Avani is trying to find the height of a radio
antenna on the roof of a local building. She
stands at a horizontal distance of 21 meters
from the building. The angle of elevation
from her eyes to the roof (point A) is 42°,
and the angle of elevation from her eyes to
the top of the antenna (point B) is 51°. If
her eyes are 1.5 meters from the ground,
find the height of the antenna (the distance
from point A to point B). Round your
answer to the nearest meter if necessary.

Answer:

x=42°

Step-by-step explanation:

take x degree as reference angle

using tan rule

tan x=opposite/adjacent

tan x=9/10

tan x=0.9

x=[tex]tan^{-1}[/tex]0.9

x=41.98

x=42 degree

Answer:

41.987° which rounds to 42 degrees

Step-by-step explanation:

Answer:

Option B : ( - 1 , 1 )   ==>    x = -1 , y = 1

Step-by-step explanation:

2x - y = - 3              -------- ( 1 )

x + y = 0 => x = - y   -------( 2 )

Substitute ( 2 ) in ( 1 ) : 2x  - y = - 3

                                 2( - y ) - y = - 3

                                  - 2y - y = -  3

                                   - 3y = - 3

                                       y = 1

Substitute y in ( 2) : x + y = 0

                              x + 1 = 0

                                x =  - 1

Answer:

- 9 + 9i

Step-by-step explanation:

(- 7 + 3i) - (2 - 6i)

- 7 + 3i - 2 + 6i

- 7 - 2 + 9i

- 9 + 9i

Answer:

the answer is w = 148-12h/12+2h

The equivalent equation is -

[tex]$w=\frac{74-6h}{h+6}[/tex]

We have the equation written by Carly → 148 = 2 (6w + 6h + hw) that represent the width and height of the box in the shape of a rectangular prism.

We have to solve for w.

Any expression written in a form different from the original form, but gives same result for any input are called equivalent expressions.

We have -  

[tex]$log(\frac{x}{\omega}) = 2\pi[/tex]

log(x) - log(ω) = 2π

log(x) = 2π + log(ω)

x = [tex]e^{(2\pi + log(\omega))} = e^{2\pi } \times e^{log(\omega)}[/tex]

According to the question, we have -

148 = 2 (6w + 6h + hw)

(6w + 6h + hw) = 74

hw + 6w = 74  - 6h

w(h + 6) = 74 - 6h

[tex]$w=\frac{74-6h}{h+6}[/tex]

Hence, the equivalent equation is -

[tex]$w=\frac{74-6h}{h+6}[/tex]

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Answer(s):

[tex]\displaystyle y = 300sin\:(\frac{\pi}{8}x + \frac{\pi}{2}) + 400 \\ y = 300cos\:\frac{\pi}{8}x + 400[/tex]

Step-by-step explanation:

[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 400 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-4} \hookrightarrow \frac{-\frac{\pi}{2}}{\frac{\pi}{8}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{16} \hookrightarrow \frac{2}{\frac{\pi}{8}}\pi \\ Amplitude \hookrightarrow 300[/tex]

OR

[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 400 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{16} \hookrightarrow \frac{2}{\frac{\pi}{8}}\pi \\ Amplitude \hookrightarrow 300[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 300sin\:\frac{\pi}{8}x + 400,[/tex]in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle 4\:units[/tex]to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle 4\:units,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-4} = \frac{-\frac{\pi}{2}}{\frac{\pi}{8}}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 300sin\:(\frac{\pi}{8}x + \frac{\pi}{2}) + 400.[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit [tex]\displaystyle [36, 400],[/tex]from there to [tex]\displaystyle [20, 400],[/tex]they are obviously [tex]\displaystyle 16\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle 16.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 400,[/tex]in which each crest is extended three hundred units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Answer:

$0.35

Step-by-step explanation:

8.40/24 = $0.35

Answer:

[tex]-\frac{3}{x} + \frac{7y}{x} = \frac{-3+ 7y}{x}[/tex]

Step-by-step explanation:

Given

[tex]-\frac{3}{x} , \frac{7y}{x}[/tex]

Required

Add

The statement can be interpreted as:

[tex]-\frac{3}{x} + \frac{7y}{x}[/tex]

Take LCM

[tex]-\frac{3}{x} + \frac{7y}{x} = \frac{-3+ 7y}{x}[/tex]

9514 1404 393

Answer:

  8 : 125

Step-by-step explanation:

The volume is proportional to the cube of the side lengths. Hence, the ratio of volumes is proportional to the cube of the ratio of side lengths.

  v1 : v2 = (2 : 5)^3 = 2^3 : 5^3 = 8 : 125

Answer:

$120

Step-by-step explanation:

constant fee = (204-183) /(140-105)

= 21/35 = $0.6 per km

so, initial fee =

183 - (105 × 0.6)

= 183 - 63

= 120

Answer:

120

Step-by-step explanation:

trust me.

Answer:

the missing angle will be 140°

Answer: 140

Step-by-step explanation:

Answer: i hope you pass that quiz

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

Francis borrowed 20$ and gives his dad 8$ he owes 12$ I hope it helps :)

Answer:

y = (3/2)x + 2

Step-by-step explanation:

The equation of a straight line is given by:

y = mx + b;

where y, x are variables, m is the slope of the line and b is the y intercept (value of y when x is 0).

From the graph, we can see that the y intercept is 2 units. Also, the line passes through point (2, 5) and (-2, -1). Therefore the slope of the line is:

[tex]slope(m)=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-5}{-2-2}=\frac{3}{2}[/tex]

Using the equation a straight line:

y = mx + b; substituting gives:

y = (3/2)x + 2

Answer: 3(2+x) or 3x+6

Step-by-step explanation:

Take this a step at a time

First is a sum of two and a number

set "a number" as x

sum of two and a number would be 2+x

triple it

3(2+x) or 3x+6

Answer:

3(x+2)

Step-by-step explanation:

Explanation:

The " sum of a number and 2

" means ADD them:

→ x+2

Triple that means multiply by

3

→ 3(x+2)

Answer:

x ≥ 40

Step-by-step explanation:

3x - 55 ≥ 65

combine like terms

3x  ≥ 65 + 55

3x  ≥120

divide both sides of the equation by 3

x  ≥ 40

Answer:

bottle top

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

Slope is rise over run

graph us going up by 2 units and going to left by 2 units

[tex]\frac{2}{ - 2} \\ - 1[/tex]

Answer:

-12x+20.

Step-by-step explanation:

I got it by multiplying the bracketed numbers by the -4.

Answer:

12313685 is the answer............happy to help u

Answer:

48 ANS.

MAY IT HELPED U

9514 1404 393

Answer:

  h₁(t) = -16t² +110

Step-by-step explanation:

Put the given initial height into the given formula. That will give the requested function. If the function name is supposed to be h₁(t), then rename it.

  f(t) = -16t² +110 . . . . . . h = 110, the initial height

  h₁(t) = -16t² +110

Answer:

P1.H.x²+y²=34

centre[h,k]=(0,0)

point=[3,5]

now

radius=[tex]\sqrt{(0-3)²+(0-5)²}=\sqrt{34}[/tex]

now

equation of a circle is;

(x-h)²+(y-k)²=[tex]\sqrt{34}²[/tex]

x²+y²=34

P:2I.(x-6)²+(y+7)²=121

centre[h,k]=(6,-7)

diameter=22

radius[r]=22/2=11

now

equation of a circle is;

(x-h)²+(y-k)²=r²

(x-6)²+(y+7)²=11²

(x-6)²+(y+7)²=121

9514 1404 393

Answer:

Step-by-step explanation:

A rectangle is a parallelogram that has right angles. A square is a rectangle that has adjacent sides the same length.

The figures that always have right angles are ...

  square

  rectangle

Answer:

The answer is [tex]t\geq 20[/tex].

Step-by-step explanation:

To solve the inequality, start by solving for the variable [tex]t[/tex].

To solve for the variable [tex]t[/tex], subtract [tex]3.5t[/tex] from both sides. The inequality will look like [tex]6.5t\geq 130[/tex].

Then, divide both sides by 6.5 in order to get the variable [tex]t[/tex] by itself. The inequality answer will look like [tex]t\geq 20[/tex].

Answer:

Data B

Step-by-step explanation:

Given the data :

A: 20347, 20327, 22117, 21762, 20864, 20102, 21684, 20063, 21728, 21580, 21720, 20920, 21442, 20766

B: 3.38, 4.64, 4.09, 3.93, 4.25, 4.63, 4.78, 4.25

The spread of a data gives the variation in the data values of a given sample.

To obtain which data has the larger spread, we obtain the coefficient of variation. Which is the ratio of the standard deviation and the mean of the dataset.

(Standard deviation / mean) * 100%

Using calculator :

Data A :

Mean, x = 21101.5714

Standard deviation, s = 700.28925

Coefficient of Variation :

(700.28925 / 21101.5714) * 100% = 3.32%

Data B :

Mean, x = 4.24375

Standard deviation, s = 0.457006955

Coefficient of Variation :

(0.457006955 / 4.24375) * 100% = 10.77%

10.77% > 3.32%

Hence. Data B has a larger spread

Answer:

1=(w=6,C=20.80

2=(W=2,C=27.05)

3=(w=11,C=14.25)

4=(w=15,C=11.05)

Step-by-step explanation:

Just do the work

0.55x15=8.25+2.80=11.05

1.10x6=6.6+14.20=20.8

11x0.65=7.15+7.10=14.25

Out of process of elimination, 2=(W=2,C=27.05)

Answer:

Below.

Step-by-step explanation:

The second option on the bottom matches the first of the top  list.

This is how we check:

w = 6 and C = 20 .80

Plug these into the top equation:

C = 14.2 + 1.10w

20.80 = 14.2 + 6(1.10) = 14.20 + 6.60 = 20.80.

So that proves that we have the right answer.

The last one on the bottom matches the second on the top list.

The third option ion the bottom matches the third equation on the top

.

The first one on bottom matches the last one the top.

The last 3 are answered in exactly the same way as the first.

Answer:

so we have to use the formula 4/3PiR^3

which if we do we get the volume of

V≈97478.08

Answer:

V≈97478.08cm³

Step-by-step explanation:

Using the formulas

V=4/3πr3

d=2r

V=1/6πd3

D=1

1/6·πd3 1/6π ·57.13≈97478.07565cm³

I hope this helps. I worked hard on this one.

Answer:

U = 1

V = -5

Step-by-step explanation:

U = -1 - (-2) = 1

V = -4 -1 = -5