From the stage of a theater, the angle of elevation to the first balcony is 19 degrees. The angle of elevation to the second balcony, 6.3 meters directly above the first, is 29 degrees. How high above stage level is the first balcony, to the nearest tenth of a meter

Answers

Answer 1

Answer:

10.3 meters.

Step-by-step explanation:

From Triangle ABC

[tex]\tan 29^\circ =\dfrac{6.3+x}{h} \\h \tan 29^\circ=6.3+x\\h=\dfrac{6.3+x}{\tan 29^\circ}[/tex]

From Triangle ADC

[tex]\tan 19^\circ =\dfrac{x}{h} \\h \tan 19^\circ=x\\h=\dfrac{x}{\tan 19^\circ}[/tex]

Since the values of h are the same

[tex]\dfrac{x}{\tan 19^\circ}=\dfrac{6.3+x}{\tan 29^\circ}\\\\x\tan 29^\circ=\tan 19^\circ(6.3+x)\\x\tan 29^\circ=6.3\tan 19^\circ+x\tan 19^\circ\\x\tan 29^\circ-x\tan 19^\circ=6.3\tan 19^\circ\\x(\tan 29^\circ-\tan 19^\circ)=6.3\tan 19^\circ\\x=\dfrac{6.3\tan 19^\circ}{\tan 29^\circ-\tan 19^\circ} \\x=10.3$ meters (to the nearest tenth of a meter)[/tex]

The height of the first balcony above stage level is 10.3 meters.

From The Stage Of A Theater, The Angle Of Elevation To The First Balcony Is 19 Degrees. The Angle Of

Related Questions

A grocery store sells a bag of 6 oranges for $2.76. How much would it cost for 5 oranges?

Answers

Answer:

$2.3

Step-by-step explanation:

6oranges=2.76$

5oranges=?

5×2.76/6.

=$2.3

Susie needs to melt some chocolate to use in a recipe she found in a cookbook. The cookbook calls for melting the chocolate at a low temperature of 30 degree celsuis . What temperature in degrees Fahrenheit will she need to set her stove to melt the chocolate? Round your answer to the nearest whole degree. The solution is

Answers

Answer:

The temperature needed to melt the chocolate = 86  degree Fahrenheit.

Step-by-step explanation:

The given temperature = 30 degrees Celsius.

Now we have to calculate the temperature in Fahrenheit. So just covert the given degree Celsius into Fahrenheit. Therefore multiply the 30 with 9/5 and add the 32 so the remaining answer is the temperature in the Fahrenheit. Below is the calculation to convert the degree Celsius into Fahrenheit.

Temperature = 30 × 9/5 + 32 = 86 Fahrenheit.

Hello!, im a little stuck on this

Answers

Answer:

61 seats.

Step-by-step explanation:

This is an example of an arithmetic sequence.

The formula for this is an = a + (n - 1)d

Where an is the number of seats in the 19th row, a is the number of seats in the first row, n is the 19th row, and d is the common difference.

We can calculate the common difference by finding how many extra seats there are from the first row to the second. 27 - 25 = 2. So, with each additional row, there are two more seats.

a19 = 25 + (19 - 1) * 2

a19 = 25 + 18 * 2

a19 = 25 + 36

a19 = 61

So, there are 61 seats in the 19th row.

Hope this helps!

Answer:

i think 61 i hope im right

Step-by-step explanation:

Nick is undertaking an expedition across the desert from A to B. In order to complete his journey he starts at A, walks 7km West and then 24km North until he arrives at B. How much shorter would Nick's journey have been if he had gone by the shortest route across the desert?

Answers

Answer:

Shorting distance = 6 km

Step-by-step explanation:

Given:

Distance walk = 7 km west

Distance walk = 24 km north

Find:

Shorting distance

Computation:

Using Pythagorean theorem:

Magnitude AB = √AC² + BC²

Magnitude AB = √7² + 24²

Magnitude AB = √49 + 576

Magnitude AB = 25 Km

Total distance Nick walk = 7 km + 24 km

Total distance Nick walk = 31 km

Shorting distance = 31 km - 25 km

Shorting distance = 6 km

The height, h metres, of a flare as a function of the time, t seconds, since the flare was fired from a boat, can be modelled by the function h = -5t2 + 15t + 20 What was the maximum height of the flare?

Answers

Answer:

31.25 metres at t=1.5 seconds.

Step-by-step explanation:

The height, h metres, of a flare as a function of the time, t seconds, since the flare was fired from a boat, can be modeled by the function

[tex]h=-5t^2+15t+20[/tex]

We need to find the maximum height of the flare.

