Simplify the number 8 ^2/3

Check the picture below.

so notice,  in a cone the height and radius are always at a ratio of each other in a right-triangle, since the water level, in red, makes a similar triangle with the cone's volume, let's use proportions to get "x".

[tex]\bf \cfrac{21}{7}=\cfrac{x}{3}\implies 3=\cfrac{x}{3}\implies 9=x \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{volume of a cone}}{V=\cfrac{\pi r^2 h}{3}}~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=3\\ h=\stackrel{x}{9} \end{cases}\implies V=\cfrac{\pi (3)^2(9)}{3}\implies \stackrel{V=27\pi }{V\approx 84.823}[/tex]

The volume of water in a conical water reservoir can be calculated using the formula for the volume of a cone, substituting the values for the radius and height of the water.

In this problem, we are trying to calculate the volume of water in a water reservoir that is shaped as a right circular cone. We are told that this cone has a depth of 21ft and a radius of 7ft, while the water in the cone has a depth of x ft and a radius of 3ft.

In order to solve this problem, we first need to understand that the volume V of a cone is calculated using the formula, V = 1/3πr²h, where r is the radius and h is the height of the cone. This formula can be applied to determine the volume of water in the cone.

Substituting the given values into the formula, the volume of the water would be as follows: V = 1/3 * π * (3ft)² * x ft.

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Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

Yes.

Step-by-step explanation:

The vertex is 1,3. The vertex is in quad 1. The graph is shifted 1 to the right and up 3.

Answer:

  (37/360)π cm² ≈ 0.322886 cm²

Step-by-step explanation:

The area of a sector is given by the formula ...

  A = (1/2)r²θ . . . . . where r represents the radius and θ is the central angle is radians

Here, you have r = 1 cm, and θ = (37°·π/180°), so the area is ...

  A = (1/2)(1 cm)²·(37π/180) = 37π/360 cm²

  A ≈ 0.322886 cm²

since height to base ratio is tan73 so approx ratio is 3.27

The approximate height-to-base ratio is 3.27: 1

Given,

A 20-foot ladder is set up against a building so that the ladder makes an angle of 73° with the ground.

The height, h, is the vertical distance from the top of the ladder to the base of the building.

The base, b, is the horizontal distance from the bottom of the ladder to the base of the building.

We need to find what is the approximate height-to-base ratio.

Sin Ф = Perpendicular / Hypotenuse

Cos Ф = Base / Hypotenuse

Tan Ф = Perpendicular / Base

Find the height in the figure.

Sin 73 = h / 20 ft

Sin 73 = 0.9563

So,

0.9563 = h / 20 ft

h = 0.9563 x 20 ft

h = 19.126 ft

Find the base in the figure.

Cos 73 = b / 20 ft

Cos 73 = 0.2924

0.2924 = b / 20 ft

b = 0.2924 x 20 ft

b = 5.848 ft

Find the approximate height-to-base ratio.

= h : b

= 19.126 : 5.848

= 3.27 : 1

Thus the approximate height-to-base ratio is 3.27: 1

Learn more about finding the height of a ladder here:

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Answers:

1.) Each person gets half a bar. (1/2) (4 is half of 8. As such, breaking each bar in half and distributing it that way would make it so that everyone gets the same amount.)

Answer: 1/2

2.) Each person gets 2 packages.

Answer: 2/1 or 2

3.) Each rabbit gets 10/17 ths of a carrot.

10/17 cannot be simplified any further than it already is, as 17 is a prime number. This means that every rabbit simply gets 10/17ths of a carrot.

Answer:

100°

Step-by-step explanation:

The sum of angles in a quadrilateral is 360°, so the missing angle has measure ...

360° -44° -89° -127° = 100°

Answer:

100°

Step-by-step explanation:

Total angle measure of a quadrilateral is 360°

Add all the angles first.

44° + 89° + 127° = 260°

Quadrilateral has only four angle measures. And you need to find the fourth angle so,

360° - 260° = 100°

The fourth angle is measured 100°

I would say an equation would look roughly as such:

y = - | x - 800 | + 50

If you want me to explain how I got to this conclusion just comment on my answer, If you were only looking for the answer then we are good. Brainliest is encouraged but not required :)

The absolute value equation representing the word count for the scholarship essay is |w - 800| <= 50, ensuring that the essay will be between 750 and 850 words long.

