A hot air balloon is released into the air. During its straight ascent, the angle of elevation was 15° and, 3 minutes later, the angle of elevation increased 20°. How fast is the balloon traveling, in km/h, if the angle measurements were taken 300m away from the launch site?

Answer: 4.6 km

Step-by-step explanation:

a^1 + b^2 = c^2

2^2 + b^2 = 5^2

4 + b^2 = 25

b = sqrt 25 - 4

b = sqrt 21 = 4.6 km

Answer: X = 86 gallons

Step-by-step explanation:

X-27=59

X=59+27

9514 1404 393

Answer:

  D.

Step-by-step explanation:

The wording "when x is an appropriate value" is irrelevant to this question. That phrase should be ignored. (You may want to report this to your teacher.)

When you look at the answer choices, you see that all of them are negative except the last one (D). When you look at the problem fraction, you see that it is positive.

The only reasonable choice is D.

__

Your calculator can check this for you.

  √12/(√3 +3) ≈ 3.4641/(1.7321 +3)

  = 3.4641/4.7321 ≈ 0.7321 = -1 +√3

__

If you want to "rationalize the denominator", then multiply numerator and denominator by the conjugate of the denominator. The conjugate is formed by switching the sign between terms.

  [tex]\displaystyle\frac{\sqrt{12}}{\sqrt{3}+3}=\frac{\sqrt{12}}{(\sqrt{3}+3)}\cdot\frac{(\sqrt{3}-3)}{(\sqrt{3}-3)}=\frac{\sqrt{36}-3\sqrt{12}}{3-9}\\\\=\frac{6-3\cdot2\sqrt{3}}{-6}=\boxed{-1+\sqrt{3}}[/tex]

_____

Additional comment

We "rationalize the denominator" in this way to take advantage of the relation ...

  (a -b)(a +b) = a² -b²

Using this gets rid of the irrational root in the denominator, hence "rationalizes" the denominator.

We could also have multiplied by (3 -√3)/(3 -√3). This would have made the denominator positive, instead of negative. However, I chose to use (√3 -3) so you could see that all we did was change the sign from (√3 +3).

Answer:

4. E=4x-15(vertically opposite)

F=E(corresponding angles)

E=4x-15

5.3x+6x+O=180(angles on a straight line)

9x+0=180

9x=180-0

9x/9=180/9

x=20

Answer:

25

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

We are given that:

[tex]\displaystyle \sin y^\circ = \frac{s}{8}\text{ and } \tan y^\circ = \frac{s}{t}[/tex]

And we want to find the value of:

[tex]\displaystyle \sec y^\circ[/tex]

Recall that tan(θ) = sin(θ) / cos(θ). Since sec(θ) = 1 / cos(θ), tan(θ) = sin(θ)sec(θ). Substitute:

[tex]\displaystyle \sin y^\circ \sec y^\circ = \frac{s}{t}[/tex]

Substitute:

[tex]\displaystyle \frac{s}{8}\sec y^\circ =\frac{s}{t}[/tex]

Solve for secant:

[tex]\displaystyle \sec y^\circ = \frac{8}{t}[/tex]

Hence, our answer is C.

Answer:

c. sec y° = 8/t

Step-by-step explanation:

I took the test

Answer:

Step-by-step explanation:

Answer: [tex]4004.76\ ft[/tex]

Step-by-step explanation:

Given

inclination is [tex]\theta=75^{\circ}[/tex]

Mountain is [tex]h=3900\ ft[/tex] high

Cable is tied [tex]x=910\ ft[/tex] from the base of the mountain

From the figure, length of the shortest path is [tex]l[/tex]

It is given by using Pythagoras theorem

[tex]\Rightarrow l^2=3900^2+910^2\\\Rightarrow l=\sqrt{(3900)^2+(910)^2}\\\Rightarrow l=4004.76\ ft[/tex]

Answer:

7^2+2ab - 4b^2

Step-by-step explanation:

A² + b² = 7b

b² + (2b-a) ²= 7²

FOIL

b^2 +4b^2-4ba+a^2= 7^2

Rewriting

a^2 -2ab + b^2    +4b^2 -2ab = 7^2

Add 2ab and subtract 4b^2 from each side

a^2 -2ab + b^2    +4b^2 - 4b^2 -2ab+2ab = 7^2+2ab - 4b^2

a^2 -2ab + b^2    = 7^2+2ab - 4b^2

(a-b)^2 = 7^2+2ab - 4b^2

Answer:

The answer is "0.1190".