In the given quadratic function, the leading coefficient is negative it means the function represents the downward parabola.

Vertex of a downward parabola is the point of maxima.

If a quadratic function is [tex]f(x)=ax^2+bx+c[/tex], then

[tex]Vertex=\left(-\dfrac{b}{2a}, f(-\dfrac{b}{2a})\right)[/tex]

In the given function, a=-5, b=15, c=20. So,

[tex]-\dfrac{b}{2a}=-\dfrac{15}{2(-5)}=\dfrac{15}{10}=1.5[/tex]

Put x=1.5 in the given function.

[tex]h=-5(1.5)^2+15(1.5)+20[/tex]

[tex]h=31.25[/tex]

Therefore, the maximum height of the flare is 31.25 metres and t=1.5 seconds.

Help
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Answers

Answer:

I can't make a table here but I will try my best to seperate the numbers in groups

4.5 -34.5   :   8,17,23,27,10,23,23,27,5,27

34.5 -64.5   :  61,46,42,46,35,46,46,42,46

64.5 -94.5   :   84,88,65,65,65,84

Step-by-step explanation:

In this question there are three categories of intervals and a set of numbers. Essentially, the question wants you to seperate the numbers within each category of interval. I could not make the table here, but it is basically laid out for you. As for the histogram, the question in and out of itself is very vague because there are many ways you can set up a histogram. The file below may not be what you're looking for but it is how I imagined it would be.

The perimeter of a triangle is 7 a − 11 b . If two of its sides are 2 a + b and a − 9 b , what is the third side?

Answers

Answer:

To find the missing side we need to calculate the sum of the two given sides and then subtract that from the perimeter.

7a - 11b - (2a + b + a - 9b)

= 7a - 11b - (3a - 8b)

= 7a - 3a - 11b + 8b

= 4a - 3b

Three numbers are in ration 3: 4: 8. The sum of the two larger numbers exceeds twice the smallest by 48. Find the numbers.

Answers

Answer:

24, 32, 64

Step-by-step explanation:

12x=6x+48

-6x  -6x

6x=48

x=8

8(3)=24

8(4)=32

8(8)=64

Answer:

24, 32, 64

Step-by-step explanation:

1st=3x

2nd=4x

3rd=8x

2(3x)+48=4x+8x

6x+48=12x

48=6x

x=8

SO:

1st =24

2nd= 32

3rd= 64

Un equipo de futbol esta compuesto por 13 personas, contando el entrenador y el masajista. Tras jugar un partido, reciben para todos un cheque con 16_41 dolares. Sabiendo que en el lugar de "_" hay una cifra que no le queremos decir y que cada uno recibe una cantidad exacta igual¿a cuanto le tocara cada uno? que sean concretos pls

Answers

Answer:

Ok, tenemos que el cheque es de 16_41.

Y también sabemos que podemos dividir este numero entre 13 personas, de acá podemos concluir que este numero es un múltiplo de 13.

Sea el dígito faltan igual a x

Sabemos que un numero es divisible por 13 cuando la suma de los productos de las  unidades, decenas, centenas,...  De dicho número  por los dígitos contenidos en la lista {1, –3, –4, –1, 3, 4 } (en ese orden) es  0  o múltiplo de 13.

Entonces, tenemos:

16x41:

1*1 + 4*(-3) + x*-4 + 6*-1 + 1*3 = 1 - 12 -4x - 6 + 3

=-14 - 4*x  

entonces, -14 - 4*x tiene que ser igual a 0, 13 o algún múltiplo de 13.

Como ambos términos son negativos, no podemos tener esta igualdad igual a 0 o a 13, entonces apuntamos por el siguiente múltiplo de 13 después de -13 (es decir, 13*-2 = -26)

-26 = -14 - 4*x

-26 + 14 = -4*x

-12 = -4*x

-12/-4 = 3 = x

Entonces nuestro dígito es igual a 3, y nuestro numero es:

16341.

Ahora podemos probar:

16241/13 = 1257

Es decir, cada miembro recibe 1257.