To represent the word count requirements for the scholarship essay using an absolute value equation, you can consider the midpoint of the word limit, which is the average between the minimum and maximum word count. This midpoint is at 800 words since (750 + 850) / 2 equals 800. Now, you can state the absolute difference from this midpoint that is allowed on either side of 800, which is 50 words, since 850 - 800 equals 50 and 800 - 750 equals 50. Therefore, the absolute value equation that represents the number of words (w) the scholarship essay should be is |w - 800| <= 50. This equation tells us that the word count can be 50 words fewer or 50 words greater than 800, perfectly capturing the range of 750 to 850 words.

Answer:

C, Plus or minus 3

Step-by-step explanation:

to solve 3x² - 27 = 0, we want to get the x by itself, so lets add 27 to both sides.

3x² = 27 < divide both sides by 3 to get x alone

3x²/2 =x²

27/3 = 9

x² = 9 < we can use the square-root property and square both sides of the equation to get x alone. we use the ± because there are 2 possible solutions to a square rooted number

√x² = x

√9 = 3

x = ±3

looking at our answer choices, the correct answer is C

Answer:

C. Plus or minus 3

Step-by-step explanation:

Take a GCF of 3 out of both terms in the binomial. You'll get 3*(x^2-9)=0. Then use FOIL to get the binomials (x+3) and (x-3). You're answers will  be -3 and 3

Answer:

The 3rd choice: 2/3 tank - 1/6 tank = 1/2 tank

Step-by-step explanation:

I assume those numbers are fractions.

The gas tank of Wendy’s car was 2/3 full. She used 1/6 of a tank of gas when driving to and from work. Which equation shows how full the gas tank is now?

We subtract 1/6 from 2/3. We need to use the common denominator 6.

2/3 - 1/6 = 4/6 - 1/6 = 3/6

Now we reduce 3/6.

2/3 - 1/6 = 1/2

Answer: 2/3 tank - 1/6 tank = 1/2 tank

Hey there! :)

-7x - 4y = -8

To find the slope, we must turn this equation into slope-intercept form.

Slope-intercept form is : y=mx+b ; where m=slope, b=y-intercept

To get here, we must isolate y by adding 7x to both sides of our original equation.

-7x + 7x - 4y = 7x - 8

Simplify!

-4y = 7x - 8

Then, divide both sides by -4.

-4y ÷ -4y = (7x - 8) ÷ -4y

Simplify!

y = -7/4x + 2

Congrats, we got y isolated! Now, review the slope-intercept form equation to figure out what our slope & y-intercept are.

After reviewing our slope intercept form equation, we can come to the conclusion that -7/4 is our slope because it's in the "m" value slot, and 2 is our y-intercept because it's in the "b" spot.

So, our answer is :

Slope = -7/4

Y-intercept = 2

Hope this helped! :)

Answer:

1

Step-by-step explanation:

Answer:

+/- 6

A squared number can be from both a positive and negative number to make a positive square.

Answer: a cube

(you could have looked this up on google that's what I did)

They are making me write an answer with at least 20 characters sorry

Answer:

cube

lol true about the 20 characters

Answer:

5. mCD is 27.8°  |  7. mAFC 52.3° |

Step-by-step explanation:

Answer:

S = 2((12(8) + 8(2) + 12(2))

= 2(96 + 16 + 24)

= 2(136)

= 272 square feet

Answer: Third option

[tex]u = -\frac{5\sqrt{29}}{29}i -\frac{2\sqrt{29}}{29}j[/tex]

Step-by-step explanation:

A unit vector [tex]u[/tex] is a vector that has magnitude 1.

To find a unit vector in the direction of the vector v we must first calculate the magnitude of v and then divide the vector v by its magnitude

The vector v is:

v = -5i - 2j

The magnitude of the vector is:

[tex]| v | =\sqrt{(-5)^2 +(-2)^2}\\\\|v|= \sqrt{29}[/tex]

Now we divide the vector v by its magnitude

[tex]u = \frac{1}{\sqrt{29}}v[/tex]

[tex]u = -\frac{5}{\sqrt{29}}i -\frac{2}{\sqrt{29}}j[/tex]

Simplifying we have to

[tex]u = -\frac{5\sqrt{29}}{29}i -\frac{2\sqrt{29}}{29}j[/tex]

Final answer:

To find the unit vector u in the direction of v = -5i - 2j, compute the magnitude of v and then divide each component of v by this magnitude. The result is u = (-5/√(29))i + (-2/√(29))j.

