operations.

The given expression is 48×3/8

Now, 48×3/8

       = 6×3

       = 18

The 2nd option is correct.

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Answer:

B: z*=1.645

Step-by-step explanation:

Khan academy step by step

Answer: z*=1.645

Step-by-step explanation:

Answer:

D. Banana

Step-by-step explanation:

Answer:

answer is A

Step-by-step explanation:

3*2=6

2pi/2=pi

The perimeter of the given figure is equivalent to (6 + π) units

Perimeter is defined as the length of the boundary of the given figure. We can write the perimeter mathematically as -

P = ∫f(x) dx

Given is to find the perimeter of the given image as shown.

We can write the area of the square as -

a² = 4

a = √4

a = 2

Also,

The perimeter of the semicircular part is -

1/2 x 2π x 2/2

π

So, the perimeter would be -

P = 2 + 2 + 2 + π

P = 6 + π

Therefore, the perimeter of the given figure is equivalent to (6 + π) units.

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Answer:

$625

Step-by-step explanation:

to find the original divide the sale price by the decreased percentage. 125/%20(or .20)

Answer:

x=10

Step-by-step explanation:

2 x 10 = 20+7=27 therefore x=10

Answer:

x=10

Step-by-step explanation:

2x+7=27

2x=27-7

2x=20

2x/2=20/2

x=10