An observatory is 150 feet high. when a person is standing in the observatory looking at an island, the angle of depression is . what is the approximate horizontal distance from the observatory to the island?

[tex] - 4y = v - 4x \\ y = \frac{ - v}{4} + x[/tex]

[tex]\\ \rm\dashrightarrow V=-4y+4x[/tex]

[tex]\\ \rm\dashrightarrow -4y=V-4x[/tex]

[tex]\\ \rm\dashrightarrow y=\dfrac{V-4x}{-4}[/tex]

[tex]\\ \rm\dashrightarrow y=x-\dfrac{V}{4}[/tex]

The solution to the system of equations that includes quadratic function f(x) and linear function g(x) is (1, 7)

The solution to the linear and quadratic equation is as follows:

For the linear, a solution is 1 and 7.

This is because when x = 1, f(x) = 7

For the quadratic equation, 1 and 7 also works.

2x² + x + 4

2(1)² + 1 + 4

2 + 1 + 4 = 7

learn more on system of equation here: https://brainly.com/question/27168614

#SPJ1

Answer:

N=[tex]\sqrt{61}[/tex]

Step-by-step explanation:

We have the first point as (2,4), and the second point as (-3,-2). This means that [tex]x_1=2, y_1=4,x_2=-3,y_2=-2.[/tex] Using the distance formula, we get [tex]\sqrt{(2-(-3))^2+(4-(-2))^2} \\\sqrt{(2+3)^2+(4+2)^2}\\\sqrt{25+36}=\sqrt{61}[/tex]

Answer:

[tex]\sqrt{61}[/tex]

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{What is the formula for finding slope?}[/tex]

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

[tex]\huge\textbf{Often people understand it better by:}[/tex]

[tex]\mathbf{\dfrac{rise}{run} = slope}[/tex]

[tex]\huge\textbf{Answering the given question:}[/tex]

[tex]\mathbf{y_2 \rightarrow 4}\\\\\mathbf{y_1 \rightarrow 7}\\\\\mathbf{x_2\rightarrow 0}\\\\\mathbf{x_1 \rightarrow -1}[/tex]

[tex]\huge\textbf{Now, that we have that information out}\\\huge\textbf{the way, we can answer the question.}[/tex]

[tex]\huge\textbf{Solving for the answer:}[/tex]

[tex]\mathbf{\dfrac{4 - 7}{0 - (-1)} = slope}[/tex]

[tex]\mathbf{\rightarrow \dfrac{4 - 7}{0 + 1} = slope}[/tex]

[tex]\mathbf{\rightarrow \dfrac{-3}{1} = slope}[/tex]

[tex]\mathbf{-3\div 1 = slope}[/tex]

[tex]\mathbf{\rightarrow -3 = slope}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\textsf{S}\frak{lope \rightarrow -3}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The area of the wetland that will be covered in purple loosestrife 7 years from now is modeled by this expression 500(1.2)^7

The exponential expression to calculate the area covered by purple loosestrife seven years from now will be:

= 500 × 1.2^7

After evaluating the expression, the model predicts that approximately 1,792 acres of the wetland will be covered in purple loosestrife 7 years from now.

This is not a valid prediction because the total area of the wetland is only 1,240 acres. Therefore, a constraint on the model is that the value of the expression 500(1.2)^t must be less than or equal to 1,240.

Learn more about exponential on:

https://brainly.com/question/12940982

#SPJ1

Answer:

x = 77/100

Step-by-step explanation:

When you solve this equation: 1.68+ 12x = 10.92

The answer is x = 77/100

The cost of each bottle of juice will be $0.77.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Adrian brought snacks for his team's practice. He bought a bag of apples for $1.68 and a 12-pack of juice bottles. The total cost before tax was $10.92.

From the given data the expression will be formed as below:-

1.68+ 12x = 10.92

12x = 10.92 - 1.68

12x = 9.24

x =9.24 / 12

x = $0.77

Therefore, the cost of each bottle of juice will be $0.77.