Explanation:

The question involves finding a unit vector in the direction of a given vector v = -5i - 2j. A unit vector is a vector with a magnitude of 1 that points in the direction of a given vector. To find the unit vector u in the direction of v, we first calculate the magnitude of v and then divide each component of v by its magnitude.

Upon calculating, the magnitude of v is sqrt(29), so the unit vector is u = (-5/√(29))i + (-2/√(29))j.

Answer: i think the answer is B for number 1

Step-by-step explanation:

Answer:

1.

The slope is : [tex]\frac{8.4-4.2}{2-1}[/tex] = 4.2

[tex]\frac{12.6-8.4}{3-2}[/tex] = 4.2

We can see that the distance is same each time.

Hence, the equation that represents the relationship between the distance traveled and the elapsed time is [tex]f=4.2p[/tex]

2.

Let the amount of money needed be = z

Total bags purchased = n

Cost of 1 bag = $1.58

So, the required equation is :

[tex]z=1.58n[/tex]

3.

When rainfall increases, the water level in the lake goes up. Rainfall is the independent variable in this situation. This is True.

Here the water level is dependent on the amount of rainfall so water level is dependent and rainfall is independent. Rainfall is not dependent on the water level in a lake.

4.

Let y represents the distance the plane has traveled.

Let z represents the time it has spent traveling.

distance = speed x time

So, [tex]y=600z[/tex]

5.

Diana can earn money for the tickets she sells. Here tickets are independent and money earned is dependent on the number of tickets sold. The more tickets sold, the more money Diana can earn.

So, the answer is : C: The number of tickets sold is the independent variable because it affects the amount of money earned.

For this case we must build a quotient, such that when multiplied by the divisor and then change the sign, go eliminating the terms of the dividend until you reach the remainder.

It must be fulfilled that:

Dividend = Divider * Quotient + Remainder

ANswer:

Option D

See attached image

Answer:

x = 8

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

x² + 6² = 10²

x² + 36 = 100 ( subtract 36 from both sides )

x² = 64 ( take the square root of both sides )

x = [tex]\sqrt{64}[/tex] = 8

The answer is in the pic below and good luck,!

Answer:

504

Step-by-step explanation:

144X3.5=504

There are [tex]\( \boxed{504} \)[/tex] square inches in 3.5 square feet.

To convert square feet to square inches, we can use the given conversion factor that there are 144 square inches in 1 square foot. We need to determine how many square inches are in 3.5 square feet.

Here is the step-by-step calculation:

1. Start with the given conversion factor:

 [tex]\[ 1 \, \text{square foot} = 144 \, \text{square inches} \][/tex]

2. Multiply the number of square feet by the conversion factor to get the number of square inches:

 [tex]\[ 3.5 \, \text{square feet} \times 144 \, \text{square inches per square foot} \][/tex]

3. Perform the multiplication:

 [tex]\[ 3.5 \times 144 = 504 \][/tex]

Answer:

per 100 pencils he looses $75

Step-by-step explanation:

If he sells 100 pencils at $1.75 he will make $175 which is less than the $250 he spent for the 100 pencils. So per 100 pencils he looses $75

Answer:

x = 4 ± [tex]\sqrt{13}[/tex]

Step-by-step explanation:

Given

x² - 8x + 3 = 0 ( subtract 3 from both sides )

x² - 8x = - 3

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 4)x + 16 = - 3 + 16

(x - 4)² = 13 ( take the square root of both sides )

x - 4 = ± [tex]\sqrt{13}[/tex] ( add 4 to both sides )

x = 4 ± [tex]\sqrt{13}[/tex]

The value of equation  x² - 8x + 3 = 0 using the completing the square method is found as  x = 4 ± √13.

To solve the equation x² - 8x + 3 = 0 using the completing the square method, follow these steps:

To solve the equation x² - 8x + 3 = 0 using the completing the square method, follow these steps:

Answer:

The monthly cost would be equivalent to [tex]=0.37x+5[/tex]

I think the answer is n-20- first choice.

