A flagpole is 45 feet tall. A rope is tied to the top of the flag pole and secured to the ground 10 feet from the base of the flagpole. Will a 35 foot piece of rope be long enough to secure the flagpole? Justify your answer.
i give brainliest

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:

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: 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:

135°

Step-by-step explanation:

Answer:34.93

Step-by-step explanation:

Using a^2+b^2=c^2we can substitute a and b in which is 34^2+8^2=c^21156+64=c^21220 = c^2Now we need to square both sides√1220 = √c^234.9284983931 ----> 34.9334.93 = cc = 34.93

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

Answer:

1875

Step-by-step explanation:

1500 x .25 is 375 add them together

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

[tex]118 = k + 70 \\ 118 - 70 = k \\ 48 = k[/tex]

Answer: 48

Step-by-step explanation:

You do opposite operations, so instead of adding 70, you subtract subtract it- 118-70=k+70-70. You do it to both sides to keep the equation balanced. Simplify to get 48=k.

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:

Moving from point A (2,40) to point B (3,8) , you move 32 units down and one unit right, meaning your slope is 32x.

Your y-intercept is 104.

Altogether, your function (in y = mx + b format) will look like this:

y = -32x + 104

Answer:

5 units

Step-by-step explanation:

Use the distance formula [tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2[/tex] where [tex]d[/tex] is the distance between points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].

Given that [tex](x_1,y_1)\rightarrow(6,4)[/tex] and [tex](x_2,y_2)\rightarrow(10,7)[/tex], then:

[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\\\\d=\sqrt{(7-4)^2+(10-6)^2}\\\\d=\sqrt{3^2+4^2}\\\\d=\sqrt{9+16}\\\\d=\sqrt{25}\\\\d=5[/tex]

This means that the distance between (6,4) and (10,7) is 5 units

Answer:

16f^3 / 3

Step-by-step explanation:

Ur mom told me trust

Answer:

16f^3/3

(A on Edge)

Step-by-step explanation:

Did Edge

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

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)

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:

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:

8

Step-by-step explanation:

It's counting by 2's

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:

W=460+460+460

W=1380

2000≠1380

2000-1380=620

2000=1380+620

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:

what is the answers is it multiple choice?

Step-by-step explanation:

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:

Step-by-step explanation:

Given equation:

Solve:

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:

3y = -2x - 5

Step-by-step explanation:

y = mx + c-----(i)

2x + 3y + 5 = 0

collect like terms to match that of (i) following where x and y are

3y + 5 = -2x

3y = -2x - 5

y = mx + c

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:

851,243,679,010

851,432,697,201

815,234,739,120

815,234,796,002