To know more about an expression follow

https://brainly.com/question/723406

#SPJ5

In a binomial​ experiment to say that each trial is independent of the other​ trials means that the outcome of one trial does not affect the other trial.

An experiment with a set number of independent trials and just two results is referred to as a binomial experiment.

To say that in a binomial experiment, each trial is independent of the other trials means that the outcome of one trial does not affect the other trials.

This means that whatever we get in the first trial, does not affect the outcome of the second or any other trial.

For example, in the tossing of a coin 10 times, the outcome of the first trial doesn't affect any of the other nine trials.

Learn more about binomial experiments at

https://brainly.com/question/24756209

#SPJ4

Let [tex]x,y[/tex] be the legs of the triangle, with [tex]x[tex]\mathrm{area}_{\rm square} = y^2[/tex]

[tex]\mathrm{area}_{\rm triangle} = \dfrac12 xy[/tex]

The square has 3 times the area of the triangle, so

[tex]y^2 = \dfrac32 xy[/tex]

Meanwhile, in the triangle we have

[tex]\tan(\theta) = \dfrac xy[/tex]

Now,

[tex]y^2 = \dfrac32 xy \implies \dfrac23 = \dfrac xy \implies \boxed{\tan(\theta) = \dfrac23}[/tex]

The reflection of the triangle DEFG will be given in the figure.

A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.

Reflection does not change the size and shape of the geometry.

The image of the figure under reflections in line m and then line t.

The reflection of the triangle DEF will be given in the figure.

More about the transformation of geometry link is given below.

https://brainly.com/question/22532832

#SPJ1

Answer:

60

Step-by-step explanation:

I'm assuming that ED is an exactly straight line, that would mean the angle is 180 degrees. So the sum of the angles in between should also equal 180. This gives you the equation

100 + 20 + x = 180

120 + x = 180

60  = x

Answer:

The linear equation for the line with an x-intercept at (-5,0) and y-intercept at (0,4) is found as [tex]$y=\frac{4}{5} x+4$[/tex].

Step-by-step explanation:

A condition is given that a line has an x- intercept at (-5,0) and y- intercept at (0,4).

It is asked to find a linear equation satisfying the given condition.

To do so, first determine the slope of the line using coordinates of the given intercepts. Then write the equation in the slope-intercept form using the slope and the y- intercept.

Step 1 of 2

Determine the slope of the line.

The points of the intercepts of the line are given as (-5,0) and (0,4). Next, the formula for the slope is given as,[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]

Substitute 4&0 for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex]respectively, and 0&-5 for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,

[tex]$$\begin{aligned}m &=\frac{4-0}{0-(-5)} \\m &=\frac{4}{5}\end{aligned}$$[/tex]

Step 2 of 2

Write the equation in the slope-intercept form.

The slope-intercept form of a line is given as follows,

[tex]$$y=m x+b$$[/tex]

The coordinates at the y- intercept is (0,4). Now, as the y- coordinate is 4 , so b=4.

So, substitute 4 for b and [tex]$\frac{4}{5}$[/tex] for m in the equation y=mx+b, as follows,

[tex]$y=\frac{4}{5} x+4$$[/tex]

This is the required linear equation.

Answer:

324.3mi

Step-by-step explanation:

Given Space Shuttle height above ground = 330mi

Airplane height above ground = 5.7mi

Difference between two aircrafts = Space Shuttle height - airplane height above ground

= 330 - 5.7

= 324.3mi

Answer:

OC. 39.3 cm²

Step-by-step explanation:

Area of a circle = πr²    (π ≈ 3.14)

45 degrees = 1/8 of a full circle

Area of the full circle : 3.14 × 10² =

3.14 × 100 = 314 cm²

Area of the sector : 314 × 1/8 = 39.25 cm² ≈ 39.3 cm²

Answer:

[tex]x= \dfrac{3-2x}{4-3x}[/tex]

Step-by-step explanation:

Given:

[tex]x=\dfrac{1}{2-\dfrac{1}{2-\dfrac{1}{2-x}}}}[/tex]

