Which statement best describes what Rutherford concluded from the motion of the particles?

Answer:

Suppose that the height (in centimeters) of a candle is a linear function of

the amount of time (in hours) it has been burning.

After 11 hours of burning, a candle has a height of 23.4 centimeters.

After 30 hours of burning, its height is 12 centimeters.

What is the height of the candle after 13 hours?

:

Assign the given values as follows:

x1 = 11; y1 = 23.4

x2 = 30; y2 = 12

:

Find the slope using: m = %28y2-y1%29%2F%28x2-x1%29

m = %2812-23.4%29%2F%2830-11%29 = %28-11.4%29%2F19

:

Find the equation using the point/slope formula: y - y1 = m(x - x1)

y - 23.4 = -11.4%2F19(x - 11)

y - 23.4 = -11.4%2F19x + 125.4%2F19

y = -11.4%2F19x + 125.4%2F19 + 23.4

y = -11.4%2F19x + 125.4%2F19 + 23.4

y = -11.4%2F19x + 125.4%2F19 + 444.6%2F19

y = -11.4%2F19x + 570%2F19

y = -11.4%2F19x + 30, is the equation

:

What is the height of the candle after 13 hours?

x = 13

y = -11.4%2F19(13) + 30

y = -148.2%2F19 + 30

y = -7.8 + 30

y = 22.2 cm after 13 hrs

Answer:

x < -8/45

Step-by-step explanation:

Step 1: Write out inequality

45x + 5 < -3

Step 2: Subtract both sides by 5

45x + 5 - 5 < -3 - 5

45x < -8

Step 3: Divide both sides by 45

45x/45 < -8/45

x < -8/45

Step 4: Graph

Answer:

vertical angles

Step-by-step explanation:

Angle 1 and 3 are vertical angles.  The angles are made from the same lines and share a vertex.  They are opposite it each other

Answer:

Three to the second power

Step-by-step explanation:

Hey there!

3 square

Can be written as the following,

Three to the second power

Hope this helps :)

Answer:

-1

Step-by-step explanation:

the common ratio in this geometric series is -1

Answer:

a) The company sold 93 Chicken dinners, 76 Beef dinners and 31 Fish dinners.

b) [tex]y=3x^{2}-4x+2[/tex]

Step-by-step explanation:

a)

In order to solve part a of the problem, we must start by setting our variables up:

C=# of Chicken dinners

B=# of Beef dinners

F=# of Fish dinners

Next we can use these variables to build our equations. We start by taking the fact that they sold a total of 200 dinners. The sum of all the variables should add up to that so we get:

C+B+F=200

Then the problem tells us the price of each dinner and the total amount of money they made from selling the dinners that day:

"A TV Dinner Company Sells Three Types Of Dinners: A Chicken Dinner For $10, A Beef Dinner For $11, Or A Fish Dinner For $12. For A Grand Total Of $2138"

So we can use this information to build our second equation:

10C+11B+12F=2138

We have two equations now but three variables, so we need an additional equation so we can finish solving this. The problem tells us that:

"they sold three times as many chicken dinners as they did fish"

which translates to:

C=3F

so now we have enough information to finish solving the problem. We can start by substituting the last equation into the previous two equations so we get:

C+B+F=200

3F+B+F=200

4F+B=200

and

10C+11B+12F=2138

10(3F)+11B+12F=2138

30F+11B+12F=2138

42F+11B=2138

So now we can take the two bolded equations and solve them simultaneously. We can solve them by using any method we wish. Let's solve it by substitution.

We start by solving the first equation for B so we get:

B=200-4F

and now we substitute it into the second equation:

42F+11(200-4F)=2138

and now we solve for F

42F+11(200-4F)=2138

42F+2200-44F=2138

-2F=2138-2200

[tex]F=\frac{-62}{-2}[/tex]

F=31

So now that we know the value of F, we can find the values of the rest of the variables so we can take the previous equations to figure this out:

B=200-4F

B=200-4(31)

B=200-124

B=76

and finally:

C=3F

C=3(31)

C=93

So

The company sold 93 Chicken dinners, 76 Beef dinners and 31 Fish dinners.

b) For the second part of the problem we need to build a system of equations to find the equation we are looking for. We were given three points:

(-1,9), (2,6) and (3,17)

so we need to substitute each of the points on the given quadratic equation so we get:

[tex]9=a(-1)^{2}+b(-1)+c[/tex]

eq.1:  [tex]9=a-b+c[/tex]

[tex]6=a(2)^{2}+b(2)+c[/tex]

eq. 2:  [tex]6=4a+2b+c[/tex]

[tex]17=a(3)^{2}+b(3)+c[/tex]

eq. 3:  [tex]17=9a+3b+c[/tex]

