Please help me with this

The height of Blue Mountain is determined by setting up two equations based on the tangent of the observed angles of elevation from two different points and solving for the distance to the mountain. The height is then calculated using this distance and rounded to the nearest tenth.

Tony is trying to find the height of Blue Mountain using trigonometry and the angles of elevation observed from two different points. We can solve this problem using right-angled triangles and trigonometric functions (specifically tangent).

Step-by-Step Calculation

First, we use the angle from the first observation point:
tan(23°) = height / distance
Height = distance * tan(23°). We call this height 'h'.

Then, when Tony moves 210 yards closer, the distance from the mountain is 'distance - 210 yards', and we use the angle from this second point:
tan(28°) = height / (distance - 210)
Height = (distance - 210) * tan(28°). We call this height 'h' as well because the height of the mountain doesn't change.

Therefore, we have two equations:
h = distance * tan(23°)
h = (distance - 210) * tan(28°).

By equating the two expressions for 'h', we find the distance 'd':
distance * tan(23°) = (distance - 210) * tan(28°).

We can now solve for 'distance' numerically. After calculating distance, we can use it to find the actual height 'h' using the tangent function with any of the two angles.

Final Result

We round intermediate results to 3 decimal places and the final height to 1 decimal place, giving us the height of Blue Mountain.

Answer:

a = 7

Step-by-step explanation:

45 45 90 right triangle so it's an isosceles triangle (A triangle with two equal sides)

a = 7

Answer:

Answer:

t = 3.8 s

option 3

Step-by-step explanation:

For this case we have the following equation:

 h (t) = at ^ 2 + v * t + h0

 Substituting values we have:

 h (t) = - 16 * t ^ 2 + 60 * t + 3

 We equate the equation to zero:

 -16 * t ^ 2 + 60 * t + 3 = 0

 We look for the roots of the polynomial:

 t1 = -0.04935053979258153

 t2 = 3.7993505397925817

 We are left with the positive root and round:

 t2 = 3.8 s

Answer:

7,55 seg

Step-by-step explanation:

Initial Velocity = 60 ft/s

High = 3ft

Acceleration = -16 ft/s2

According to the next formula

H = Vi(t) - 1/2 gt2

We got a cuadratic formula which roots are

t1 = -0,04 seg and t2 = 7,55 seg

the time not negative so t= 7,55 seg

Check the picture below.

let's notice that the angle -150° has a reference angle of 30°, so any trigonometric function for either angle will be the same value, however, let's recall that the sine or y-coordinate is negative on the III Quadrant, so sin(-150°) is the same as sin(30°) BUT negative, -sin(30°).

Answer:

C. -sin(30°)

Step-by-step explanation:

180-150=30

-sin(30) = -.5 on calculator j like sin(-150) is

Answer:

D.

Step-by-step explanation:

Lines EG and CD are cut by transversal CF.

By construction, ∠FEG=∠FCD. These two angles are corresponding angles.

Since two corresponding angles are congruent, then lines EG and CD are parallel (by  converse of the corresponding angles postulate).

Converse of the Corresponding Angles Postulate: If the corresponding angles formed by two lines and a transversal are congruent, then lines are parallel.

Answer:

The measure of angle VPJ is [tex]140\°[/tex]

Step-by-step explanation:

Let

x-----> the measure of arc PIV

y-----> the measure of arc PKV

we know that

The inscribed angle is half that of the arc it comprises.

so

[tex]m<VPJ=\frac{1}{2}(x)[/tex]

[tex]x=3.5y[/tex] -----> equation A

[tex]x+y=360\°[/tex] -----> equation B

substitute equation A in equation B

[tex]3.5y+y=360\°[/tex]

[tex]4.5y=360\°[/tex]

[tex]y=80\°[/tex]

Find the value of x

[tex]x=3.5(80\°)=280\°[/tex]

Find the measure of angle VPJ

[tex]m<VPJ=\frac{1}{2}(280\°)=140\°[/tex]

Answer:

So the maximum amount of gasoline the tank can contain is 13 gallons and there are already 7 gallons of gasoline in the tank. Therefore, we want to make sure that the amount of gasoline put in the tank doesn't reach any higher than 13 gallon.

The amount of gasoline that Lou bought with x dollars is x/2.50 gallons.

We have the inequality:

x/2.50 + 7 ≤ 13

*If you solve it, x should be smaller or equal to $15.