ANSWER

n-20

EXPLANATION

The terms of the sequence are:

-19,-18,-17,-16,-15,...

The first term of the sequence is

a=-19 and the common difference is d=-18--19=1

The rule is given by:

f(n)=a+d(n-1)

f(n)=-19+1(n-1)

f(n)=-19+n-1

f(n)=n-20.

Therefore the rule for the given sequence is n-20.

The first option is correct.

Answer:

d. Set A and Set B

Step-by-step explanation:

We have been given three sets:

Set A: (5, 2), (4, 3), (3, 4), (2, 5)

Set B: (-1, -6), (0, 2), (1, 2), (3, 6)

Set C: (2, 1), (4, 2), (2, 3), (8, 4)

Now we need to state about which of the following sets of ordered pairs represent a function.

We know that a function can't have repeated values in domain that is x-value can't repeat.

we see that set C has repeated x-value "2".

Then set C is not a function.

Hence correct choice is:

d. Set A and Set B

Answer:

A and B represent functions.

Step-by-step explanation:

In a function, any input (x-) value may have only one associated y value.  If the same input appears more than once, we know immediately that the data do not represent a function.

A:  The inputs are unique:  {5, 4, 3, 2} so this is a function.

B:   The inputs are unique:  {-1, 0, 1, 3}, so this is a function.

C:   2 is used twice as input, so this is not a function.

Answer:

3 points, I believe.  

Step-by-step explanation:

ANSWER

[tex] \sqrt{5} [/tex]

EXPLANATION

The given points are (1,0) and (0,2).

We use the distance formula:

[tex]d = \sqrt{(x_2-x_1)^2 +(y_2-y_1)^2} [/tex]

We substitute the given points into the formula to get:

[tex]d = \sqrt{(0-1)^2 +(2-0)^2} [/tex]

We simplify to get:

[tex]d = \sqrt{1+4} [/tex]

[tex]d = \sqrt{5} [/tex]

Therefore the distance between the two points is √5 units.

g(x) =f(x) +3

given f(x) =3x

i.e. g(x) =3x+3

For F(x) to be same as g(x)

3 must be added to f(x)

i.e. h(x) =3x+3

->h(x)= 3x +3(1)

-> h(x) = f(x) +f(1)

-> h(x) =f(x+1)

Hence Option (a) is your answer...

Hope it helps...

Regards

Leukonov/Olegion

Answer:

A) h(x) =  f(x +1).

Step-by-step explanation:

Given : f(x) = 3x and g(x) = 3x + 3.

To find : Which transformation of f(x) will produce the same graph as g(x).

Solution : We have given

f(x) = 3x

For x = 1.

f(1) = 3 (1)

f(x) = 3.

Plug the value of f(x) =3x and f(1) = 3 in g(x).

g(x) = 3x + 3.

g(x) = f(x) + f(1).

We can write  f(x) + f(1) = f(x +1).

g(x) = f(x +1)

h(x) = f(x +1)

So, it is a new function produce the same graph as g(x).

h(x) =  f(x +1).

Therefore, A) h(x) =  f(x +1).

Answer:

10th term of the sequence 64,16,4... = 1/4096

Step-by-step explanation:

Points to remember

nth term of GP is given by.

Tₙ = ar⁽ⁿ⁻¹⁾

Where r is the common ratio and a is the first term

To find the 10th term of given GP

It is given that,

64, 16, 4,......

a = 64 and 6 = 1/4 Here

T₁₀ = ar⁽ⁿ⁻¹⁾

 = 64 * (1/4)⁽¹⁰⁻¹⁾ = 64 * (1/4⁹)

 = 4³/4⁹ = 1/4⁶ = 1/4096

Answer: Approximately 3799 or 3800 cubic inches

Step-by-step explanation:

To find the volume of a cylinder I imagine I'm first finding the area of one of the circular "bases" (top or bottom) using the formula: Area = pi x radius squared. Once you have the area of a base, imagine you "stack" as many of them on top of each other until you get to the given height (here, it's 10 in. tall).

So . . . pi (3.14) x 11 (radius)^2 (3.14 x 11 squared) = 3.14 x 121 = 379.94 x 10 in. tall = 3799.4 cubic inches (in^3)