A famous instance of variation is Newton’s Law of Gravity. It states that the magnitude of the Force, F, of gravitational attraction between two masses, m1 and m2, varies directly with the product of the masses and inversely with the square of the distance, r, between them. Write a variation equation relating F, m1, m2, and r.

Answer:

See below.

Step-by-step explanation:

Compare our equation with one  standard form of a circle:

x^2 + y^2 = r^2    where r = the radius.

So x^2 + y^2 = 9 is the equation of a circle with it's center at the origin and it's radius is 3 units.

x^2 + y^2 = 0 is not a circle because r = 0  ( a radius of 0). A circle of radius 0 is really a point!!

The value of the radius of a circle  must be positive  so it cannot have a radius of -3.

Answer

[tex]x ^{2} + {y}^{2} = r^{2} [/tex]

since all the terms are squared so there can be a negative number

but in number line

...... -4,-3,-2,-1,0,1,2,3.......

as we know negative sign indicates only the direction so -3 means in which coordinates will it lie.

.

.

.

[tex] {x}^{2} + {y}^{2} = 9[/tex]

it means the origin is (0,0) and radius 3

Answer:

see below

Step-by-step explanation:

12.5x − 10.2 = 3(2.5x + 4.2) - 6  

Use the distributive property to distribute the 3

12.5x − 10.2 = 7.5x + 12.6 − 6  

Combine like terms

12.5x − 10.2 = 7.5x + 6.6  

Add 10.2 to each side of the equation by using the addition property of equality

12.5x = 7.5x + 16.8

Subtraction 7.5x from each side of the equation by using the subtraction property of equality

5x = 16.8  

Divide by 5 on each side by using the division property of equality

x = 3.36

Answer:

Step 1:  

✔ distributive property

Step 2:  

✔ combining like terms

Step 3:  

✔ addition property of equality

Step 4:  

✔ subtraction property of equality

Step 5:  

✔ division property of equality

Step-by-step explanation:

Just did the assignment.

Answer:

17.167 rounded

Step-by-step explanation:

17+(1/6)

17+0,166

17.167

well, firstly convert the mixed fraction to improper fraction, and then simply divide the numerator by the denominator and round as needed.

[tex]\bf \stackrel{mixed}{17\frac{1}{6}}\implies \cfrac{17\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{103}{6}}~\hfill \stackrel{\textit{to a decimal}~\hfill }{103\div 6 = 17.166\overline{6}}\implies \stackrel{\textit{rounded up}}{17.167}[/tex]

The volume of the cone is one third of the volume of the cylinder when they have the same radius and height.

The volume of the sphere is two thirds the volume of the cylinder when the sphere and the cylinder have the same radius and the height of the cylinder is twice its radius.

If a cone has the same radius (r) and height (h) as a cylinder, then the volume of the cone is one third the volume of the cylinder.

This can be determined using the formula for the volume of a cone, which is V = (1/3)πr²h, compared to the volume of a cylinder, which is V = πr²h. Since we have the same 'r' and 'h' for both, the cone's volume will be one third of the cylinder's.

Similarly, if a cylinder and a sphere have the same radius and the cylinder’s height is twice its radius, we can say h = 2r. Thus, the volume of the sphere is calculated to be V = (4/3)πr³.

On the other hand, the cylinder's volume with h=2r would be V = πr²(2r) = 2πr³. The sphere's volume is two thirds of the cylinder's volume, because (4/3)πr³ is two thirds of 2πr³.

Answer:

I think it would be 11:1.

Step-by-step explanation:

360,000 / 30,000 = 12

11/12 of the yearly budget was used on other costs

1/12 of the yearly budget was used for leasing office

space.

Answer:

Step-by-step explanation:

Okay so I may be wrong BUT since it's asking for the other costs, I'm assuming we're subtracting the $30,000 from the $360,000 first. Therefore the original ratio would be 30,000: 330,000 which is simplified to 1:11 ($ on office space: $ on other costs)

Answer:

Mary = 24

Chau = 15

David = 48

Step-by-step explanation:

The formula is

Mary + Chau + David = 87

And we know that

Chau = Mary - 9

David = Mary * 2

So when we fill this in

Mary + Mary - 9 + Mary * 2 = 87

4Mary - 9 = 87

4Mary = 96

Mary = 24

Chau = Mary - 9 = 15

David = Mary * 2 = 48

Final answer:

The problem is solved using basic algebra, yielding Chau has $15, Mary has $24, and David has $48, all adding up to the total amount of $87.