1.) The ratio of red flowers to yellow flowers is 4 to 5. If there are 48 red
flowers, what is the number of yellow flowers? *

Answers

Answer:

Son 27 flores amarillas, redondeando*

Step-by-step explanation:

pues pongamos de constante f, entonces la formula sera 4f+5f=48 luego de esto seguira 9f=48 lo que dara como respuesta 5,3; reemplazamos la constante por 5,3 lo que quedaria como: 4x5,3 que es igual a 21,2 (el numero de flores rojas); luego reemplazamos la constante en 5f lo que quedaria como 5x5,3 lo que da 26,5 pero si lo redondeamos nos da 27 y listo uwu

What is the solution set of {xlx<-3}{xlx>5)?
all real numbers
all numbers except -3 and 5
the empty set
the numbers between -3 and 5

Answers

Answer: C. Empty set

Explanation:

The first set {x | x < -3} means we're talking about numbers smaller than -3. This includes -4, -5, -6, etc

The second set {x | x > 5} means we're talking about numbers larger than 5. So things like 6,7,8,...

Combining both at the same time, we want to find a number that is both smaller than -3 and larger than 5. This is impossible as no such number exists. You can pick one or the other, but not both.

There are no solutions. Since there are no solutions, the solution set is the empty set.

Use the rule y=-x+ 7 to fill in the blank.
If (-1, y) is on the graph, then y=

Answers

Answer:

(-1,6)

Step-by-step explanation:

y=-x+ 7

Let x = -1

y = -1+7

y = 6

PLEASE HELP ! ! ! pleaseeeee ! ! ! ! ! :C

Answers

Answer:

5/2

Step-by-step explanation:

When you multiply exponents, you add the powers, and when you subtract exponents, you subtract the powers.

Step 1: Move negative exponents

[tex]\frac{2^25^6}{2^35^35^2}[/tex]

Step 2: Combine exponents

[tex]\frac{2^25^6}{2^35^5}[/tex]

Step 3: Remove like terms

[tex]\frac{5^1}{2^1}[/tex]

Step 4: Exponent

5/2

Seven lamps labeled A through G are arranged in a row. Each lamp has its own switch. Now lamps A, C, E, and G are on and other lamps are off. Ben starts to flip each switch from A to G the following way: if the lamp is on, he turns it off; if the lamp is off, he turns it on. He repeats the pattern until he flips the switches 2011 times. Which lamps are on finally? dont bully me im in 5th grade also this is due in 4 days

Answers

Answer:

O=on

X=off

OXXOXOX  after 2011 flips.

Step-by-step explanation:

There are many ways to get the answer.

A. Actually flip them 2011 times.

One way is to put 7 cards on the table, and name them A to G, with A,E,C,G facing up, and the other facing down.

Now flip the cards in order A to G 2011 times and find the answer.  

Since you have four days to find the answer, you only have to flip about 500 times a day.

B. Simplify procedure A above.

Do the same as above, actually flip the cards, but only 14 times.

You will find that the cards are restored to the original position after 14 flips.  

If we divide 2011 by 14, we get a quotient of 143 with a remainder of 9.

We know we don't have to make 143 sets of 14 flips.  We only need to make 9!

Then again, we know that after 7 flips, the lights will be all opposite.

If O=on, and X=off then the situations are

OXOXOXO  initial

XOXOXOX  after 7 flips

OXXOXOX  after 9 flips, which is also after 2011 flips, and that is the final answer.

The length of a photo is 14 inches, which is 3 inches longer than its width. Write an equation that gives the photo's width (w) in inches. i need this asap!

Answers

Answer:

w+3=14

Step-by-step explanation:

The length is 3 more than the width, and more can be expressed as a plus sign, so w+3=14.

The solution to an inequality is given in set-builder notation as {x l x > two-thirds}. What is another way to represent this solution set? (–∞ , two-thirds] (–∞ , two-thirds) (two-thirds, ∞) [two-thirds, ∞)

Answers

Answer:

correct choice is C  ( ,∞).

Step-by-step explanation:

A set-builder notation is a mathematical notation for describing a set by enumerating its elements or stating the properties that its members must satisfy. In your  case, the set builder notation  {x l x > } means that the set consists of all elements that are greater than.

Consider number line. Plot the point as unfilled circle that goes after > sigh and shade the ray that goes from this point to the right. Then another way to represent this solution is

Answer:

c) (two-thirds, ∞)

Step-by-step explanation:

59.6487 to 2 decimal places

Answers

Answer:

59.65

Step-by-step explanation:

2 decimal places is to the hundredths place.

Answer: 59.65

Step-by-step explanation: When rounding a number to a given place, look at the next place y o the right. If that digit is 5 or more, "round up" by adding one to the given place.

If the number to the right is 4 or less, leave the given place "as is"

In this example, the hundredths place is 4, the place to the right has an 8. So you round up the 4 to a 5. You end up with 59.65

Use the Quadratic Formula to solve y=3x2+9x-13

Answers

The answer is y= 3x^2+9x-13

Hope it help u

Mark noticed that the probability that a certain player hits a home run in a single game is 0.165. Mark is interested in the variability of the number of home runs if this player plays 150 games. If Mark uses the normal approximation of the binomial distribution to model the number of home runs, what is the variance for a total of 150 games? Answer choices are rounded to the hundredths place.