Simplify:

[tex]\begin{aligned}2-\dfrac{1}{2-x} & =\dfrac{2(2-x)-1}{2-x}\\\\ & =\dfrac{3-2x}{2-x}\end{alilgned}[/tex]

Therefore:

[tex]x=\dfrac{1}{2-\dfrac{1}{\dfrac{3-2x}{2-x}}}[/tex]

Simplify:

[tex]\begin{aligned}2-\dfrac{1}{\dfrac{3-2x}{2-x}} & =2-\dfrac{2-x}{3-2x}\\\\ & =\dfrac{2(3-2x)-(2-x)}{3-2x}\\\\ & = \dfrac{6-4x-2+x}{3-2x}\\\\ & = \dfrac{4-3x}{3-2x}\end{aligned}[/tex]

Therefore:

[tex]x & =\dfrac{1}{\dfrac{4-3x}{3-2x}}[/tex]

[tex]\textsf{Apply the fraction rule}: \quad \dfrac{1}{\frac{b}{c}}=\dfrac{c}{b}[/tex]

[tex]\implies x& = \dfrac{3-2x}{4-3x}[/tex]

Work Shown:

16% of x = 17

0.16x = 17

x = 17/(0.16)

x = 106.25

Judy travel's 15.125 miles or 15[tex]\frac{1}{8}[/tex] miles in 2 3/4 hours

How to solve such time related questions?

The key concept for solving such questions is the relationship between speed, distance and time.

The relationship between them is Distance = Speed x Time

Given:

Substituting it in the relationship we get,

Distance = Speed x Time

Distance =  5 1/2 miles per hour  x 2 3/4 hours

Distance = [tex]\frac{11}{2} X \frac{11}{4}[/tex] miles

Distance =  [tex]\frac{121}{8}[/tex] miles or 15[tex]\frac{1}{8}[/tex] miles

Thus Judy travel's 15.125 miles or 15[tex]\frac{1}{8}[/tex] miles in 2 3/4 hours

Learn more about time related questions here :

https://brainly.com/question/16403317

#SPJ4

Answer:

[tex] - \frac{2}{3} [/tex]

Step-by-step explanation:

Given (6x18)(3x+2) = 0

[tex]108(3x + 2) = 0 \\ 324x + 216 = 0 \\ 324x = - 216 \\ x = \frac{ - 216}{324} \\ = - \frac{2}{3} [/tex]

The probability that both of them have landed 5 is 1/7.

Two fair dice have been tossed,

The total of their top faces is found to be divisible by 5,

Probability is a branch of mathematics that deals with calculating the likelihood of a given event's occurrence, which is expressed as a number between 1 and 0.

The probability that both of them have landed 5 is

E={(x,y)|x+y=5 or x+y=10, 1≤x,y≤6},

F={(5,5)}.

P(F|E)= 1/7.

Hence, The probability that both of them have landed 5 is 1/7.

Learn more about probability here https://brainly.com/question/13016819

#SPJ4

Answer:

a

Step-by-step explanation:

this is the anser on e2020

Answer:

Step-by-step explanation:

Answer:

None of them are correct i believe

Step-by-step explanation:

its sideways lol

From the given graph, and using the scatter plot function of a graphing calculator, the residuals are;

-0.08693, -0.019376, -0.518, -0.183, -0.083, 0.135, 0.318, and 0.578

From the diagram, the given points are;

(14, 4), (15, 4), (16.5, 3.5), (18, 4), (18, 3.9), (19.5, 3.85), (20, 4), (26.8, 3.8)

Utilizing a graphing calculator, using the scatter plot function we have the following predicted values;

Best fit line; y = 5.032 - 0.0676•x

Residuals = Actual - Predicted from equation

The residuals are;

y1 = 4 - 4.08693 = -0.08693

y2 = 4 - 4.019376 = -0.019376

y3 = 3.5 - 3.918 = -0.518

y4 = 4 - 3.817 = -0.183

y5 = 3.9 - 3.817 = -0.083

y6 = 3.85 - 3.715 = 0.135

y7 = 4 - 3.682 = 0.318

y8 = 3.8 - 3.222 = 0.578

The residuals are therefore;

The residuals are;

Learn more about finding the residuals of a scatter plot here:

https://brainly.com/question/16511034

#SPJ1

When two variables are being examined, and one variable moves one way and the other variable moves in the opposite direction, this is called an inverse relation.