The math problem can be solved by setting up a compound inequality expressing the range that Lou can spend on gasoline. This factors in the total capacity of his tank, the current amount of gas, and the price per gallon. The result is 0 <= x <= $15.

For this problem, Lou needs to fill the remainder of his gas tank, which is 13 gallons total but already has 7 gallons. That means he needs to fill 13 - 7 = 6 gallons more. Gasoline costs $2.50 per gallon, so the total amount of money he spends, represented by x, can be calculated using the inequality $2.50 * number of gallons <= x.

But because Lou can add anywhere from 0 to 6 gallons, we will have a compound inequality. So, the inequality will be: $2.50 * 0 <= x <= $2.50 * 6.

This simplifies to 0 <= x <= $15, meaning Lou can spend anywhere from $0 to $15 on gasoline, depending on how much more he wants to put in his tank.

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Answer:

amplitude; [tex]\frac{2}{3}[/tex]

Phase shift; [tex]\pi[/tex] units right

Period;[tex]\frac{2\pi}{3}[/tex]

Step-by-step explanation:

The given function is

[tex]y=-\frac{2}{3}\cos(3t-3\pi)[/tex]

This function is of the form;

[tex]y=A\sin (Bt+C)[/tex]

The period is given by:

[tex]|A|=|-\frac{2}{3}|= \frac{2}{3}[/tex]

The period is given by:

[tex]T=\frac{2\pi}{|B|}= \frac{2\pi}{|3|}=\frac{2\pi}{3}[/tex]

The phase shift is given by;

[tex]\frac{C}{B}=\frac{-\3pi}{3}=- \pi[/tex] or [tex]\pi[/tex] units right.

Answer:

[tex](1-\sqrt{2})a^2[/tex]

Step-by-step explanation:

Consider irght triangle PRS. By the Pythagorean theorem,

[tex]PS^2=PR^2+RS^2\\ \\PS^2=a^2+a^2\\ \\PS^2=2a^2\\ \\PS=\sqrt{2}a[/tex]

Thus,

[tex]MS=PS-PM=\sqrt{2}a-a=(\sqrt{2}-1)a[/tex]

Consider isosceles triangle MSC. In this triangle

[tex]MS=MC=(\sqrt{2}-1)a.[/tex]

The area of this triangle is

[tex]A_{MSC}=\dfrac{1}{2}MS\cdot MC=\dfrac{1}{2}\cdot (\sqrt{2}-1)a\cdot (\sqrt{2}-1)a=\dfrac{(\sqrt{2}-1)^2a^2}{2}=\dfrac{(3-2\sqrt{2})a^2}{2}[/tex]

Consider right triangle PTS. The area of this triangle is

[tex]A_{PTS}=\dfrac{1}{2}PT\cdot TS=\dfrac{1}{2}a\cdot a=\dfrac{a^2}{2}[/tex]

The area of the quadrilateral PMCT is the difference in area of triangles PTS and MSC:

[tex]A_{PMCT}=\dfrac{(3-2\sqrt{2})a^2}{2}-\dfrac{a^2}{2}=\dfrac{(2-2\sqrt{2})a^2}{2}=(1-\sqrt{2})a^2[/tex]

Answer: The probability of the histogram is 0.6.

Step-by-step explanation:

Look at the images below for the step-by-step explanation. It's a lot easier to write on docs, rather than on this website. Anyway, I hope you've learned something. Bye!!!

Answer:

Option c.

No damping

Step-by-step explanation:

We can easily solve this question by using a graphing calculator or any plotting tool.

The function is

f(x) = (√11)*cos(3.7x)

Which can be seen in the picture below

We can notice that f(x) is a cosine with maximum amplitude of  (√11). Neither this factor nor the multiplication of x by 3.7 serve as a damping factor since they are constants.

f(x) does not present any dampening

Answer:

C) No damping.

Step-by-step explanation:

This is the correct answer on ed-genuity, hope this helps! :)

Certain means the event will happen.

Impossible means the event would never happen.

To be "certain" to occur means the event will definitely happen without any doubt.

For an event to be "impossible" to occur means that there is no chance whatsoever that the event will happen.

When we say an event is "certain" to occur, we mean that the event will definitely happen. In terms of probability, if an event has a probability of (1) (or 100%), it is certain to occur. For example, if you flip a fair coin, the probability of it landing either heads or tails is (1), meaning it's certain to land on one of the two sides.