Answers

Answer:

Variance for a total of 150 games is 20.67

Step-by-step explanation:

If x follows binomial distribution with parameters n and p then the probability distribution of  [tex]\frac{x-np}{\sqrt{npq}}[/tex] tends to N (0.1)

As [tex]n\rightarrow \infty[/tex] where E(x)= np,  var (x) = npq

[tex]\therefore[/tex] var (x) = 150[tex]\times[/tex]0.165 [tex]\times[/tex] (1-0.165)      

(since, n= 150, p=0.165,

q = 1-p = 1-0.165)

= 20.66625

var (x) = 20.67

[tex]\therefore\\[/tex] variance for a total of 150 games is 20.67

Given to us:

Mark uses the normal approximation of the binomial distribution to model the number of home runs. Therefore,

Probability, p=0.165;

Number of samples, n=150;

Chances of failure, q = 1-p = 1-0.165 = 0.835;

According to binomial distribution,

Variance, var(x) = npq;

var (x) = npq

           = 150 x 0.165 x 0.835

           =  20.66625

Hence, the variance for a total of 150 games is  20.66625.

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https://brainly.com/question/12734585

X/8 - 9 = 1 Solve for x

Answers

Answer:

x=80

Step-by-step explanation:

x/8-9=1x/8=9+1x/8=10x=80

A right triangle has a side of length 1 fourth and a hypotenuse of length 1 third. What is the length of the other side?

Answers

Answer:

The other side = [tex]\frac{1}{12}[/tex] units

Step-by-step explanation:

A right triangle has a side of length [tex]\frac{1}{4}[/tex] units and;

the hypotenuse is [tex]\frac{1}{3}[/tex]

According to Pythagorean theorem,

a² + b² = c² , where a and b are the two legs of a triangle and c is the hypotenuse.

Lets say a² = [tex](\frac{1}{4}) ^2[/tex]   and  c² = ([tex](\frac{1}{3} )^2[/tex]

b² = c² - a²

b² = [tex]\frac{1}{9}[/tex] - [tex]\frac{1}{16}[/tex] = [tex]\frac{1}{144}[/tex]

So b = [tex]\sqrt{1/144}[/tex] = [tex]\frac{1}{12}[/tex] units.

So the other side = [tex]\frac{1}{12}[/tex] units.

Determine the statements that characterize cylinders and cones. Check all that apply. Cylinders have two circular bases. Cones have one circular base. The lateral area of a cylinder is a triangle. The lateral area of a cone is a rectangle. The lateral area of a cylinder is related to circumference of the circular bases.

Answers

Answer:

Cylinders have two circular bases

Cones have one circular base

The lateral area of a cylinder is related to circumference of the circular bases.

Step-by-step explanation:

In Determining the statements that characterize cylinders and cones. All that apply in this context are :

1) Cylinders have two circular bases

2) Cones have one circular base

3) The lateral area of a cylinder is related to circumference of the circular bases.

Furthermore, in a general context, A cylinder has traditionally been or comprises of a three-dimensional solid, one of the most basic of curvilinear geometric shapes or curves. It is the idealized version of a solid physical tin can which processed lids on top and bottom. While a cone is a three-dimensional geometric shape or a set of line segment that taper smoothly from a flat base (though not necessarily, but mostly circular) to a point called the vertex.

Answer:

a b and e

Step-by-step explanation:

ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.

Answers

Answer:

[tex]t = 2.86 \: s[/tex]

The ball remains in the air for 2.86 seconds.

Step-by-step explanation:

A baseball is hit into the air, and its height above the ground is described by the function

[tex]H(t) = -16t^2 + 45t + 2[/tex]

Where H(t) represents the height of the ball t seconds after it is hit.

The ball remains in the air before it hits the ground.

When the ball hits the ground,

[tex]H(t) = 0[/tex]

So,

[tex]0 = -16t^2 + 45t + 2[/tex]

The equation may be solved using the quadratic formula.

