A line passes through the point (3,6) and has a slope of 7. Write an equation in point-slope form for this line.​

Step-by-step explanation:

1 mile = 5280 ft

1 hour = 3600 seconds (60 minutes of 60 seconds each).

the open question here is : do we need the ground distance, or really the line of sight distance (e.g. directly above the intersection the distance is 0 ft ground distance but 95ft line of sight distance) ?

based on the above conversions the speed

30 miles per hour = 30×5280 ft per 3600 seconds =

= 158,400 ft / 3600 s = 44 ft/s

so, the balloon moves away from the intersection 44 ft every second.

so, just for ground distance in ft we would have

d = 44t

for the line of sight distance we need to use Pythagoras, as we need to calculate the length of the Hypotenuse (= the line of sight) of the right-angled triangle of ground distance, height and line of sight.

the ground distance is again the same function as before (44t). height is constant (95 ft).

so,

d² = (44t)² + 95² = 1936t² + 9025

d = sqrt(1936t² + 9025)

so, e.g. after 1 second the line of sight distance would be

d = sqrt(1936×1 + 9025) = sqrt(1936 + 9025) =

= sqrt(10961) = 104.6947945... ft

that means although the ground distance increased by 44 ft, the line of sight distance increased only by roughly 10 ft.

that's how right-angled triangles work.

after 2 seconds d = 129.4951737... ft, so, roughly a 25 ft increase compared to 1 second. the change rate of the line of sight distance (the Hypotenuse) will get closer and closer to the (constant) change rate of the ground distance (but will never fully reach it - only in infinity ...).

Answer:

2.97 with the line

Step-by-step explanation:

the line tells you that the 97 will repeat

2.9797 is more than 2.9782

Answer:

5

Step-by-step explanation:

Pyramid

[tex]\textsf{volume of a square based pyramid} =\frac{1}{3} a^2h[/tex]

(where [tex]a[/tex] = base edge, and [tex]h[/tex] = height)

Given:

[tex]\implies \textsf{volume} =\frac{1}{3} \times 9^2\times10=270 \ \mathsf{cm^3}[/tex]

Wax cubes

volume of a cube = w³, where w is the length of one edge

⇒ volume = 4³ = 4 x 4 x 4 = 64 cm³

Solution

To calculate how many wax cubes are needed, divide the volume of the pyramid by the volume of a wax cube:

⇒ 270 ÷ 64 = 4.21875

⇒ 5 wax cubes are needed to make the candle

We need to round this up to 5, since we need to know the number of whole wax cubes.  (If we rounded down to 4, there would not be quite enough to fill the pyramid as 4 x 64 = 256 < 270)

Answer:

The two numbers are 6 and 9

Step-by-step explanation:

Let the two numbers be x and y

x+y = 15

x-y = 3

Add the two equations together to eliminate y

x+y = 15

x-y = 3

----------------

2x = 18

Divide by 2

2x/2 = 18/2

x = 9

Now we can find y

x+y = 15

9+y = 15

y = 15-9

y = 6

The two numbers are 6 and 9

hello againn

okay, so lets see how 32 can become 20. We can subtract 12, so that is possible. Lets check with our other inputs.

if all inputs - 12 = the output, that is the function.

14 - 12 = 2. 2 is our output, so that is a very good sign.

We cant check the third one, so lets skip that for now.

-2 - 12 = -14, which is our output. (yay!!!)

And we cant fill in the last one, which is okay.

So now we know our function is y = x - 12.

Now we fill in the question marks.

The third one. -6 + 12 = 6. The input for 3. is 6.

Last one, 10 - 12 = -22.

Function: y = x-12

Fill ins, third = 6

Last = -22.

:D!!!

Answer:

the period of this graph is 2[tex]\pi[/tex]

Step-by-step explanation:

The period is the length of the section that repeats.  So for this graph, we need to calculate the distance between 2 peaks or 2 troughs of the curve.

Let's look at the peaks (maximums).

One is at x = 0 and the next is at x = 2[tex]\pi[/tex]

2[tex]\pi[/tex] - 0 = 2[tex]\pi[/tex]

Therefore, the period of this graph is 2[tex]\pi[/tex]

Answer:

((75 +45)÷5-10)×2

Step-by-step explanation:

Simplified:

((120÷5)-10×2

=(24-10) ×2

=14 ×2

=28

Answer:

Step-by-step explanation:

m ∠ D + m ∠ E + m ∠ F = 180°

m ∠ D = m ∠ F - 14

m ∠ E = 2( m ∠ F ) + 10

m ∠ F - 14 + 2( m ∠ F ) + 10 + m ∠ F = 180°

4( m ∠ F ) = 180 + 4

m ∠ F = 46 °

m ∠ E = 2 × 46 + 10 = 102 °

m ∠ D = 46 - 14 = 32 °

Answer:

D = 32°

E = 102°

F = 46°

Step-by-step explanation:

The measure of angle D is 14 less than the measure of angle F

⇒ D = F - 14

The measure of angle E is 10 more than twice the measure of angle F:

⇒ E = 2F + 10

So we have now constructed two equations:

Equation 1:  D = F - 14

Equation 2:  E = 2F + 10

Also, we know that the sum of the interior angles of a triangle is 180°.

Therefore, D + E + F = 180

Substitute the two equations we have constructed for D and E into the sum of the interior angles equation and solve for F

     D + E + F = 180

⇒ (F - 14) + (2F + 10) + F = 180

⇒ 4F - 4 = 180

⇒ 4F = 180 + 4 = 184

⇒ F = 184 ÷ 4

⇒ F = 46°

Now substitute the found value of angle F into the two equations for D and E:

   D = F - 14

⇒ D = 46 - 14

⇒ D = 32°

   E = 2F + 10

⇒ E = 2(46) + 10

⇒ E = 92 + 10

⇒ E = 102°

Answer (Left to right per row):

-1, 2, 4, 6, 6.9, 6.99, 6.999

Step-by-step explanation:

y is anything less than 7

Answer:

$2,411.20

Step-by-step explanation:

Use the simple interest formula: A = P(1 + rt)

A = Final amount (?)

P = Starting amount (2200)

r = Rate (0.024)

t = Time in years (4)

A = 2200(1 + 0.024 · 4)

A = 2200(1.096)

A = 2411.2

Answer:

W=460+460+460

W=1380

2000≠1380

2000-1380=620

2000=1380+620

Answer:

The answer is -15.75 because 4= -16= -79 you have to turn 16 positive so add 16 to -79 to get -63 then divide by 4 to get the answer -15.75.

Answer:

8

Step-by-step explanation:

It's counting by 2's

Answer:

100 waffles

Step-by-step explanation:

Answer: 35

Step-by-step explanation:

The total number of students who voted is 35.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

A class votes for their class president Candidate A receives 21 votes, which is 60% of the vote.

The total number of students who voted,

= 21 x100 / 60

= 2100/60

= 35

Therefore, 35 students voted.

To learn more about the percentage;

https://brainly.com/question/24159063

#SPJ2

Answer:

  α² +β² = 3 4/9

Step-by-step explanation:

Assuming α and β are solutions to the equation, it can be factored as ...

  (x -α)(x -β) = 0

Expanding this, we get ...

  x² -(α +β)x +αβ = 0

Dividing the original equation by 3, we find ...

  x² +(1/3)x -5/3 ≡ x² -(α+β)x +αβ   ⇒   (α+β) = -1/3, αβ = -5/3

We know that the square (α+β)² can be expanded to ...

  (α +β)² = α² +β² +2αβ

  α² +β² = (α +β)² -2αβ . . . . . . subtract 2αβ

Substituting the values for (α+β) and αβ, we find the desired expression is ...

  α² +β² = (-1/3)² -2(-5/3) = 1/9 +10/3 = 31/9

  α² +β² = 3 4/9

Answer:

1875

Step-by-step explanation:

1500 x .25 is 375 add them together

[tex]=Solution,\\\\Diameter(d)=10yd\\\\Radius(r)=10yd/2=5yd\\\\Now,\\\\Volume=\frac{4}{3} \pi r^{3} \\\\Volume=\frac{4}{3} *\pi*(5yd)^{3} \\\\Volume=\frac{4}{3}*3.14*125yd^{3} \\\\Volume=523.33yd^{3}[/tex]

Answer:

6 and 7

Step-by-step explanation:

6^2 = 36

7^2 = 49

36 < 47 < 49

so the two consecutive whole numbers are 6 and 7

Answer:

Step-by-step explanation:

Given equation:

Solve:

Answer:

I am not too sure but I think the answer would be 6

Step-by-step explanation:

Step-by-step explanation:

a=> let t denote the number of t

n(t)=1

number of total letters, n(s) = 8

Now,

probability of getting t ,P(t)

= n(t)/ n(s)

= 1/8

b=> let o denote the number of o and

m

n(o)=2

number of total letters, n(s) = 8

Now,

probability of getting t ,P(o)

= n(o)/ n(s)

= 2/8

= 1/4

c=> let x denote the number of x

n(x)=0

number of total letters, n(s) = 8

Now,

probability of getting a x, P(x)

= n(x)/n(s)

= 0/8

= 0

d=> let v denote the number of vowel

letters

n(v)=3

number of total letters, n(s) = 8

Now,

probability of getting a vowel

letter,P(v) = n(v)/n(s)

= 3/8

I hope my answer was helpful

The random nature of the process is why Gina doesn't get the theoretical probability. If she were to repeat this experiment say 1000 or perhaps 10,000 times, then her experimental probability value should get closer to 1/2. It likely won't land *exactly* on 1/2 because again of the random nature of the outcomes.

For more information, check out the Law of Large Numbers.

Answer:

The theoretical probability of spinning a head = 1/2 = 0.5

Therefore, if Gina spins a penny 100 times, the theoretical number of times it will land head side up = 0.5 x 100 = 50 times

Gina's experimental probability is 38/100 = 0.38

Therefore, the experimental probability is less than the theoretical probability.

The main difference between experimental and theoretical probability is that experimental probability is based on the actual results of an experiment (gathered by experimenting repeatedly), whereas theoretical probability is based on possible outcomes based on assumptions.

If Gina continued to spin the penny, as the number of times she spun it increased, you would expect for the experimental probability to get nearer to the theoretical probability of 0.5.

Answer:

35 < x

Step-by-step explanation:

the greater than symbol (<) indicates its previous number to be smaller than the next number. as Deandre exercises more than 35 hrs, the inequality would be 35 < x

Answer:

135°

Step-by-step explanation:

Answer: 2295 ft ^2, 255 yd^2

Step-by-step explanation:

The area of the field is the length times the width.

Since there are 3 feet in 1 yard, 15 yards = 45 feet.

So the area in square feet = 45*51 feet^2 = 2295 ft ^2

Since there are 1/3 yard in 1 feet, 51 feet = 17 yards

So the area in square yards = 15*17 yard^2 = 255 yd^2