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Answer:

The equation that describes the path of the water balloon is:

[tex]y =-\frac{1}{10}\cdot (x-10)^{2}+15[/tex]

Step-by-step explanation:

The motion of the water balloon is represented by quadratic functions. Tommy launches a water balloon from [tex]A(x,y) = (0\,ft, 5\,ft)[/tex] and hits Arnold at [tex]B(x,y) = (20\,ft, 5\,ft)[/tex]. Given the property of symmetry of quadratic function, water ballon reaches its maximum at [tex]C(x,y) = (10\,ft,15\,ft)[/tex], which corresponds to the vertex of the standard equation of the parabola, whose form is:

[tex]y = a\cdot (x-h)^{2}+k[/tex] (Eq. 1)

Where:

[tex]a[/tex] - Vertex parameter, measured in [tex]\frac{1}{ft}[/tex].

[tex]h[/tex], [tex]k[/tex] - Horizontal and vertical components of the vertex, measured in feet.

[tex]x[/tex], [tex]y[/tex] - Horizontal and vertical location of the ball, measured in feet.

If we know that [tex]x = 0\,ft[/tex], [tex]y = 5\,ft[/tex], [tex]h = 10\,ft[/tex] and [tex]k = 15\,ft[/tex], the vertex parameter is:

[tex]5\,ft = a\cdot (0\,ft-10\,ft)^{2}+15\,ft[/tex]

[tex]a = \frac{5\,ft-15\,ft}{(0\,ft-10\,ft)^{2}}[/tex]

[tex]a = - \frac{1}{10}\,\frac{1}{ft}[/tex]

The equation that describes the path of the water balloon is:

[tex]y =-\frac{1}{10}\cdot (x-10)^{2}+15[/tex]

Answer:

x = 37, y = 9

Step-by-step explanation:

3x + 11 and x + 21 are same- side interior angles and are supplementary, thus

3x + 11 + x + 21 = 189 , that is

4x + 32 = 180 ( subtract 32 from both sides )

4x = 148 ( divide both sides by 4 )

x = 37

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

3x + 11 = 3(37) + 11 = 111 + 11 = 122

14y - 4 and 3x + 11 are vertical angles and congruent, thus

14y - 4 = 122 ( add 4 to both sides )

14y = 126 ( divide both sides by 14 )

y = 9

Answer:

B

Step-by-step explanation:

The metric system uses one unit for each category of measurement.

Answer:

Step-by-step explanation:

18 · (-4) = -72

-72 · (-4) = 288

288 · (-4) = -1,152

answer is c because if it's not a and b then the only answers will be c and d and d is the same as the number so it's c

Answer: 30 small bags

Step-by-step explanation:

From the question, we are informed that Daniel works in a market and that he has a large bag of potatoes that weighs 6514 pounds and he is going to sell them in smaller bags of 214 pounds each.

When he uses up all the potatoes, the number of smaller bags of potatoes that Daniel will have filled will be 6514 divided by 214. This will be:

= 6514/214

= 30.43

= 30 small bags

Answer:

27

Step-by-step explanation:

If we divide 18 by 2, we get 9. 9 is how many glasses each container of ice tea can fill. 3 x 9 = 27

Answer:

-3/4

Step-by-step explanation:

Slopes are equal for parallel lines

Slope of line v is -3/4

Answer:

1.3 kg/cm

Step-by-step explanation:

Answer:

the others are right

Step-by-step explanation:

good work keep going

Step-by-step explanation:

Please write complete question

Answer:

lol u gotta put the thing first bro

Step-by-step explanation:

Answer: choice A

Step-by-step explanation:

The linear inequality represented by the graph  is y≥1/3x-1

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Let us find slope of line passing through points (0, -1) and (3, 0)

Slope = 0+1/3

=1/3

y intercept we have to find

0=1/3(3)+b

b=-1

So equation of line is y=1/3x-1

As the shading is away from origin, we use the greater than or equal to symbol.

y≥1/3x-1

Hence, the linear inequality represented by the graph  is y≥1/3x-1

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• Height of the equilateral triangle = 5/3 cm .

• The area of the triangle .

• First find side :

As we know that:

• Height = √3/2 (side)

=> 5/3= √3/2 (side)

=> side = 10/3√3 cm

• Area of equilateral triangle = √3/4 (side)².

=> Area = √3/4(10/3√3)²

=> Area = √3/4(100/27)

=> Area = 25√3/27

=> Area = 43.30/27

=> Area = 1.60 cm².

Hence, the area of equilateral triangle is 1.60cm²

I hope it will help you.

Regards.

Answer:

$884.99

Step-by-step explanation:

Just took the quiz and this was the right answer. :)

Answer:

884.99

Step-by-step explanation:

Answer:

Neptune is 80 times farther from the Sun than Mercury.

It takes 4 hours to reach the light from the Sun to Neptune.

Step-by-step explanation:

Given that the average distance between the Sun and Mercury,

[tex]d_1=35,000,000[/tex] miles [tex]=3.5\times 10^7[/tex] miles.

The time to reach the light from the sun to Mercury, [tex]t_1 = 3[/tex] minutes

Let v m/s  be the speed of light.

So, [tex]v=\frac{d_1}{t_1}\cdots(i)[/tex]  [as speed = distance/time]

Now, the average distance between the Sun and Neptune,

[tex]d_2=2.8\times 10^9[/tex] miles.

The ration of the average distance of Neptune and Mercury from Sun,

[tex]\frac{d_2}{d_1}=\frac{2.8\times 10^9}{3.5\times 10^7}[/tex]

[tex]\frac{d_2}{d_1}=80\cdots(ii)[/tex]

So, Neptune is 80 times farther from the Sun than Mercury.

The time to reach the light from the sun to Neptune,

[tex]=\frac{d_2}{v}[/tex] [as time=distance/speed]

[tex]=\frac{d_2}{d_1/t_1}[/tex] [using equation(i)]

[tex]=\frac {d_2}{d_1}\times t_1[/tex]

[tex]=80\times 3[/tex]  [using equation(ii)]

=240 minutes

=4 hours [as 1 hour =60 minutes]

Hence, it takes 4 hours to reach the light from the Sun to Neptune.

Using the speed - distance relationship, we can deduce that Neptune is 80 times farther from the sun than Mercury and it will take 240 minutes for light from the sun to reach Neptune.

Given the Parameters :

Number of times Neptune is father from the sun than Mercury :

Hence, Neptune is 80 times farther from the sun than Mercury.

Time taken for light to reach Neptune :

3 minutes × 80 = 240 Minutes

60 minutes = 1 hour

240 minutes = (240 ÷ 60) = 4 hours

Therefore, it would take 4 hours for light to reach Neptune.

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Answer:

10.6 hours

Step-by-step explanation:

Answer:

y=8

Step-by-step explanation:

(y-2)/(-1-9)=(y-2)/-10    (11-16)/(-8-(-5))=-5/-3=5/3  Perpendicular slope is -3/5

(y-2)/10=-3/5 cross multiply 5(y-2)=3(10)    5y-10=30   add 10 to both sides

5y=40  divide both sides by 5 and y is equal to 8.

The value of y is 8 if AB is perpendicular CD after using the slope formula.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

It is given that:

A(9, 2), B(-1, y) C.(-5, 16) and D(-8, 11),

AB is the perpendicular CD

Using the slope formula to find the slope between A and B:

(y-2)/(-1-9)

= (y-2)/-10    

(11-16)/(-8-(-5)) =

-5/(-3)

= 5/3  

The perpendicular slope is -3/5

(y-2)/10=-3/5

5(y-2)=3(10)    

5y-10=30  

5y=40  

y = 8

Thus, the value of y is 8 if AB is perpendicular CD after using the slope formula.

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Answer:

Step-by-step explanation:

b-5 ≤ 16

Answer:

b - 5 ≤ 16

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

HI

Answer:

- 1

Step-by-step explanation:

Using the trigonometric identity

cos(- x) = cosx and exact value cos60° = [tex]\frac{1}{2}[/tex]

Given

f(x) = - 2cosx , then

f(- 300° )

= - 2cos(- 300)°

= - 2cos(300)°

= - 2cos(360 - 300)°

= - 2cos60°

= - 2 × [tex]\frac{1}{2}[/tex]

= - 1

Answer:

8.22 × 10²

Step-by-step explanation:

Scientific Notation: x.xx × 10ⁿ

We simply follow the base 10 decimal system to convert from standard form to scientific notation:

822 = 8.22 × 10²

Answer:

If one angel is 74 so the solution is

[tex]74 + 2x = 180 \\ 2x = 180 - 74 \\ x = 106 \div2 \\ \: x = 53 \\ u = 74 \\ v = 53 \\ w = 53[/tex]

Step-by-step explanation:

Please mark as brainliest

The hourly wage increase each employee receives each year depends on their number of years of service. Every three years of service means an increase of $0.50 per hour. So, employees that have been with the company for less than three years can expect to receive an increase of $0.50 per hour. Employees that have been with the company for at least three years, but less than six years can expect an increase of $1.00 per hour. Employees that have been with the company for at six years, but less than nine years, receive an increase of $1.50 per hour. And, employees of at least nine years, but less than twelve years receive an increase of $2.00 per hour.

Choose a function to represent this scenario

Answer:

12.625

Step-by-step explanation:

12 is a whole so it would go before the decimal point.

5/8 or 5 divided by 8 is equal to 0.625.

12 + 0.625 = 12.625

Answer:

b

Step-by-step explanation:

Answer:

I would have to say B, because 2/3 divided by 6 = 1/9. Plus, I think this would make sense considering we're dealing with a fraction problem. I hope this will help m8! ;)

Step-by-step explanation:

Answer:  B. 202.5 miles

Step-by-step explanation:

Multiply the scale ratio by the number of inches given on the map.

2.7 × 1 inch  and  2.7 × 75 miles    2.7×75=202.5

2.7 inches represents 202.5 miles

Answer:

Yes it is rational.

Step-by-step explanation:

Answer:

Rational I think

Step-by-step explanation:

Rational means it can be expressed as a fraction

Answer:

Hot, Dim, Small

Answer: 1,6,3,8

Step-by-step explanation: that one, and its opposite and the other one is the same

Answer:

1, 3, and 8

Step-by-step explanation:

You should know this because, 88 degrees and 2 are in a straight line which there means that 2 would be 92 degrees. So every length would be slightly shorter or longer than the other. As you can observe 1, 3, and 8 other than 6 are all the ones that are slightly shorter than their counterpart 2, 4, 5, and 7. Which means that 1, 3, and 8 all equal 88 degrees just like 6.

Answer:

11.25

Step-by-step explanation:

Multiply 4.5 by the reciprocal of 2/5, which is 5/2. You will then get 11.25. Hope this helped :)

Total number of cups of water needed to prepare 5 cups of rice are 11.25.

What is mean by Ratio?

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

Given that;

When rice is prepared, the amount of rice varies directly as the amount of water required.

And, 2 cups of rice requires 4.5 cups of water.

Now,

Since, 2 cups of rice requires 4.5 cups of water.

Hence, For 1 cup of rice, number of cups of water = 4.5 / 2

                                                                             = 2.25

So, For 5 cups of rice, number of cups of water = 5 x 2.25

                                                                          = 11.25

Thus, Total number of cups of water needed to prepare 5 cups of rice are 11.25.

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