Explanation:

The question involves a three-person word problem focusing on algebraic relationships and equation solving. Mary, Chau, and David have a total of $87 in their wallets. Mary has $9 more than Chau, and David has twice what Mary has. To find out how much each person has, we'll let 'c' represent the amount that Chau has.

Accordingly, Mary has c + $9, and David has 2(c + $9). Together, they have a total of c + (c + $9) + 2(c + $9) = $87. Simplifying this, we get 4c + $27 = $87. Subtracting $27 from both sides gives us 4c = $60. Dividing both sides by 4, we find that Chau has $15.

Now, since Mary has $9 more than Chau, Mary has $24 ($15 + $9). David, having twice what Mary has, possesses $48 (2 x $24). These amounts add up to the total of $87.

Final answer:

38% of eight hundred registered voters said yes, so 62% said no. By calculating 62% of 800, we find that 496 voters said no.

Explanation:

If 38% of eight hundred registered voters said yes to a measure, this means 62% said no because the total percentage must add up to 100%. To find out how many said no, we calculate 62% of 800. Here is the step-by-step calculation:

First, convert the percentage to a decimal by dividing it by 100: 62% / 100 = 0.62.

Next, multiply this decimal by the total number of voters to find the number who said no: 800 * 0.62 = 496.

Therefore, 496 voters said no to the measure.

ANSWER

[tex]( 8 ,7 )[/tex]

EXPLANATION

Use the midpoint formula to find the center of this circle.

The midpoint formula is

[tex]( \frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]

The reason is that, the midpoint of the diameter RS gives the center of the circle.

Point R is located at (11, 10) and point S is located at (5, 4).

We plug in the values to get:

[tex]( \frac{11+5}{2} ,\frac{4+10}{2} )[/tex]

[tex]( \frac{16}{2} ,\frac{14}{2} )[/tex]

[tex]( 8 ,7 )[/tex]

Answer:

(8,7)

Step-by-step explanation:

I got it correct on founders edtell

The Cube Root Of -343 is ( -7)

Answer:

Cube root of -343 is -7

Step-by-step explanation:

If we square a negative value it becomes positive as ² is an even number

eg: -7² = -7 × -7

= +49

But if we cube it is the value becomes negative as ³ is an odd number

eg: -7³ = -7 × -7 × -7

= -343

Hope it helps u ...

Answer:

A=$538.82

Step-by-step explanation:

We're going to use the compounded interest formula:

A=P(1+r/n)^n*t

Where,

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per unit t

t = t is the amount of time at which you're checking how much it's worth (yrs)

Using this information, we can use:

A=500(1+0.025/4)^3*4

A=500(1+0.00625)^12

A=500(1.00625)^12

A=500(1.07763259886)

A=538.82

A=$538.82....

f(12)= square root of(12-3)

f(12)=square root of 9

f(12)=3

Answer:

3

Step-by-step explanation:

[tex]f(12) = \sqrt{12-3}=\sqrt{9} = 3[/tex]

Answer:

Step-by-step explanation:

B and c

The correct statement is that set A is a subset of set B, as they contain exactly the same elements. The statements about set B containing the number 4 and set A being infinite are false, while the empty set is a subset of every set, including B.

The correct statement regarding the sets A = {1, 2, 3} and B = {3, 2, 1} is A ⊆ B. This is because every element in set A is also in set B, regardless of the order the elements are listed. Sets are collections of distinct objects and their definition does not depend on the order of the elements. Therefore, A and B have exactly the same members, making them equal sets, and conversely, every set is a subset of itself. This can also be seen as both sets having the same cardinality, which is the number of members in a set, and for both A and B, this is 3.

As for the other statements, the number 4 is not an element of set B (4 ∈ B), the set A is not infinite since it has a finite cardinality of 3 (A is not an infinite set), and the empty set is actually a subset of every set, including B ⊂ \⊆cannot be true.

Answer:

b: 44%

Step-by-step explanation:

From grades 9-10 there are 55 students who like country music.

While there are 125 grades 9-10 students in total.

This gives us a percentage of (55/125) *100% = 44%

Answer:

b.44%

Step-by-step explanation:

44% of the students in grades 9–10 like country music.

Round to the nearest whole percent.

(55/125)

100% = 44%

To find the minimum of a divided by b, round a and b and then divide.

To find the minimum of a divided by b, we need to divide the rounded values of a and b. First, round a to the nearest 10, which is 310. Next, round b to 1 decimal place, which is 66.1. Now divide 310 by 66.1 to get the minimum value. The result, rounded to 2 decimal places, is 4.69.