Step-by-step explanation:

Given:

[tex]\to \frac{2}{3} -x +\frac{1}{6} = 6x\\\\\to \frac{2}{3} +\frac{1}{6} = 6x+x\\\\\to \frac{4+1}{6} = 7x\\\\\to \frac{5}{6} = 7x\\\\\to x=\frac{5}{6\times 7} \\\\\to x=\frac{5}{42}\\ \\\to x= 0.1190[/tex]

Answer:

A.) 4 - 6x + 1 = 36x

B.) 5/6 - x = 6x

F.) 5 = 42x

Step-by-step explanation:

edge.

enjoy it

it best answer for you

Step-by-step explanation:

we see, for x=-1 we get 3³

x=0 we get 3²

x=1 we get 3¹

so the function is definitely a 3 to the power of x version.

but we need to adapt the exponent a bit and correct x, so that at least for these 3 values of x the result is "running backwards".

the easiest way : 2-x as exponent.

it fits.

for x=-1 we get 2 - -1 = 3 as exponent.

for x=0 we get 2-0 = 2 as exponent.

for x=1 we get 2-1 = 1 as exponent.

so, the exponential function passing through these 3 points is

[tex]f(x) = {3}^{2 - x} [/tex]

Answer:

[tex] \frac{(c - 7)}{2} = - 5 \\ c - 7 = - 5 \times 2 \\ c - 7 = - 10 \\ c = - 10 + 7 \\ c = - 3[/tex]

I hope I helped you^_^

Answer:

7

Step-by-step explanation:

We can solve this problem by making an equation for the monthly bill. First, the cost is $59.99 per month, and that cannot be decreased, so we must add all costs to that amount. Next, it costs $5.49 per first run movie, so for each first run movie, we add $5.49 to the total. Therefore, we can write our equation as

59.99 + 5.49 per first run movie = monthly bill

Representing the number of first run movies as r, we can say

59.99 + 5.49 * r = monthly bill

Next, the monthly bill should be less than or equal to 100, so we can say

monthly bill ≤ 100

59.99 + 5.49 * r = monthly bill ≤ 100

Moreover, we want to maximize r, or the amount of first run movies. Because we add money to the monthly bill for each movie, to maximize r, we have to find the maximum money we can spend on the monthly bill that is still less than or equal to 100. To do this, we set the monthly bill to its maximum limit, or 100, so we have

59.99 + 5.49 * r = 100

subtract 59.99 from both sides to isolate the f and its coefficient

40.01 = 5.49 * r

divide both sides by 5.49 to isolate the variable

r ≈ 7.29

Since we can't buy .29 of a movie, and rounding up to 8 movies would cause us to go past 100 dollars, the maximum movies he can watch if he wants to keep his monthly bill ≤ 100  is 7

Answer:

- 14

Step-by-step explanation:

x = - 6

x^2 - 9x + 4

= ( - 6 )^2 - 9 ( - 6 ) + 4

= 36 + 54 - 4

= 36 - 50

= - 14

Answer:

[tex]94[/tex]

Step-by-step explanation:

[tex]x^2 - 9x + 4[/tex]

[tex](−6 {)}^{2} −9 (−6) + 4[/tex]

[tex]36 − 9 (−6) + 4[/tex]

[tex]36 + 54 + 4[/tex]

[tex]90+4[/tex]

[tex]94[/tex]

Answer:

40. A c=60

41 B z= 40

Step-by-step explanation:

The sum of the angles in a triangle is 180

40.  61+59+c = 180

Combine like terms

120+c = 180

c = 180-120

c =60

41.  90+50+z = 180

140 +z = 180

z = 180-140

z = 40

Answer:

10/2=15/?

Step-by-step explanation:

I can help you to your all question but it need time. I have to write short.

?=3

Answer:

Price elasticity of demand = 1

Step-by-step explanation:

Old quantity demanded = 200

New quantity demanded = 150

Old price = 8

New price = 10

Price elasticity of demand = percentage change in quantity demanded / percentage change in price

percentage change in quantity demanded = change in quantity demand / old demand × 100

= 50/200 × 100

= 0.25 × 100

= 25%

percentage change in price = change in price / old price × 100

= 2/8 × 100

= 0.25 × 100

= 25%

Price elasticity of demand = percentage change in quantity demanded / percentage change in price

= 25% / 25%

= 1

Price elasticity of demand = 1

question 3

Step-by-step explanation:

i only able to show you the step of question 3..so sorry

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

Explanation:

The table headers will look like choice A or choice C. Notice that we have simple yes or no questions along either the row or column labels; also, the labels are consistent. Choice B can be ruled out because the labels aren't consistent (or don't match up). Choice D is overcomplicated so it can be ruled out also.

We're told that 35 students play an instrument. That means 35 goes at the end of the "plays instrument" row, in the "total" column.

This is enough to see that choice A is the final answer

Furthermore, 30 students are in a band. So we have "30" at the bottom of the "band" column, and in the "total" row. The same applies to the 30 people not in band.

Answer:

[tex]BW \approx 132.589[/tex]

Step-by-step explanation:

The given triangle (BWS) is a right triangle. This is indicated by the box around one of its angles, signifying that it is a right angle. One property of a right triangle is the right angle trigonometric ratios. These are a set of ratios that can be used to describe the relationship between the sides and angles in a triangle. These ratios are as follows:

[tex]sin(\theta) = \frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]

Please note that the (opposite) and (adjacent) sides are subjective, the sides that are named these terms depend on the angle of reference. However the term (hypotenuse) refers to the sides opposite the right angle of a right triangle, this term is the same no matter the angle used in the ratio.

In this case, one is given the length of the side (SB) and the measure of angle (<W), one is asked to find the length of the side (BW). The best ratio to use in this case is the ratio tangent (tan).

[tex]tan(\theta)=\frac{opposite}{adjacent}[/tex]

Substitute,

[tex]tan(9)=\frac{21}{adjacent}[/tex]

Inverse operations,

[tex]tan(9)=\frac{21}{adjacent}[/tex]

[tex]adjacent=\frac{21}{(tan(9))}[/tex]

[tex]adjacent\approx132.688782[/tex]

[tex]BW \approx 132.589[/tex]

Answer:

2 miles per hour

Step-by-step explanation:

To find her walking pace in 'miles per hour' we need to divide the distance (in miles) by the time (in hours).

Speed = Distance/ Time

The time is given in minutes , but 50 minutes = 50/60 hours

=5/6 hours

1 2/3 ÷ 5/6

=5/3 × 6/5 miles per hour

Now cut it

= 2 miles per hour

Answer:

452.16 cm²

Step-by-step explanation:

Given :-

To find :-

Solution :-

As we know that ,

Step-by-step explanation:

[tex]area = \pi {r}^{2} \\ = \pi \times {12}^{2} \\ = \pi \times 144 \\ = 3.14 \times 144 \\ = 452.16 {cm}^{2} \\ thank \: you[/tex]

Answer:

2010: 1.79 dollars, 2012: 1.59 dollars

Step-by-step explanation:

In 2010,

1 Canadian dollar = .56 British pounds.

We want to find how many pounds go into a dollar, so we somehow have to make the equation equal to 1 pound. To do this, we can multiply the amount of pounds by its reciprocal to equal 1. To find the reciprocal of a number, we simply divide 1 by it. For .56, this is (1/.56). Therefore, we can multiply both sides by (1/.56) to get

1.79 Canadian dollars = 1 British pound

Similarly, for 2012, we have 1 dollar = .63 pounds. Multiplying both sides by 1/.63, we get

1.59 Canadian dollars = 1 British pound

Answer:

D

Step-by-step explanation:

380

Answer:

10,000

Step-by-step explanation:

cuhcuhcuhcuhcuhcuhc

Answer:

$2.50

Step-by-step explanation:

Sally pays 2.5 lbs of chuck for 6.25. We need to convert this to 1 pound, to see how much money it take to equal 1 pound .

Set up proportion.

[tex] \frac{1}{x} = \frac{2.5}{6.25} [/tex]

[tex]2.5 x = 6.25[/tex]

[tex]x = 2.5[/tex]

it takes 2 dollar and 50 cents for 1 lb of ground chuck

Answer:

$2.50

Step-by-step explanation:

In my theory, I suppose that the key word to look at is "per"in the question above. All you need to do is to is to divide $6.25 with 2 1/2 lb

Answer:

Hello,

First equation is false

Second equation is true

Step-by-step explanation:

1)

(4,-3) is a point of the line y=4x-19  since

-3=?4*4-19

-3=-3

2)

(4,-3) is not a point of the line y=1/4x-2 since

-3=? 1/4*4-2

-3=? 1-2

-3≠-1

I have written that because it is difficult for me to understand

"the negative reciprocal of the slope of the first"

the negative reciprocal of 4 should be -1/4.

Equation y=1/4x-2 is false.