A spherical balloon is inflated so that its volume is increasing at the rate of 3 cubic feet per minute. How fast is the radius of the balloon increasing when the radius is 2 feet?

Answer:

See Below

Step-by-step explanation:

We are given 3 equations.

3x + 8

5x - 20

and

5x + 4y

First lets solve for x using the first two

3x + 8 = 5x -20

Move the variables to one side

3x + 8 = 5x -20

-3x        -3x

8 = 2x -20

+20     +20

28 =2x

28/2 =2x /2

14 = x

Now we have x = 14

Lets plug this into the second equation to solve for the angle

3(14) + 8

42 + 8 = 50

5(14) - 20

70 - 20 =50

Now, lets plug the x and the angle into the third equation to find y

5 (14) +4y = 50

70 + 4y = 50

-70           -70

4y = -20

4y/4 = -20/4

y = -5

So now we have:

x = 14

y = -5

and the angle = 50

Hope this helps!

The graph of the rational equation is solved and f ( x ) = 1/ ( x + 2 ) ( x - 5 )

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = 1/ ( x + 2 ) ( x - 5 )

The function will have increasingly large values as the denominator approaches zero. When x -2, the denominator is positive and the function tends to the upside. When x -2 x 5, the function is negative. When x 5, the function becomes positive once more.

Hence , the rational function is f ( x ) = 1/ ( x + 2 ) ( x - 5 )

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The complete question is attached below :

Which of the following rational functions is graphed below?

A. F(x) =(x-2)/(x+5)

B. F(x) =1/(x-2)(x + 5)

C. F(x) =1/(2x + 5)

D. F(x)= 1/(x+2)(x-5)

Answer:

1.875

Step-by-step explanation:

mark brainlist pls

not to sure about that try researching that

depends on ur teacher for me its really hard but the material wouldnt be too bad if you have a good teacher. it contains a lot of logistics and specific wording but memorization is key

Answer: 26/3 or 8 2/3

Step-by-step explanation:

In the addition or subtraction of fraction, first, you have to convert all of them into improper fraction if they are mixed; then, you need to find the LCD (Least Common Denominator).

Converting fraction:

5 3/4=23/4

2 11/12=35/12

Finding LCD:

4 and 12 is 12

Converting fraction into common denominator:

23/4=69/12

35/12=35/12

Solve:

 5 3/4 + 2 11/12

=69/12 + 35/12

=104/12

Answer:

it is x=7

x=-1

Step-by-step explanation:

i using the quadratic formula

Step-by-step explanation:

Hey there!!

The equation is;

\( {x}^{2} - 6x + 7 = 0\)

Now, Comparing it with ax^2 + bx + c = 0. we get;

a = 1, b= -6 and c = 7

Use quadratic formula.

\(x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} \)

Put all values.

\(x = \frac{ + 6 + - \sqrt{( { - 6)}^{2} - 4 \times 1 \times 7} }{2 \times 1} \)

Simplify them.

\(x = \frac{6 + - \sqrt{36 - 28} }{2} \)

\(x = \frac{ 6 + - \sqrt{8} }{2} \)

\(x = \frac{6 + - 2 \sqrt{2} }{2} \)

Taking positive (+).

\(x = \frac{6 + 2 \sqrt{2} }{2} \)

Simplifying them.

\(x = \frac{2(3 + \sqrt{2} )}{2} \)

\(x = 3 + \sqrt{2} \)

Now, Taking negative (-).

\(x = \frac{6 - 2 \sqrt{2} }{2} \)

Simplifying them.

\(x = \frac{2(3 - \sqrt{2} )}{2} \)

\(x = 3 - \sqrt{2} \)

Therefore the answer is;

\(x = 3 + \sqrt{2} \: and \: 3 - \sqrt{2} \)

Hope it helps...

The linear velocity expression of the given problem is: 8π/7 feet per second

Angular velocity is defined as the time rate at which an object rotates, or revolves, about an axis, or at which the angular displacement between two bodies changes.