On the other hand, when we say an event is "impossible" to occur, we mean that the event will definitely not happen. In terms of probability, if an event has a probability of (0) (or (0%), it is impossible to occur. For example, if you roll a six-sided die and ask for a result that is not within the range of 1 to 6, the probability of that happening is (0), so it's impossible for the die to show that result.

These concepts are fundamental to understanding the certainty or impossibility of events in probability theory and are essential for making predictions and decisions based on probabilistic models.

Answer: OPTION C

Step-by-step explanation:

 Given the equation [tex]\frac{\sqrt{3-2x} }{\sqrt{4x} } =2[/tex], you need to solve for  the variable "x".

First, you need to multiply both sides of the equation by [tex]\sqrt{4x}[/tex]:

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

Now you need to square both sides of the equation:

[tex](\sqrt{3-2x})^2=(2\sqrt{4x})^2\\\\3-2x=4(4x)\\\\3-2x=16x[/tex]

Subtrac 3 and 16x from both sides:

[tex]3-2x-(3)-(16x)=16x-(3)-(16x)\\\\-18x=-3\\[/tex]

Divide both sides by -18:

[tex]\frac{-18x}{-18}=\frac{-3}{-18}\\\\x=\frac{1}{6}[/tex]

Answer:

A) {x | -1 < x < 7}

Step-by-step explanation:

Given in the question two inequalities,

Inequality 1

(x - 2 < 5)

 x < 5 + 2

 x < 7

x is smaller than 7

Inequality 2

(x + 7 > 6)

 x > 6 - 7

 x > -1

x is greater then -1

When (x - 2 < 5) U (x + 7 > 6).

              (x < 7)   U  (x > -1)    

                    -1 <  x  < 7

When combined, x is greater than -1 but smaller than 7

Answer:

4

Step-by-step explanation:

The value of Side DC is 4.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

We have three similar triangles because each has a right angle and shares an angle.   Let's write the angles in order: opposite to the short leg, long leg, and the hypotenuse.

CAB ≡ BAD ≡ CBD

Or as ratios,

CA:AB:CB = BA:AD:BD = CB:BD:CD

We also know

AC = AD + CD

(AD+CD):AB:CB = BA:AD:BD = CB:BD:CD

(AD+CD)/CB=CB/CD

Let CD = x

(5 +x )/6 = 6/x

(5+x)*x = 6*6

5x + x² = 36

x² + 5x - 36 = 0

x² + 9x -4x -36 = 0

x(x+9 ) -4 (x +9 ) = 0

(x-4)(x+9) = 0

x= 4, -9

We reject the negative root and conclude x=4

Therefore, Side DC is 4.

To know more about similar triangles refer to :

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[tex] \sqrt{ - 75} = \sqrt{ - 1 \times 75} = \sqrt{ {i}^{2} \times 75 } = 5i \sqrt{3} \\(therefore \: {i}^{2} = - 1)[/tex]

Answer:

[tex]\large\boxed{\sqrt{-75}=5\sqrt3\ i}[/tex]

Step-by-step explanation:

[tex]i=\sqrt{-1}\\\\\sqrt{-75}=\sqrt{(25)(3)(-1)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{25}\cdot\sqrt3\cdot\sqrt{-1}=5\cdot\sqrt3\cdot i=5\sqrt3\ i[/tex]

Answer:

12x^2=6

Divide by 12

x^2=1/2or.5

square root

x=0.707

Step-by-step explanation:

12 is the diameter. We need the circumference which you get by multiplying 12x2 sides which = 24 which is the circumference

Answer:

c. 4.0

Step-by-step explanation:

To find a, we'll use the Law of Sines that says:

[tex]\frac{a}{sin(A)} = \frac{c}{sin(C)}[/tex]

And we'll isolate a to get:

[tex]a = \frac{sin(A) * c}{sin(C)}[/tex]

Then we will plug-in the information we already have (changing 16°55' into 16.92)

[tex]a = \frac{sin(16.92) * 13.7}{sin(90)} = 3.99[/tex]

So, let's round it to 4 to match the answer number C.

Answer:

C

Step-by-step explanation:

Use the definition of the sine function:

[tex]\sin \angle A=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{BC}{AB}.[/tex]

Substitute [tex]\angle A=16^{\circ}55'[/tex] and [tex]c=13.7[/tex] into the previous formula:

[tex]\sin 16^{\circ}55'=\dfrac{a}{c},\\ \\\sin 16^{\circ}55'=\dfrac{a}{13.7},\\ \\a=13.7\cdot \sin16^{\circ}55',\\ \\a\approx 13.7\cdot 0.284\approx 4[/tex]

Answer

TRUE

Step-by-step explanation:

We can easily solve this question by using a graphing calculator or any plotting tool, to check if it is a sinusoid.

The function is

f(x) = 2*cos(π*x) + sin(π*x)

Which can be seen in the picture below

We can notice that f(x) is a sinusoid. It has periodic amplitudes, and the function has a period T = 2

The maximum and minimum values are

Max = 2.236

Min = -2.236

Hence, the probability that the two coins are of different denomination is:

                            2/3

Let N denote nickel, D denotes dime and Q denotes Quarter.

Now when two coins are drawn one after the other with replacement then the outcomes is given by:

         (N,N)     (N,D)      (N,Q)

         (D,N)     (D,D)      (D,Q)

         (Q,N)     (Q,D)      (Q,Q)  

This means that there are a total of  9 outcomes.

The outcomes such that both the denominations are different i.e. the number of favorable outcomes are:  6

{ (N,D) (N,Q) (D,N) (D,Q) (Q,N) (Q,D) }

The probability that the two coins are of different denomination is:

                             6/9=2/3

Answer:

the answer is c 60%, may i have brainlyiest

Final answer:

To find the probability that a voter did not vote for a new school tax when 2/5 did, subtract 2/5 from 1 to get 3/5, then convert to a percentage to get 60%.

Explanation:

In the given problem, we know that 2/5 of the voters voted for a new school tax. To find the probability that a randomly selected voter did not vote for the tax, we need to calculate the fraction of those who did not vote for the tax. Since the total probability must be 1 (or 100%), those who did not vote for the tax would account for the remaining fraction of 1 - 2/5, which is 3/5. To express this as a percentage, we convert 3/5 into a decimal and then into a percentage.

First, calculate 3/5 as a decimal: 3/5 = 0.6. Then, to convert it to a percentage, multiply by 100: 0.6 × 100 = 60%.

Therefore, the probability that a randomly selected voter did not vote for the new school tax is 60%, which corresponds to answer choice c. 60%.

Answer:

Option d.

Amplitude: None

Period: π

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The equation is:

f(t) = 2.5 tan (t)

We can see from the graph that the amplitude goes up to infinity, and the period is equal to π.

Option d.

Amplitude: None

Period: π

The amplitude of the function f(t)=2.5 tan t is 2.5, as it's the coefficient of the tangent function. The period is π, as it's obtained by dividing π by the number multiplying 't', which in this case, is 1.

The function given, f(t)=2.5 tan t, is a trigonometric function, which represents a wave. In the context of a wave represented by a trigonometric function such as this, there are several key components. The two most important for this question are:

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Answer:

c=20

Step-by-step explanation:

200=10c

200/10=c

20=c

Answer:

12 pack for $15.00

Step-by-step explanation:

4 pack for $7.00:  7 ÷4  = 1.75

6 pack for $10.25:  10.25 ÷6 ≈ 1.71

10 pack for $13.00:  13 ÷10  = 1.30

12 pack for $15.00:  15.00 ÷12 = 1.25

25 pack for $32.50:  32.50 ÷25 = 1.30

Answer:

-2

Step-by-step explanation:

Since it would be immensely helpful to know the equation of this parabola, we need to figure it out before we can continue.  We have the work form of a positive upwards-opening parabola as

[tex]y=a(x-h)^2+k[/tex]

where a is the leading coefficient that determines the steepness of lack thereof of the parabola, x and y are coordinates of a point on the graph, and h and k are the coordinates of the vertex.  We know the vertex: V(-3, -3), and it looks like the graph goes through the point P(-2, -1).  Now we will fill in the work form equation and solve for a:

[tex]-1=a(-2-(-3))^2-3[/tex]

which simplifies a bit to

[tex]-1=a(1)^2-3[/tex]

and

-1 = a(1) - 3.  Therefore, a = 2 and our parabola is

[tex]y=2(x+3)^2-3[/tex]

Now that know the equation, we can find the value of y when x = -3 (which is already given in the vertex) and the value of y when x = -4.  Do this by subbing in the values of x one at a time to find y.  When x = -3, y = -3 so the coordinate of that point (aka the vertex) is (-3, -3).  When x = -4, y = -1 so the coordinate of that point is (-4, -1).  The average rate of change between those 2 points is also the slope of the line between those 2 points, so we will use the slope formula to find it:

[tex]m=\frac{-1-(-3)}{-4-(-3)} =\frac{2}{-1}=-2[/tex]

And there you have it!  I'm very surprised that this question sat unanswered for so very long!  I'm sorry I didn't see it earlier!

Answer:

Second option

g(x), and the maximum is 5.’

Step-by-step explanation:

In the graph it can easily be seen that the maximum value reached by the function f(x) is y = 3.

Then, the function g (x) is:

[tex]g(x) = 3cos(\frac{1}{4}(x + \frac{1}{3}x)) + 2[/tex]

By definition the function

[tex]y = cos(x)[/tex] reaches its maximum value when x = 0,  [tex]2\pi[/tex],  [tex]4\pi[/tex], ..., [tex]2k\pi[/tex]

So

When [tex](\frac{1}{4}(x + \frac{1}{3}x)) = 0[/tex]  entonces [tex]cos((\frac{1}{4}(x + \frac{1}{3}x)) = 1[/tex].

Thus:

[tex]g(0) = 3(1) + 2\\\\g(0) = 5[/tex].

Therefore the function that has the greatest maximum is g(x) when [tex]g(x) = 5[/tex]

The answer is the second option

About 13099.6 square miles of Wisconsin is not land area.

To find the amount of square miles of Wisconsin that is not land area, we need to calculate 20% of the total area. First, we find 1% of the total area by dividing it by 100. 65498 square miles / 100 = 654.98 square miles. Then, we multiply this by 20 to find 20%: 654.98 square miles * 20 = 13099.6 square miles. Therefore, about 13099.6 square miles of Wisconsin is not land area.

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If you know that [tex]\sin\dfrac\pi3=\dfrac12[/tex], then you know right away

[tex]\tan\left(\sin^{-1}\dfrac12\right)=\tan\dfrac\pi3=\dfrac1{\sqrt}3=\dfrac{\sqrt3}3[/tex]

###

Otherwise, you can derive the same result. Let [tex]\theta=\sin^{-1}\dfrac12[/tex], so that [tex]\sin\theta=\dfrac12[/tex]. [tex]\sin^{-1}[/tex] is bounded, so we know [tex]-\dfrac\pi2\le\theta\le\dfrac\pi2[/tex]. For these values of [tex]\theta[/tex], we always have [tex]\cos\theta\ge0[/tex].

So, recalling the Pythagorean theorem, we find

[tex]\cos^2\theta+\sin^2\theta=1\implies\cos\theta=\sqrt{1-\sin^2\theta}=\sqrt{1-\left(\dfrac12\right)^2}=\dfrac{\sqrt3}2[/tex]

Then

[tex]\tan\theta=\tan\left(\sin^{-1}\dfrac12\right)=\dfrac{\sin\theta}{\cos\theta}=\dfrac{\frac12}{\frac{\sqrt3}2}=\dfrac1{\sqrt3}=\dfrac{\sqrt3}3[/tex]

as expected.

Answer:

c. square root 3/3

Step-by-step explanation:

just did it on edg

ANSWER

x+y=1

EXPLANATION

We want to find the equation of line CD which passes through (0, 1) and is parallel to x + y = 3.

In slope intercept form, the given line is

y=-x+3

The slope of this line is m=-1

Line CD also has the same slope

The equation is given by:

y=mx+b

The given point (0,1) means the y-intercept;is b=1

Hence the equation is

y=-x+1

In standard form the equation is:

x+y=1

Answer:

The answer is x + y = 1

Step-by-step explanation:

Given: Line CD passes through (0, 1) and is parallel to x + y = 3.

We know that if two line are parallel then they have equal slopes.

Thus, the slope of line = slope of line x + y = 3

 x + y = 3  when we compare this to the standard linear equation

= 3 - x

y = m x + c  .we get m = -1 .

The slope of CD (m)= -1

Now, the equation of line CD passing through (0,1) is given by :-

( y - 1 ) = m ( x - 0 )

⇒ ( y - 1 ) = ( -1 ) x

⇒ x + y = 1

The equation of line CD = x + y = 1