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Answer:

8x - 5y = - 30

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 8x - 5y = 2 into this form

Subtract 8x from both sides

- 5y = - 8x + 2 ( divide all terms by - 5 )

y = [tex]\frac{8}{5}[/tex] x - [tex]\frac{2}{5}[/tex] ← in slope- intercept form

with slope m = [tex]\frac{8}{5}[/tex]

• Parallel lines have equal slopes, hence

y = [tex]\frac{8}{5}[/tex] x + c ← is the partial equation of the parallel line

To find c substitute (- 5, - 2) into the partial equation

- 2 = - 8 + c ⇒ c = - 2 + 8 = 6

y = [tex]\frac{8}{5}[/tex] x + 6 ← in slope- intercept form

Multiply through by 5

5y = 8x + 30 ( subtract 5y from both sides )

0 = 8x - 5y + 30 ( subtract 30 from both sides )

8x - 5y = - 30 ← in standard form

Answer:

c)

[tex]f(x)=\frac{1}{x(x+4)}[/tex]

Step-by-step explanation:

Hi there!

This is a Rational Function. The process of graphing it takes a lot more hard work than graphing other functions like linear, quadratic, modulus, and so on.

Here a list on how to proceed

First

1) Find the point of intersections by calculating the zeros of the function on the Numerator. In this case, we just have a 1 on top, so our graph won't intercept x-axis.

2) Calculate the vertical asymptotes by calculating the zeros of the function in the denominator, x²+4x=0 S=(0,-4) on green on the graph below.

3) Construct the table of values for x, and y

4) Trace the graph

By analyzing the asymptotes on the graph, we conclude that the correct option is C.

To do it, we need to see at which x-values we have asymptotes. These are the values of x where the denominator becomes equal to zero.

Here we can see that we have asymptotes at:

x = 0 and x = -4

Then the denominator must be a polynomial with roots at x = 0 and x = -4, this is written as:

(x - 0)*(x - (-4)) = x*(x + 4)

So the rational function is something like:

[tex]f(x) = \frac{1}{x*(x + 4)}[/tex]

So the correct option is C.

If you want to learn more about rational functions, you can read:

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Answer:

Step-by-step explanation:

The correct answer would be -18

To solve this, you would substitute x with the x value, which in this case is -2

That would make it so f(x)= 9(-2)

9*-2=-18

Therefore f(x)=-18

Note that f(x) is another way to write y, therefore...

y = 9x

To solve for this plug -2 in for x in this equation like so...

y = 9 * -2

When a positive number is being multiplied with a negative number the answer will be negative.

y = -18

C. is the answer (assuming that you meant to write -18 instead of 1 18)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

b. (m^2 + 6)(m^2 - 6)

Step-by-step explanation:

m^4 - 36

m^2 ^2 -36

Replace m^2 with x

x^2 -36

This is the difference of squares

(x-6) (x+6)

Replace x with m^2

(m^2 -6) (m^2+6)

Answer:

Step-by-step explanation:

2y + 4 = 0               subtract 4 from both sides

2y = -4       divide both sides by 2

y = -2

The slope-intercept form of an equation of a line:

y = mx + b

m - slope

b - y-intercept → (0, b)

In the equation

y = -2

slope: m = 0

y-intercept: b = -2 → (0, -2)

y = -2 - it's a horizontal line

Answer:

7(a + 2b)(a² - 2ab + 4b²)

Step-by-step explanation:

Given

7a³ + 56b³ ← factor out 7 from each term

= 7(a³ + 8b³) ← sum of cubes which factors in general as

a³ + b³ = (a + b)(a² - ab + b²)

8b³ = (2b)³ ⇒ b = 2b

a³ + 8b³ = (a + 2b)(a² - 2ab + (2b)²) = (a + 2b)(a² - 2ab + 4b²)

Hence

7a³ + 56b³ = 7(a + 2b)(a² - 2ab + 4b²) ← in factored form

Answer:

See below in bold.

Step-by-step explanation:

A.  On one roll the possible ways to get a sum of 5 is (2,3, ) and (4, 1).

There are 36 possible outcomes from the one roll of the 2 dice.

So the probability of getting  a sum of 5 on one roll =  2/36 = 1/18.

So the probability of 5 on 4 rolls = (1/18)^4

= 1/104976.

B.  

The probability of the first 3 rolls being a 5 and the last one being not 5

= (1/18)^3 * (17/18)

= 17/104976

There are 4 ways to  pick 3 out of 4 so the required probability

=  4 * 17/104976

= 68/104976.

Final answer:

The detailed answer explains the probability of rolling specific sums with two fair dice in four rolls, covering events A and B.