Correlation is a statistical degree (expressed as various) that describes the size and path of a courting among or extra variables. A correlation between variables, however, does now not robotically suggest that the trade in a single variable is the purpose of the alternate inside the values of the opposite variable.

A positive correlation is clear while variables move within an equal course. An inverse correlation is clear whilst variables circulate inside the opposite route.

A negative correlation is a relationship among variables that pass in contrary instructions. In other phrases, while variable A increases, variable B decreases. A poor correlation is likewise known as an inverse correlation.

Learn more about Correlation here: https://brainly.com/question/4219149

#SPJ4

When two variables are being examined, and one variable moves one way and the other variable moves in the opposite direction, this is called a(n): Inverse Relationship.

Consumption is subject to diminishing marginal utility. -A lower price increases the purchasing power of a buyer's income, enabling a buyer to purchase more of a product.

The law of supply and demand is a keystone of modern economics. According to this theory, the price of goods is inversely related to the quantity offered. This makes sense for many goods, since the more costly it becomes, fewer people will be able to afford them and demand will subsequently drop.

Learn more about Modern economics here https://brainly.com/question/639998

#SPJ4

Answer:

680π dm² = 2136.28 dm²

Step-by-step explanation:

Recall:

lateral area of cone = πrs; where s = slant height = 17 dm

area of circle = πr²

lateral area of cylinder = πdh

Lateral area of cone: (3.14159)(8 dm)(17 dm) = 427.26 dm²

Area of base of cylinder: (3.14159)(8 dm)² = 201.06 dm²

Lateral area of cylinder: (3.14159)(16 dm)(30 dm) = 1507.96 dm²

Total surface area = 427.26 dm² + 201.06 dm² + 1507.96 dm²

Total surface area = 680π dm² = 2136.28 dm²

The set of equation that is known to have 5 and 0 as solutions is A and B.

From the graph that we have here in this question, we are supposed to identify the equations that have this point.

We can do this by tracing the lines in order to locate 5 and 0 on the grid.

When we trace the bine that has 5 and 0, We would find out that it is traceable to A and B.

Read more on graphs here:

https://brainly.com/question/10465970

#SPJ1

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

First off, let's write the line in point-slope form:

  [tex]\rm \hookrightarrow (y-y_0)=m(x-x_0)[/tex]

Let's calculate the slope:

 [tex]\rm \hookrightarrow Slope = \frac{y_2-y_1}{x_2-x_1}[/tex]

                 [tex]\rm \hookrightarrow slope = \frac{-3--6}{2--2} =\frac{3}{4}[/tex]

Now that we found the slope, let's put it into the point-slope form

  ⇒ we need (x₀, y₀) ⇒ let's use (2,-3)

     [tex](y-(-3))=\frac{3}{4} (x-2)\\y+3=\frac{3}{4} (x-2)[/tex]

The equation, however, could also be put into 'slope-intercept form'

     ⇒ gotten by isolating the 'y' variable to the left

          [tex]y = \frac{3}{4}x-\frac{9}{2}[/tex]  

Answer:[tex]y = \frac{3}{4}x-\frac{9}{2}[/tex] or [tex]y+3=\frac{3}{4} (x-2)[/tex]

   *Either equations work, put the one that you are the most familiar with

Hope that helps!

#LearnwithBrainly

Answer:

a = -5/3

Step-by-step explanation:

3/a × -4 = 20

3a × -4/-4 = 20/-4

3a = -5

a = -5/3

Check:

3/(-5/3) × - 4 = 20

-5 × - 4 = 20