[tex]$t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]

Where

[tex]a = -16 \\\\b = 45 \\\\c = 2 \\\\[/tex]

So,

[tex]t=\frac{-(45)\pm\sqrt{(45)^2-4(-16)(2)}}{2(-16)} \\\\t=\frac{-45\pm\sqrt{(2025 - (-128)}}{-32} \\\\t=\frac{-45\pm\sqrt{(2153}}{-32} \\\\t=\frac{-45\pm 46.4004}{-32} \\\\t=\frac{-45 + 46.4004}{-32} \: and \: t=\frac{-45 - 46.4004}{-32}\\\\t= -0.04 \: and \: t = 2.86 \\\\[/tex]

Since the time cannot be negative, discard the negative value and accept the positive value

[tex]t = 2.86 \: s[/tex]

Therefore, the ball remains in the air for 2.86 seconds.

What is the quotient of 8 1/4×3/4

Answers

Answer:

6 3/16

Step-by-step explanation:

8.25x.75=6.1875, or 6 & 3/16

Answer:

[tex]6\frac{3}{16}[/tex]

Step-by-step explanation:

[tex]8 \frac{1}{4} * \frac{3}{4} \\\\\frac{33}{4} * \frac{3}{4} = \frac{99}{16} \\\\\frac{99}{16} = 6\frac{3}{16}[/tex]

Hope this helps! :)

- Clout Answers

Brainliest is greatly appreciated :)

Graphing Exponential Functions: Which function is graphed below?
A) y=1/3(3)^x
B) y=3(1/3)^x
C) y=)1/2)^+2
D) y=(2)^x-1
Thank you!!

Answers

Answer:

B

Step-by-step explanation:

The y-intercept (or initial value) is 3 which means the coefficient of the exponential term is 3. The only answer choice that follows this is choice B.

What is the value of A when we rewrite... (PLZ HELP QUICK)

Answers

Answer:

[tex] \frac{133}{8} [/tex]

Step-by-step explanation:

Given,

[tex] {( \frac{5}{2} )}^{x} + {( \frac{5}{2} )}^{x + 3} [/tex]

[tex] = {( \frac{5}{2}) }^{x} + {( \frac{5}{2}) }^{x} \times {( \frac{5}{2} )}^{3} [/tex]

[tex] = ( \frac{5}{2} ) ^{x} (1 + {( \frac{5}{2} )}^{3} [/tex]

[tex] = {( \frac{5}{2} )}^{x} (1 + \frac{125}{8} )[/tex]

[tex] = {( \frac{5}{2} )}^{x} ( \frac{1 \times 8 + 125}{8} )[/tex]

[tex] = {( \frac{5}{2}) }^{x} ( \frac{8 + 125}{8} )[/tex]

[tex] {( \frac{5}{2} )}^{x} ( \frac{133}{8} )[/tex]

Comparing with A [tex] {( \frac{5}{2}) }^{x} [/tex]

A = [tex] \frac{133}{8} [/tex]

Hope this helps...

Good luck on your assignment...

The isosceles triangle and the square shown here have the same area in square units. What is the height of the triangle, $h$, in terms of the side length of the square, $s$?

Answers

Answer:

h = 2s

Step-by-step explanation:

Area of square is equal to the area of triangle in this question.

the area of the square is s²

the area of the triangle is [tex]\frac{1}{2}[/tex] *h*s

s²=  [tex]\frac{1}{2}[/tex] *h*s

s = [tex]\frac{1}{2}[/tex] *h

2s = h

hope that helps

HELP PLZ Javier and his study group designed a word problem, equation, table, and graph that were all supposed to represent the same information, as shown below. Word Problem A movie theater charges $8.00 for each ticket. What is the total cost, y, for x tickets? Equation y = 8x Graph Movie Theater Costs A graph with number of tickets sold on the x-axis and total cost on the y-axis. A line goes through points (8, 1), (16, 2). Table A 2-column table with 4 rows. Column 1 is labeled x with entries 5, 8, 12, 13. Column 2 is labeled y with entries 40, 64, 96, 104. Which piece of information does not represent the same information as the other three parts? word problem equation graph table

Answers

Answer:

Graph

Step-by-step explanation:

The graph swapped the y and x axis values.

Answer:

Graph

Step-by-step explanation:

additional expenses made after purchasing an article added to its actual cost are called————

Answers

Answer:

by definition : Additional expenses made after buying an article are included in the cost price and are known as overhead expenses.

Step-by-step explanation:

Find the percentage change: The price was $60. Now it is $40.

Answers

Answer:

33.33%

Step-by-step explanation:

The percentage was a decrease.

Let the percent be x.

60 × (1 - x%) = 40

60 × (1 - x/100) = 40

1 - x/100 = 40/60

-x/100 = 40/60 - 1

-x/100 = -1/3

x/100 = 1/3

x = 1/3 × 100

x = 33.33333

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