So now that we have our three equations we can solve them simultaneously to get the values of a, b and c by using the method you feel more comfortable with. Let's solve it by elimination:

So let's take the first equations and let's subtract them:

[tex]9=a-b+c[/tex]

[tex]-6=-4a-2b-c[/tex]

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

3=-3a-3b

And now we repeat the process with the first and third equations:

[tex]9=a-b+c[/tex]

[tex]-17=-9a-3b-c[/tex]

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

-8=-8a-4b

So now we have two new equations we can solve simultaneously, but they can be simplified by dividing the first one into -3 and the second one into -4 so they become:

a+b=-1

2a+b=2

We can now solve them by substitution. Let's solve the first one for a and then let's substitute it into the second equation:

a=-1-b

let's substitute

2(-1-b)+b=2

and solve for b

-2-2b+b=2

-b=4

b=-4

Now we can find a:

a=-1-b

a=-1+4

a=3

and now we can find c:

c=9-a+b

c=9-3-4

c=2

So we can use these answers to build our equation:

[tex]y=ax^{2}+bx+c[/tex]

[tex]y=3x^{2}-4x+2[/tex]

Answer:

1.56x+10.15

Step-by-step explanation:

Answer:

1.56x + 10.15

Step-by-step explanation:

(5.23x + 3.76) – (3.67x – 6.39)

(a + b) – (c – d) = a + b – c + d

Remove the parentheses and change the signs as needed:

5.23x + 3.76 – 3.67x + 6.39.

Group the like terms and simplify:

5.23x – 3.67x + 3.76 + 6.39

1.56x +10.15.

The simplified form of (5.23x + 3.76) – (3.67x – 6.39) is 1.56x + 10.15.

Answer:

y - 3 = -1/2(x - 1)

Step-by-step explanation:

Hey there!

Well point slope form is,

[tex]y - y_{1} = m(x - x_{1})[/tex]

We can use the point (1,3)

y - 3 = m(x - 1)

Now we need to find slope with the following formula,

[tex]\frac{y^2-y^1}{x^2-x^1}[/tex], we’ll use the points (1,3) and (5,1).

[tex]\frac{1-3}{5-1}[/tex]

-2/4

Slope or m = -1/2

y - 3 = -1/2(x - 1)

Hope this helps :)

Answer: y=23

Step-by-step explanation:

If Points and A,B and C lines on the same line then they will have the same slopes so since we have the coordinates of  A and B we will use the to write an equation in slope intercept form.

To write it in slope intercept form we will need to find the slope and the y intercept.

To find the slope you will find the change in the y coordinates and divide it by the change in the x coordinates.

Using the coordinates (-1,7) and (2,19)  the y coordinates are 7 and 19 and the x coordinates are -1 and 2.

Slope :  [tex]\frac{7-19}{-1-2} \frac{-12}{-3} = 4[/tex]   In this case the slope is 4 so we will use that to find the y intercept by using point A coordinate.

  The slope intercept formula says that y=mx +b  where me is the slope and b is the y intercept.

 7=4(-1) + b  

7 = -4 + b

+4   +4

 b= 11       The y intercept is 11.

Now we can write the whole equation as y=4x + 11   .

To answer the question now, where we need to find y , we will plot the x coordinate which is 3 into the equation and solve for y.

 y = 4(3) + 11  

y = 12 + 11

 y = 23

Answer:

$24

Step-by-step explanation:

You simply do $42-$18

=24

Answer:

$24

Step-by-step explanation:

At the start, Jaime had $42. In order to find out how much the T-shirt he purchased costs, we must subtract 18 from 42.

42 - 18 = 24

Jaime spent $24 on the T-shirt.

Answer:

She must consider 3507 components to be 90% sure of knowing the mean will be within ± 0.1 mm.

Step-by-step explanation:

We are given that an engineer wishes to determine the width of a particular electronic component. If she knows that the standard deviation is 3.6 mm.

And she considers to be 90% sure of knowing the mean will be within ±0.1 mm.

As we know that the margin of error is given by the following formula;

The margin of error =  [tex]Z_(_\frac{\alpha}{2}_) \times \frac{\sigma}{\sqrt{n} }[/tex]  

Here, [tex]\sigma[/tex] = standard deviation = 3.6 mm

         n = sample size of components

         [tex]\alpha[/tex] = level of significance = 1 - 0.90 = 0.10 or 10%

         [tex]\frac{\alpha}{2} = \frac{0.10}{2}[/tex] = 0.05 or 5%

Now, the critical value of z at a 5% level of significance in the z table is given to us as 1.645.