We are given the angular velocity as:

ω = π/7

The formula that shows the relationship between angular velocity and linear velocity is:

v = ωr

Thus:

v = (π/7) * 8

v = 8π/7 feet per second

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Answer:

Step-by-step explanation:

$100x0.5x1=$5

A. The function to represent the balance in the account after t years is:

\(A = 1500(1 + (0.012 / 4))^{(4t)}\)

B. The balance in the account after 3 years will be $1566.66.

C. The balance in the account after 6 years will be $1639.98.

Compound interest is defined as interest paid on the original principal and the interest earned on the interest of the principal.

A = P(1+r/100)ⁿ

A. The function to represent the balance in the account after t years can be represented as:

\(A = 1500(1 + (0.012 / 4))^{(4t)}\)

where A is the balance in the account after t years, 1500 is the initial deposit, 0.012 is the annual interest rate as a decimal, 4 is the number of compounding periods per year, and (0.012 / 4) is the interest rate per compounding period.

B. To find the balance after 3 years:

A = 1500(1 + (0.012 / 4))⁴ˣ³ = 1500 (1 + (0.012 / 4))¹²

A = 1500 × 1.0444

A = 1566.66

So, the balance in the account after 3 years will be $1566.66.

C. To find the balance after 6 years:

A = 1500 (1 + (0.012 / 4))⁴ˣ⁶ = 1500 * (1 + (0.012 / 4))²⁴

A = 1500 × 1.0932

A = 1639.98

So, the balance in the account after 6 years will be $1639.98.

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The values of {m} that is greater than 4.6 represent the solution of the given inequality.

An inequality is used to compare two or more expressions or numbers.

For example -

2x > 4y + 3

x + y > 3

x - y < 6

The given inequality is -

5m - 7 > 16

Adding 7 on both sides, we get -

5m - 7 + 7 > 16 + 7

5m > 23

m > 23/5

m > 4.6

Therefore, the values of {m} that is greater than 4.6 represent the solution of the given inequality.

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The total amount that the person with base salary 42000; total sales 175000; commission 4% gets is $51000.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. In this case, the percentage of commission is given as 4%.

The commission will be:

= Percentage × Amount

= 4% × 175000

= 7000

Therefore, the total amount that the person gets will be:

= Salary + Commission

= 42000 + 7000

= $51000

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Using the properties of sets, (BU A)'n C = {h,q}

Null set or an empty set There isn't even one element in it. Finite Set: It only has a finite number of components. The element count of an infinite set is infinite. Two sets with the same members are said to be equal sets.

An object collection that is taken into account as a whole is referred to as a set. The elements or members of the set are the things that make it up. A set's components can be any type of object, but for our purposes, they are most frequently mathematical components like integers, functions, or other sets.

The list of all subsets of a,b,c,d is ϕ ,{a},{b},{c},{d},{a,b},{a,c},{a,d},{b,c},{b,d},{c,d},{a,b,c},{a,b,d},{a,c,d},{b,c,d},{a,b,c,d}

(B U A) = {f,g,r,x,y,z}

(BU A)'n C = {h,q}

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Answer:

5

Step-by-step explanation:

9) y=12x+6

I've attached a photo for #10

Apply the fraction rule:

\(\text{a}\times\dfrac{\text{b}}{\text{c}} =\dfrac{\text{a}\times\text{b}}{\text{c}}\)

Answer:

\(\longrightarrow\boxed{\bold{\frac{\text{fx}}{\text{g}}}}\)

Answer:

B

$63

Step-by-step explanation:

1 medium 2 topping pizza is $13, 1 large one-topping pizza is $12

We need to find the cost for 3 medium two-toppings and 2 large one-toppings.

Let's find the mediums first:

1 medium two-topping is $13

To find the total cost of 3 is:

$13 + $13 + $13 =

$26 + $13 =

$39

So, it costs $39 for 3 medium two-topping pizzas

Let's calculate the larges next:

1 large one-topping is $12

The total cost of 2 is:

$12 + $12 =

$24

So, it costs $24 for 2 large one-topping pizzas

We know what the separate prices are for the pizzas, now let's combine them:

$39 + $24 =

$63

So, it costs $63 for 3 medium two-topping and 2 large one-topping pizzas.

The theoretical probability is 0.04 (2162/54145)

Here, we want to find a theoretical probability

A five card hand means a selection of five cards from a total of 52

Before we go on to answer, we need to know the number of 10's in a standard deck of cards

In a deck of cards, there are 4 suites, with each suites having a single 10

So in total, there are 4 10's

Out of the 52 cards, we are selecting five cards

The number of ways we can do this can be calculated using combination

This will be;

Out of the 4 available 10's, we are selecting 2

The number of ways we can do this is;

Now, out of the remaining 48, we are selecting 3

The number of ways to do this will be

So the theoretical probability would be;

This is same as; 2162/54145

The only possible value of "a" that satisfies the given equations is a = 5.

The possible values of "a" that satisfy the given equations, let's solve the system of equations:

a + ab = 250 ---(1)

a - ab = -240 ---(2)

We can solve this system by using the method of substitution. Rearranging equation (2), we get:

a = ab - 240 ---(3)

Substituting equation (3) into equation (1), we have:

(ab - 240) + ab = 250

2ab - 240 = 250

2ab = 250 + 240

2ab = 490

ab = 490/2

ab = 245

Now we have the value of "ab."

We can substitute this back into equation (3) to solve for "a":

a = (245) - 240

a = 5

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Answer:

A2 + B2 = C2, so 4 squared + 19 squared = C2, 16 + 361 = 377. 377's square root is 19.4.

Step-by-step explanation:

The measure of the hypotenuse is 19.4 cm.

Given that, one of the legs of a right triangle measures 4 cm and the other leg measures 19 cm.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Let the measure of the hypotenuse be x.

Using Pythagoras theorem,

x² = 4² + 19²

⇒ x² = 16 + 361

⇒ x² = 377

⇒ x = √377

⇒ x = 19.4 cm

Therefore, the measure of the hypotenuse is 19.4 cm.

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We need to assume the sample was randomly selected because we are making inferences about parameters.

In mathematics, the parameter is a variable for which the range of possible values identifies a collection of distinct cases in a problem. Any equation expressed in terms of parameters is a parametric equation. The general equation of a straight line in slope-intercept form, y = mx+b, in which m and b are parameters, is an example of a parametric equation.

In statistics, the parameter in a function is a variable whose value is sought by means of evidence from samples. The resulting assigned value is the estimate or statistic.

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Answer:

(1) How many equilateral triangles are there? ___6__

(2) What is the measure of each of the three angles in the equilateral triangle? __60°_

(3) If we cut an equilateral triangle down the middle (green line), what special right triangle do you create? _30-60-90_

(4) What is the vocabulary word for the green line? _Perpendicular bisector_

(5) What is the length of the short side of one 30-60-90 triangle? __4_cm_

(6) What is the length of the hypotenuse of one 30-60-90 triangle? __8 cm

(7) Using the properties of 30-60-90 triangles, calculate the length of the long leg. _4√3_cm

(8) What is the height of the equilateral triangle?  _4√3_cm

(9) Apply the formula for the area of a triangle to find the area of one equilateral triangle. ½(8)(4√3) = 16√3 cm²

(10) Calculate the area of the complete hexagon by multiplying the area of one equilateral triangle by the number of triangles. _8(16√3) = 128√3 cm²_

Step-by-step explanation:

In geometry, a hexagon can be defined as a polygon with six sides. The two-dimensional shape has 6 sides, 6 vertices and 6 angles

In geometry, a hexagon can be defined as a polygon with six sides. The two-dimensional shape has 6 sides, 6 vertices and 6 angles

The answers of all the fill in the blanks are given below:

(1) How many equilateral triangles are there ___6__

(2) What is the measure of each of the three angles in the equilateral triangle __60°_

(3) If we cut an equilateral triangle down the middle (green line), what special right triangle do you create? _30-60-90_

(4) What is the vocabulary word for the green line? _Perpendicular bisector_

(5) What is the length of the short side of one 30-60-90 triangle? __4_cm_

(6) What is the length of the hypotenuse of one 30-60-90 triangle? __8 cm

(7) Using the properties of 30-60-90 triangles, calculate the length of the long leg. _4√3_cm

(8) What is the height of the equilateral triangle?  _4√3_cm

(9) Apply the formula for the area of a triangle to find the area of one equilateral triangle. ½(8)(4√3) = 16√3 cm²

(10) Calculate the area of the complete hexagon by multiplying the area of one equilateral triangle by the number of triangles. _8(16√3) = 128√3 cm²

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Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.

Answer:

8700kg

Step-by-step explanation:

b = mass of bricks

l = mass of lorry

b+l = total mass = 11600kg

b = 3l  ==>  l = b/3

substitute: b + b/3 = 11600

multiply every term by 3 to get rid of denominator: 3b + b = 34800

simplify and solve:  4b = 34800  ==>  b = 8700

check:  l = 8700/3 = 2900

2900 + 8700 = 11600?  YES

Answer:

160 pounds

Step-by-step explanation:

If she has 3 boxes and there's 40 more pounds than if she had one, that means each box is 20 pounds so multiply 20 by 8 and you get 160 pounds

Answer:

P(A or B) = P(A) + P(B) - P(A and B)

0.87 = 0.8 + P(B) - 0.23

0.87 = P(B) + 0.57

P(B) + 0.57 = 0.87

P(B) + 0.57-0.57 = 0.87-0.57

P(B) = 0.3

Answer: 0.3

The value of P(B)= 0.3

It is a branch of mathematics that deals with the occurrence of a random event.

Given:

P(A)=0.8, P(A OR B)=0.87, P(A AND B)=0.23,

Now, using

P(A or B) = P(A) + P(B) - P(A and B)

0.87 = 0.8 + P(B) - 0.23

0.87 = P(B) + 0.57

P(B) + 0.57 = 0.87

P(B) = 0.87-0.57

P(B) = 0.3

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Answer:

i = 1, (3/7)

Step-by-step explanation:

7|14i-10|+9 = 37,    

             -9    -9                  

------------------------    

7|14i - 10| = 28          

÷7               ÷7

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

|14i - 10| = 4

14i - 10 = 4

     +10   +10

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

14i = 14

÷14   ÷14

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

i = 1

|14i - 10| = -4

14i - 10 = -4

     +10    +10

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

14i = 6

÷14  ÷14

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

i = (3/7)

I hope this helps!

The total surface area of the solid shape made from the cube and cylinder is approximately 583.31 cm².

The side length of the cube is 8.7 cm, so the surface area of one face is A = 8.7²

= 75.69 cm²

Since there are six faces, the total surface area of the cube is 6 * 75.69 = 454.14 cm²

Since there are two circular bases, the total surface area of the bases is 2 * 22.91 = 45.82 cm².

In this case, the radius of the cylinder is 2.7 cm and the height is 4.9 cm, so the curved surface area is A_curved = 2 * π * 2.7 * 4.9 ≈ 83.35 cm².

Total surface area = surface area of the cube + surface area of the cylinder

Total surface area = 454.14 cm² + 45.82 cm² + 83.35 cm²

Total surface area ≈ 583.31 cm²

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Answer:

Communist countries use authoritarian governments because it requires the absolute obedience to authority figures. Communism is an extreme form of socialism because there is no private ownership or political freedom.

Step-by-step explanation:

Answer:

\((3b)^{8}\)

Step-by-step explanation:

N/A