Explanation:

The Probability of Rolling Sums with Two Fair Dice

For event A, the probability of getting a sum of 5 on each of the four rolls is (4/36)⁴.

For event B, the probability of getting a sum of 5 exactly three times in the four rolls is 4*(4/36)³*(32/36).

Answer:

t=x+yb

Step-by-step explanation:

I have answered ur question

Answer: Our required equation be t = x+yb.

Step-by-step explanation:

Let the number of notebooks be 'x'

Let cost of each notebook be $1

Let cost of pens be $b.

Let the number of pens be y.

Let the total amount be 't'.

So, According to question, equation becomes

[tex]t=x\times 1+y\times b\\\\t=x+yb[/tex]

Hence, our required equation be t = x+yb.

The medium pizza with a 14-inch diameter has approximately 41 square inches more area than the small pizza with a 12-inch diameter, using the formula for the area of a circle, πr², where r is the radius (half of the diameter).

The subject of this question is area comparison between two circles, which is a topic in Mathematics. The areas of the two pizzas (which we can represent as circles) can be found using the formula for the area of a circle, which is πr^2, where r is the radius (half of the diameter).

For the medium pizza, the diameter is 14 inches, so the radius is 7 inches. The area is thus π*(7)^2 = 153.94 square inches. For the small pizza, the diameter is 12 inches, so the radius is 6 inches. The area is thus π*(6)^2 = 113.10 square inches.

So, the medium pizza has 153.94 - 113.10 = 40.84 square inches more area than the small pizza. Rounded to the nearest square inch, the medium pizza has approximately 41 square inches more area than the small pizza.

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Answer:

380 cubic feet of air

Step-by-step explanation:

Volume = height * width * length.

So

Volume = 10 * 2 * 19 = 380 cubic feet of air

Answer:

[tex]380\text{ ft}^3[/tex]

Step-by-step explanation:

We have been that a classroom is 19 ft long 2 ft wide and 10 feet high. We are asked to find the number of cubic feet of air in the room​.

To find the number of cubic feet of air in the room​, we will find the volume of the given room by multiplying all of its side as:

[tex]\text{Volume of the room}=\text{19 ft}\times \text{2 ft}\times\text{10 ft}[/tex]

[tex]\text{Volume of the room}=380\text{ ft}^3[/tex]

Therefore, there are 380 cubic feet of air in the room.  

If polygon ABCD with vertices A (1, 2), B (1,4), C(2,6), and D (5, 4) is dilated by a factor 3, the coordinates of the dilated polygon are A' (3, 6), B' (3, 12), C' (6, 18), and D' (15, 12).

When a polygon is dilated by a scale factor, all the coordinates of its vertices are multiplied by that scale factor. In this case, the scale factor is 3. Thus, we should multiply the x and y coordinates of each vertex by 3.

Let's calculate:

So, the coordinates of the dilated polygon ABCD are A' (3, 6), B' (3, 12), C' (6, 18), and D' (15, 12).

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Answer:

It is a Right Triangle.

Step-by-step explanation:

30^2 = 900

24^2 =  576

18^2 = 324

576 + 324 = 900

This satisfies the Pythagoras theorem so it is a Right Triangle.

Answer:

Step-by-step explanation:

For a ≤ b ≤ c:

if a² + b² = c², then a triangle is a right triangle

if a² + b² < c², then a triangle is an obtuse triangle

if a² + b² > c², then a triangle is an acute triangle.

We have a = 18, b = 24, c = 30. Substitute:

18² + 24² = 324 + 576 = 900

30² = 900

18² + 24² = 30² → a² + b² = c²

Answer:

B. (3, 0), (0, -6)

Step-by-step explanation:

Plug 0 in for each variable one at a time, and you will get both intercepts.

Answer:it would be C.2

Step-by-step explanation:

Final answer:

The data set has A) 3 modes, which are 4, 11, and 134.

Explanation:

The data set provided is: 4, 4, 4, 6, 6, 11, 11, 11, 134, 134. The mode is the number that appears most frequently in a set of numbers. In this data set, the modes are 4, 11, and 134, so the data set has 3 modes.

Answer:

4

Step-by-step explanation:

-5x/6=-10/3

or..5x/6=10/3

or..X/2=2

so X=4

Answer:

x = 4

Step-by-step explanation:

note that - [tex]\frac{5}{6}[/tex] x = [tex]\frac{-5x}{6}[/tex], hence

[tex]\frac{-5x}{6}[/tex] = [tex]\frac{-10}{3}[/tex] ( cross- multiply )

- 15x = - 60 ( divide both sides by - 15 )

x = [tex]\frac{-60}{-15}[/tex] = 4, that is

x = 4