A hot air balloon was flying at an altitude of 300 meters when the pilot decided to land by descending at a rate of 2 meters per second. For which of these rules does y represent the altitude of the hot air balloon, if x represents the number of seconds since the pilot started her landing?

Answer:

[tex]y=2x-6[/tex]

Step-by-step explanation:

A locus can be defined as a curve or figure formed by all the points satisfying a particular equation of the relation between coordinates.

The condition stated in the question is such that a generic (x,y) point of the curve is equidistant from the points A(2,3) and B(6,1).

The distance d1 from (x,y) to (2,3) is:

[tex]d_1=\sqrt{(x-2)^2+(y-3)^2}[/tex]

The distance d2 from (x,y) to (6,1) is:

[tex]d_2=\sqrt{(x-6)^2+(y-1)^2}[/tex]

Since d1=d2:

[tex]\sqrt{(x-2)^2+(y-3)^2}=\sqrt{(x-6)^2+(y-1)^2}[/tex]

Squaring both sides:

[tex](x-2)^2+(y-3)^2=(x-6)^2+(y-1)^2[/tex]

Operating:

[tex]x^2-4x+4+y^2-6y+9=x^2-12x+36+y^2-2y+1[/tex]

Simplifying all the squares:

[tex]-4x+4x+4-6y+9=-12x+36-2y+1[/tex]

Moving the variables to the left side and the numbers to the right side:

[tex]-4x+12x-6y+2y=36+1-4-9[/tex]

Simplifying:

[tex]8x-4y=24[/tex]

Dividing by 4:

[tex]2x-y=6[/tex]

Or, equivalently:

[tex]\boxed{y=2x-6}[/tex]

Answer:

5.25

Step-by-step explanation:

Answer:

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Step-by-step explanation:

Answer:

Hello

1.  B. 2.35 * 10^11

2. A. 3 * 10^-2

Answer:

a₅ = 37

Step-by-step explanation:

The term to term rule ' subtract 3 ' is the common difference d of an arithmetic sequence with n th term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₁₂ = 16, then

a₁ + 11d = 16 ← substitute d = - 3

a₁ + 11(- 3) = 16

a₁ - 33 = 16 ( add 33 to both sides )

a₁ = 49 , then

a₅ = 49 + (4 × - 3) = 49 - 12 = 37

Distance = rate * time

Let r = rate

Distance is the same for both runs,  so:

.5r = D =  3/4(r - 2)

Distribute (and convert .5):

2/4r = 3/4r - 3/2

Subtract 3/4 r from both sides:

-1/4r = -3/2

Multiply both sides by -4 to get a solitary r:

r = -3 * -4 / 2

r = 3 * 2

r = 6 miles per hour

.5 hours * 6 mi/hr = 3 miles

check:

6 - 2 = 4

3/4 hours * 4 mi/hr = 3 miles

Answer:

m∠A = 39°

Step-by-step explanation:

From the figure attached,

BE ≅ BC

m∠C = 32°

m∠BFD = 103°

In ΔBCE,

m∠E = m∠C = 32°  [Since, BE ≅ BC]

m∠E + ∠C + m∠EBC = 180°

32° + 32° + m∠EBC = 180°

m∠EBC = 116°

m∠EBC + m∠EBA = 180° [Linear pair of angles]

116° + m∠EBA = 180°

m∠EBA = 64°

Similarly, m∠AFB + m∠DFB = 180° [Linear pair of angles]

m∠AFB + 103° = 180°

m∠AFB = 77°

Now in ΔAFB,

m∠A + m∠AFB + m∠FBA = 180° [Sum of internal angles of a triangle = 180°]

m∠A + 77° + 64° = 180°

m∠A = 39°

Answer:

5.4 feet

Step-by-step explanation:

Let the reference line [tex]A_0B_0[/tex] represents the sea level without any elevation.

At 1 P.M. the ocean surface was at an elevation of 2.2 feet along the line [tex]A_1B_1[/tex] in the figure and the surf shop was  8.2 feet above of this elevated ocean's surface along the line [tex]A_2B_2[/tex] in the figure.

Similarly, at 7 P.M. the ocean surface was at an elevation of -2.4 feet along the line [tex]A_3B_3[/tex] in the figure and the deck in the restaurant was  8.2 feet above of this elevated ocean's surface along the line [tex]A_4B_4[/tex] in the figure.

From the figure, the distance between the deck and the ocean's surface at 1 P.M.= The distance between the lines [tex]A_1B_1[/tex] and [tex]A_4B_4[/tex].

[tex]d= 10- (d_1+d_2)[/tex]

[tex]=10-(2.2+2.4)[/tex]

=5.4 feet

Hence, the distance between the deck and the ocean's surface at 1 P.M. is 5.4 feet.

The distance between the deck and the ocean surface at 1 P.M. is 5.4 feet.

This is a problem of relative and absolute distances. First, we determine the absolute elevation of the surf shop at 1 P.M.:

[tex]x_{1} = 8.2\,ft + 2.2\,ft[/tex]

[tex]x_{1} = 10.4\,ft[/tex]

Now we determine the absolute elevation of the deck at 7 P.M.:

[tex]x_{2} = 10\,ft - 2.4\,ft[/tex]

[tex]x_{2} = 7.6\,ft[/tex]

Lastly, we calculate the elevation of the deck relative to the ocean surface at 1 P.M.:

[tex]x' = 7.6\,ft - 2.2\,ft[/tex]

[tex]x' = 5.4\,ft[/tex]

The distance between the deck and the ocean surface at 1 P.M. is 5.4 feet.

To learn more on distances, we kindly invite to check this verified question: https://brainly.com/question/989117

Answer: √20

Step-by-step explanation:

4.47213595 (the 5 repeats)

Answer: 498,173.26.

Step-by-step explanation:

Place value of the 9 in 329,513 = 9,000

9 is 10 times the value of the 9 in 329,513.

Then, place value of 9 in required number = 10x 9,000 = 90,000

from options only  95,826 and 498,173.26 has 9 at ten thousands place. (cancel all other options)

Also,  2 is [tex]\dfrac1{10}[/tex] the value of the 2 in 7,562.

place value of 2 in required number =[tex]\dfrac1{10}\times2=0.2[/tex]

i.e. place value of 2 in required number 2 tenths

which is in  498,173.26   [place value of 6 is  [tex]\dfrac1{10}[/tex] the value of the 6 in 4.68]

Hence, th required number is 498,173.26.

Answer:

y=1/3-1 ...............

Answer:

C.

Step-by-step explanation:

Answer:

5, 9, and 17

Step-by-step explanation:

Did it on Edg. 2021 and got it right.

Answer:

Step-by-step explanation:

Answer:

60°

140°

Step-by-step explanation:

From the given figures,

 a. we use the concept of alternate angles.

   Two parallel lines cut by a transversal will have equal alternate angles;

  So;

       6x + 12 = 7x + 4

    collect like terms and solve for x;

     6x - 7x = 4 - 12

         -x = -8

         x = 8

Now, 6x + 12 = 6(8) + 12

                     = 48 + 12

                     = 60°

b. Here we use alternate angles and angles on a line;

     4x is an alternate angle to that angle to the left of 13x + 10

And sum of angles on a line = 180

    4x + 13x + 10 = 180

        17x = 170

          x = 10

Now,  13x + 10 = 13(10) + 10 = 140°

Answer:

B and D are the answer's.

Step-by-step explanation:

Answer:

296,518.4 the one is in the tenths place sunce it's after the decimal

296,518,417 the first 1 in 518 is in the tenths place but the 2nd .. 1 is in the tens place bc no decimal

Answer: C

Step-by-step explanation: I could tell just by looking at the first two, they’re negative

Step-by-step explanation:

option b is the correct answer

Answer: There are actually 3 answers for this ahaha, but this is the EXACT ONE: 21/16 in DECIMAL FORM it's 1.3125 in MIXED NUMBER FORM it's 1 5/16

Step-by-step explanation:

Answer:

10t - 16

Step-by-step explanation:

4(t + 2)+ 6(t - 4)

4t + 8 + 6t -24

10t - 16

(3,5)

Step-by-step explanation:

Answer:

5,0

Step-by-step explanation:

Use the website Desmos to help u in this question

Answer:

the answer is 62

Step-by-step explanation:

you take  180 and subtract 118

Answer:

The answer should be 62, but i'm not positive so correct me if i'm wrong!

Explanation:

What I did is i added 118 and 118 then subtracted 360 by the sum. After that I divided the result by two which gave me 62, and I am almost sure that is the answer, but like I said i'm not positive. :)

Answer:

then it would 50 no? i first divided 100 from x and game me 100x and then since i knew that 2 plus 3 is 5 and if i add a 0 then it would make 50

Step-by-step explanation:

Answer:

[tex]3d - 9[/tex]

Step-by-step explanation:

[tex](-7d - 3)+(10d - 6)\\-7d - 3 + 10d - 6\\-7d + 10d -3 - 6\\3d - 9[/tex]

Answer:

-5/3

Step-by-step explanation:

-2 to 1 =3   x=3

4 to -1=5   y=-5

y/x      slope=-5/3 or -1  2/3

Answer:

three shirts an hour

Step-by-step explanation:

Answer:

omg im finding the answer too i go to bcms i see the travid isd thing on ur tabs

Step-by-step explanation:

Answer:

Option A. y=-100/3x+450 is correct.

Step-by-step explanation: