A circular running track is 1/2 a mile long. Elena runs on this track, completing each lap in 1/16 of an hour. What is Elena's running speed? Include the unit of measure.

Answer:

x + 20°​ = 35.56​​°

3x + 10​​° = 56.68°

5x + 10​° = 87.8°

Step-by-step explanation:

Assume;

Given measures are angle of a triangle

x + 20°​

3x + 10​°​

5x + 10​°

Find:

Value of each angle

Computation:

We know that, sum of all interior angle in a triangle is 180°​

So,

We say that

x + 20°​  + 3x + 10​°​  + 5x + 10°​ = 180°

9x + 40° = 180°

9x = 140°

x = 15.56°

So,

x + 20°​ = 15.56 + 20 = 35.56​​°

3x + 10​​° = 3(15.56) + 10 = 56.68°

5x + 10​° = 5(15.56) + 10 = 87.8°

Answer:

8 trips

Step-by-step explanation:

she will be making 8 trips to each table 8x8=64     9x8=72 and so on

Answer:

A

Step-by-step explanation:

sin x° = opposite/Hypotenuse

Answer:

4608

Step-by-step explanation:

4x4x4x6x12

Answer: take a picture of the work please

Step-by-step explanation:

Answer

the top one on the right

Step-by-step explanation:

Answer and Step-by-step explanation:

0 to the power of 4 is 0.

#teamtrees #PAW (Plant And Water)

Answer:

I probably think the qns is no A

Answer:

A

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

Answer:

0.16666666

repeated

or≈0.17

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

180-(100+45)= 35

Answer:

Step-by-step explanation:

Area = πr²

The area formula can be found by breaking apart the circle and forming a parallelogram.

The area of a circle is in square units.

Answer:

Step-by-step explanation:

Opposite angles in parallelogram are congruent:

m∠D = 6*13° - 17° = 61°

Answer:

[tex]m\angle D = 61\textdegree[/tex]

Step-by-step explanation:

In a parallelogram, opposite angles are congruent, so they have the same measure by the definition of congruence. Therefore, [tex]\angle B \cong \angle D[/tex], so [tex]m\angle B = m\angle D[/tex]. We are given the measures of these two angles, so we can write the following equation to solve for [tex]x[/tex]:

[tex]4x+9=6x-17[/tex]

Solving for [tex]x[/tex], we get:

[tex]4x+9=6x-17[/tex]

[tex]-2x+9=-17[/tex] (Subtract [tex]6x[/tex] from both sides of the equation)

[tex]-2x=-26[/tex] (Subtract [tex]9[/tex] from both sides of the equation to isolate [tex]x[/tex])

[tex]x=13[/tex] (Divide both sides of the equation to get rid of [tex]x[/tex]'s coefficient)

Therefore, [tex]m\angle D = 6x-17=6*13-17=78-17=61\textdegree[/tex].

Hope this helps!

Part (a)

In decimal form, this is a = -0.125

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

Explanation:

When it says "she takes the shot 24 feet away", that means that the horizontal distance from the basket to Allie is 24 feet. It's not measuring the slanted or diagonal distance directly from Allie's hand to the net itself. We can think of it as the distance from her feet to the base of the hoop.

When measuring the distance from Allie to the ball, we use the same idea. We simplify things using horizontal distance. Things get way too complicated if we measure the direct distance from the ball (wherever it may be in the air) to the net, or from the ball to Allie's hand.

x and y have units in feet.

The info "when the ball is 4 feet away from her, it is at a height of 10 feet above the floor" means we know the point (x,y) = (4,10) is on the parabola.

The other piece of info that "the ball reaches its greatest height of 18 ft above the floor when it is 12 feet away from her". This tells us the vertex is (h,k) = (12,18)

We have these four pieces of info

Plug those values into the equation below to isolate 'a'

y = a(x-h)^2 + k .... vertex form

10 = a(4-12)^2 + 18

10 = a(-8)^2 + 18

10 = 64a + 18

64a + 18 = 10

64a = 10-18

64a = -8

a = -8/64

a = -1/8

This converts to the decimal -1/8 = -0.125

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

Part (b)

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

Explanation:

From part (a), we found a = -1/8 = -0.125

This means that the vertex form equation y = a(x-12)^2 + 18 updates to y = -0.125(x-12)^2 + 18

This parabola represents the path the ball takes. Plug in y = 10 and solve for x. We do this because the hoop is 10 ft high, and we want to know what x values will make the equation true when y = 10. In other words, we want to know what two locations on the parabola in the form (x,10).

So,

y = -0.125(x-12)^2 + 18

10 = -0.125(x-12)^2 + 18

10-18 = -0.125(x-12)^2

-8 =  -0.125(x-12)^2

-0.125(x-12)^2 = -8

(x-12)^2 = -8/(-0.125)

(x-12)^2 = 64

x-12 = 8 or x-12 = -8

x = 8+12 or x = -8+12

x = 20 or x = 4

The two solutions are x = 4 and x = 20.

The two points we focus on are (4,10) and (20,10). This is when the ball is 10 ft off the ground. Earlier we were told that when the ball is 4 ft away from her, the ball is 10 ft off the ground. So that helps confirm why x = 4 works as a solution. We'll ignore this value though because we want the ball to come down through the hoop, not go up through the hoop. See the diagram below.

Therefore, she needs to be 20 ft away from the hoop to make the shot. Her being 24 ft away means that she's 24-20 = 4 ft too far.

Check out the graph below. We have the following points

As you can see in the diagram below, the green arc represents her shot if she's 24 ft away. She misses point D (the hoop). To make the hoop, she needs to move 4 ft closer to the basket. The red arc is the path the ball takes that will land in the hoop. Every point on the green arc has been shifted over 4 units to the right to arrive at a corresponding point on the red arc.

The vertex form of the parabola can be given as,

[tex]y=a(x-h)^2+k[/tex]

The vertex form of the parabola can be given as,

[tex]y=a(x-h)^2+k[/tex]

Given information-

Allie takes a shot of 24 ft away.

At the distance of 4 feet the ball achieve the height of 10 feet from the ground.

The greatest height achieved by the ball is 18 ft above the floor.

The vertex form of the parabola can be given as,

[tex]y=a(x-h)^2+k[/tex]

Here, [tex](h,k)[/tex] are the vertex of the parabola.

As the ball was 4 feet away from Allie, it is at a height of 10 feet above the floor. Thus the distance on the coordinate on x axis should be 4 feet and The distance on the y axis should be 10 feet.

Now when the ball is 12 feet away the height is 18 ft. Thus the vertex of the parabola is (12,18).

Put the values in the above equation as,

[tex]10=a(4-12)^2+18\\10=a(-8)^2+18\\10-18=64a\\a=-\dfrac{2}{64} \\a=-\dfrac{1}{8}[/tex]

Thus the value of [tex]a[/tex] is -1/8.

Now the value of y is 10 and x is not known.

All the other values are same. Put these values in the vertex form, we get,

[tex]10=-\dfrac{1}{8} (x-12)^2+18\\\\10-18=-\dfrac{1}{8}(x-12)^2\\(x-12)^2=8\times 8 \\(x-12)^2=64\\(x-12)=\pm8[/tex]

By taking positive sign and negative sign one by one the values of x occurs 20 and 4.

Thus the two points we get are (4,10) and (20,10).

Thus If the hoop is 10 ft high, the distance close to Allie have to be in order to make the basket should be 20 feet.

Hence,

Learn more about the vertex form of the parabola here;

https://brainly.com/question/17987697

Answer:

y = -3x+7

Step-by-step explanation:

i hope this helps :)

Answer:

Sine = Opposite/Hypotenuse

Sine^-1 = 55/73

Angle = 48.89

Let me know if this helps!

Answer:Yes I believe it does use strong evidence. Hope this helps

Step-by-step explanation:

Answer:

ccccccc

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

The slope is -1/2

Answer:

-(1/2) or -0.5

Step-by-step explanation:

select two coordinates. for example, (2,2) and (4,1).

do (y2 - y1) ÷ (x2 - x1).

in this case, (1 - 2) ÷ (4 - 2). you should end up with -(1/2), or -0.5

Answer:10

Step-by-step explanation:

2+4+6+6+9+13+30=70

70 divided by 7= the mean should be 10

Answer:

the mode is 6 the median is also 6 the range is 28 the mean is 10

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

y + 0 - 2 = 15

y - 2 = 15

y - 2 + 2 = 15 + 2

y = 17

Answer:

9=4+5, 9=7+2, 9=6+3 are correct

Step-by-step explanation:

Answer:

I think it is 9.33 because the full answer is 9.327 so rounded it would be 9.33??

Answer:

x=9

Step-by-step explanation:

i hope this helps :)