So, the margin of error =  [tex]Z_(_\frac{\alpha}{2}_) \times \frac{\sigma}{\sqrt{n} }[/tex]  

                  0.1 mm        =  [tex]1.645 \times \frac{3.6}{\sqrt{n} }[/tex]

                    [tex]\sqrt{n} = \frac{3.6\times 1.645}{0.1 }[/tex]

                    [tex]\sqrt{n}[/tex] = 59.22

                     n = [tex]59.22^{2}[/tex] = 3507.0084 ≈ 3507.

Hence, she must consider 3507 components to be 90% sure of knowing the mean will be within ± 0.1 mm.

Answer:

Step-by-step explanation:

If  the path of the longest shot put by the Women’s track team at Sun Devil U is modeled by h(x) = -0.015x² + 1.08x + 5.8 where x represents the horizontal distance from the start and h(x) is the height of the shot put above the ground, to determine h(24), we will have to substitute x = 24 into the modeled equation as shown;

[tex]h(x) = -0.015x^2 + 1.08x + 5.8\\\\if \ x = 24;\\\\h(24) = -0.015(24)^2 + 1.08(24) + 5.8\\\\h(24) = -0.015(576)+25.92+5.8\\\\h(24) = -8.64+31.72\\\\h(24) = 23.08\\[/tex]

Hence the value of the height at the horizontal distance of 24 feet is 23.08 feet to 2 decimal place.

Answer:

slope = 2

Step-by-step explanation:

will make it so simple and short

slope = rise / run

slope = 6 / 3

slope = 2

Answer:

B

Step-by-step explanation:

The formula for slope is (y2-y1)/(x2-x1)

In this case it is (1+5)/(3-0)

6/3

2

Answer:

  x^2 +y^2 = 4y

Step-by-step explanation:

Using the usual translation relations, we have ...

  r^2 = x^2+y^2

  x = r·cos(θ)

  y = r·sin(θ)

Substituting for sin(θ) the equation becomes ...

  r = 4sin(θ)

  r = 4(y/r)

  r^2 = 4y

Then, substituting for r^2 we get ...

  x^2 +y^2 = 4y . . . . . matches the first choice

Answer:

A natural number is a number that occurs commonly and obviously in nature. As such, it is a whole, non-negative number.

Step-by-step explanation:

Answer:

Finite

Step-by-step explanation:

please give me brainliest

Answer: The triangles are not congruent

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

Explanation:

For triangle DEF, the missing angle D is

D+E+F = 180

D+80+60 = 180

D+140 = 180

D = 180-140

D = 40

While the missing angle K in triangle JKL is

J+K+L = 180

80+K+50 = 180

K+130 = 180

K = 180-130

K = 50

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

The three angles for triangle DEF are

The three angles for triangle JKL are

We don't have all the angles matching up. We need to have the same three numbers (the order doesn't matter) show up for both triangles in order for the triangles to be congruent. This is because congruent triangles have congruent corresponding angles.

The only pair that matches is E = 80 and J = 80, but everything else is different. So there is no way the triangles are congruent.

Notice how triangle JKL has two congruent base angles (K = 50 and L = 50), so this triangle is isosceles. Triangle DEF is not isosceles as we have three different angles, so this triangle is scalene.

Answer:

D

Step-by-step explanation:

To determine the range we must solve this inequality;

● 1200000<1800000-250x<1300000

Substract 1800000 from both sides.

● 1200000-1800000<1800000-250x<1300000-1800000

● -600000< -250x < -500000

Divide both sides by 250

● -600000/250 < -250x/250 < -500000/250

● -2400 < -x < -2000

Multiply both sides by -1 and switch the signs

● 2000 < x < 2400

The correct option is D. 2000<= x <= 2400

Given, the value of an airplane depends on the flight hours,

[tex]V= 1800000-250x[/tex], here x is the flight hours.

We have to calculate the range of x After one year.

Since, [tex]V= 1800000-250x[/tex]

[tex]250x=1800000-V\\\\x=\dfrac{1800000-V}{250}[/tex]

Since the value of the plane is between $1,200,000 and $1,300,000. So,

[tex]x=\dfrac{1800000-1200000}{250}[/tex]

[tex]x=\dfrac{600000}{250}[/tex]

[tex]x=2400\\[/tex]

When V is 1300000 then x will be,

[tex]x=\dfrac{1800000-1300000}{250} \\[/tex]

[tex]x=\dfrac{500000}{250}[/tex]

[tex]x=2000[/tex]

Hence the range of x will be from 2000 to 2400.

The correct option is D. 2000<= x <= 2400.

For more details on range follow the link:

https://brainly.com/question/10185991

Answer:

  A. D=sqrt( (x2-x1)^2+(y2-y1)^2 )

Step-by-step explanation:

The distance between two points is the root of the sum of the squares of the differences in their corresponding coordinates. The equation of choice A is the usual formulation.

__

Comment on answer choices

Because the square of a number is the same as the square of its opposite, the formula in choice D is also correct.

Answer:

The answer is D)90

Hope I helped

Answer:

x=0 and x=2

Step-by-step explanation:

We need to check at each  point where the function changes definition

At x= -2

On the left side  -4   on the right side = -( -2)^2 = -4  continuous

At  x=0

The point is not defined since neither side has an equals sign

discontinuous

x =2

on the left side 2^2 =4  on the right side 2

It is discontinuous

Answer:

x = 0

x = 2

Step-by-step explanation:

Edge 2020

~theLocoCoco

Answer:

16% of 242 = 38.72

Step-by-step explanation:

16% = 16/100 = 0.16

242 * 0.16 = 38.72

Answer:

38.72

Step-by-step explanation:

242 * .16 = 38.72

Answer:

3

Step-by-step explanation:

a is 4 and 3 is x so 4+3=7

Answer: a=2 {x=3} r=1.         2(3)+ 1= 7

Step-by-step explanation:

Answer:

The first pyramid:

      63x

  39x  24x  

23x  16x  8x

The second pyramid:

     162x

 82x  80x  

4x  78x  2x

The third pyramid:

     12a+2b

9a+b   3a+b  

9a     b     3a

The fourth pyramid:

      -19a

  -5a   -14a  

3a   -8a  -6a

Step-by-step explanation:

All that an alegbra pyramid is is adding the two terms below it.

So you can see how I added the terms that lied below each number, such as in number 1:  I added 23x and 16x to get me 39x, and I added 16x and 8x to get me 24.

Hope this helped!

Answer:

2 13/15 miles

Step-by-step explanation:

Hey there!

Well first we need to find the distance between Lancaster and Hillsdale and Lancaster to Silvergrove.

9 + 7 13/15

= 16 13/15

LS is just 14 miles.

Now we can do,

16 13/15 - 14

= 2 13/15 miles

Hope this helps :)

Answer:

9

Step-by-step explanation:

First, find x. Since x is the average of the three number, add the three up and then divided by three. Thus:

[tex]x=\frac{13+-16+6}{3}=3/3=1[/tex]

y is the cube root of 8. Thus:

[tex]y=\sqrt[3]{8}=2[/tex]

So:

[tex]x^2+y^3\\=(1)^2+(2)^3\\=1+8=9[/tex]

Answer:

ljih

Step-by-step explanation:

Answer:

[tex]71,100[/tex]

Step-by-step explanation:

If you are trying to find a number that is written in word form, we can just use place values to find what goes where.

A number is broken down into this:

Ten thousands, thousands, hundreds, tens, ones.

If they have 7 ten thousands, the first digit will be a 7.

If they have 1 thousand, the second digit will be a 1.

If they have 1 hundred, the third digit will be a 1.

Since nothing is stated about tens, we assume it's value is 0.

And since there are no ones, it's value is 0.

So:

71,100.

Hope this helped!

Answer:

See below.

Step-by-step explanation:

Using the right triangle altitude theorem, the correct proportions are:

[tex] \dfrac{AB}{AC} = \dfrac{AC}{AD} [/tex]

[tex] \dfrac{AB}{x} = \dfrac{x}{AD} [/tex]

[tex] \dfrac{25}{x} = \dfrac{x}{16} [/tex]

[tex] x^2 = 25 \times 16 [/tex]

[tex] x = 20 [/tex]

AC = 20 cm

[tex] \dfrac{AB}{CB} = \dfrac{CB}{DB} [/tex]

[tex] \dfrac{AB}{y} = \dfrac{y}{DB} [/tex]

[tex] \dfrac{25}{y} = \dfrac{y}{9} [/tex]

[tex]y^2 = 25 \times 9[/tex]

[tex]y = 15[/tex]

CB = 15 cm

Answer:

Speed of plane in still air is 270 mph

Wind speed is 30 mph

Step-by-step explanation:

Check the picture.

The speed of the plane in still air is 270 mph and the speed of the wind will be 30 mph.

The distance traveled by an object is the product of the speed of an object and the time taken.

Distance = speed x time

An airplane travels 1200 miles in 4 hours with the wind. The same trip takes 5 hours against the wind.

Let the speed of the plane be x

The speed of wind be y

Distance covered with the wind = (x + y)t

                  1200   =  (x + y)4

                   (x + y) = 1200/4

                     (x + y)= 300       .....(a)

Distance covered against the wind = (x - y)t

                                              1200   =  (x - y)5

                                               (x - y) = 1200/5

                                                 (x - y) = 240         .......(b)

By solving both the equation

(x + y)= 300    

(x - y) = 240    

Therefore the values will be x= 270mph and  y = 30 mph

Learn more about the distance formula:

https://brainly.com/question/15172156

Answer:

the answer is a=b

Step-by-step explanation: