Two functions are given below. Make sure to explain!

Volume of a right cone with base radius r cm and height h cm :

V = 1/3 π r² h cm³

Surface area :

A = (π r² + π r √(h² + r²)) cm²

Volume of a sphere with radius r cm :

V = 4/3 π r³ cm³

Surface area :

A = 4 π r² cm²

Volume of a cuboid with dimensions r cm × r cm × h cm :

V = r² h cm³

Surface area :

A = 2 r² + 4 r h

a. If the cone and sphere have the same volume, then

1/3 π r² h = 4/3 π r³   ⇒   h = 4r

b. If the area of the cuboid is 98 cm², then

2 r² + 4 r h = 98   ⇒   r (r + 2 h) = 49

c. Since h = 4r, substituting this into the equation from (b) gives

r (r + 8 r) = 9 r² = 49   ⇒   r² = 49/9   ⇒   r = 7/3

d. With r = 7/3, we have

h = 4 × 7/3 = 28/3

and so the volume of the cuboid is

V = (7/3 cm)² (28/3 cm) = 1372/27 cm³

The regular polygon that has a rotation of 240 degrees to carry the polygon onto itself is the equilateral triangle.

Options

Equilateral triangle

Octagon

Rectangle

Pentagon

A polygon that can carry itself onto itself after a rotation of 240 degrees must obey the following rule:

Angle of rotation = 360/Sides

Next, we test the options:

Option (a) equilateral triangle

Angle of rotation = 360/3

Evaluate

Angle of rotation = 120

Next, we list the multiples of 120

120, 240, 360.....

See that 120 is a factor of 240.

This means that the equilateral triangle would be rotated onto itself when rotated by 240 degrees.

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Answer:

No, because both of them will never be able to match; become equivalent. You would have to multiply 2 different numbers to make them match, meaning they would not be proportional. For a comparison to be proportional, the ratio you are trying to simplify to must be achieved by multiplying 2 numbers from the previous ratio by one LCD.

[tex]\frac{3\cdot 4}{7 \cdot 3} = \frac{12}{21}[/tex]

They are able to make 12/21, but that does not mean they are proportional.

t=2/61

1 Rearrange terms

2

Multiply the numbers

3

Combine like terms

4

Add

10

to both sides

5

Simplify

6

Add

303t

to both sides

7

Simplify

8

Divide both sides by the same factor

9

Simplify

[tex]-5x\sqrt{192x^3} + \sqrt{3x^5}\\\\=-5x\left(192x^3 \right)^{\tfrac 12} + \left(3x^5 \right)^{\tfrac 12}\\\\=-5\cdot (192)^{\tfrac 12} \cdot x \cdot x^{\tfrac 32} + 3^{\tfrac 12} \cdot x^{\tfrac 52}\\\\=-5\left( 64 \cdot 3 \right)^{\tfrac 12} \cdot x^{1+\tfrac 32} + 3^{\tfrac 12} \cdot x^{\tfrac 52}\\\\=-5\cdot 8\cdot 3^{\tfrac 12} \cdot x^{\tfrac 15} + 3^{\tfrac 12} \cdot x^{\tfrac 52}\\\\=-40\cdot 3^{\tfrac 12} \cdot x^{\tfrac 52}+3^{\tfrac 12} \cdot x^{\tfrac 52}\\\\[/tex]

[tex]=-39\cdot 3^{\tfrac 12} \cdot x^{\tfrac 52}\\\\=-39\sqrt 3 \sqrt{x^5}[/tex]

Usando proporciones, hay que no se trabajaron en 65 dias durante el año de 2018 en la empresa SAC-OLC.

Una proporción es una fracción de la cantidad total, e los problemas pueden ser resolvidos con una regla de três.

En este problema, hay que se fabricaran 24000 ollas en el año de 2018, con una taja de 80 ollas al dia. Así, el número de dias trabajados es dado por:

n = 24000/80 = 300.

El año de 2018 tuvo 365 dias, así, el número de dias no trajados fue de:

365 - 300 = 65.

Puede-se aprender mas a cerca de proporciones es brainly.com/question/26950887

Answer:

Step-by-step explanation:

Let x be the unknown number.

(5÷8)x = 200

Then

x = (8×200) ÷ 5

  = 1600 ÷ 5

  =320

……………………………

(7/10)x = (7/10)×320

           = (7×320) ÷ 10

           = 224

Answer:

= 224

Step-by-step explanation:

Hi there!, here is how we solve the problem;

To begin, the question wants us to determine

[tex] \frac{7}{10} [/tex]

of the number x (unknown).

[tex] \frac{5}{8} = 200 \\ \frac{8}{8} = x \\ ( \frac{ \frac{8}{8} \times 200 }{ \frac{5}{8} } ) \\ = \frac{8}{8} \times 200 \times \frac{8}{5} \\ = 320 \\ x = 320[/tex]

We have found our x = 320

Lets now determine

[tex] \frac{7}{10} [/tex]

Which is given by;

[tex]( \frac{7}{10} \times 320 \\ = 224[/tex]

[tex] \frac{7}{10} [/tex]

of the number is therefore 224.

= 224 <<<<<< Ans

I hope this helps.

Have a nice studies.

Answer:

c; 6

Step-by-step explanation:

to find the rate of change from x = 2 to x = 4 you use the (y2 - y1) / (x2 - x1) formula

so

(21 - 9) / (4 - 2)

12 / 2

6

the average rate of change is 6

Answer:

West North West

Step-by-step explanation:

West North West would be the bottom half of North West after you split the compass heading into 2 again.

Answer:

north of west = 290 degrees

north of east = 70

Step-by-step explanation:

The angle of triangle are ∠A = 86, ∠B = 55, ∠C = 39. The side of the triangles are a = 0.99, b = 0.81, c = 0.62.

Law of sines is a formula relating the length of the sides of a triangle to the angles of the triangle.

[tex]\dfrac{sin A}{a} = \dfrac{sin B}{b} = \dfrac{sin C}{c}[/tex]

We have given angles of the triangle as

∠A = 86

∠B = 55

∠C = 39

So,

[tex]\dfrac{sin 86}{a} = \dfrac{sin 55}{b} = \dfrac{sin 39}{c}[/tex]

Now,

a = 0.99

b = 0.81

c = 0.62

The side of the triangles are a = 0.99, b = 0.81, c = 0.62.

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Answer:

Answer Option C

Step-by-step explanation:

They make a big plus sign, PLUS=PERPENDICULAR

Answer:

m=1/3

equation y=1/3x+10

Step-by-step explanation:

Find the rise and run.

1. -6--9=run=3

2. 8-7=rise=1

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find the slope of the line that passes through (-6, 8) and (-9, 7).

[tex]\triangle~\fbox{\bf{KEY:}}[/tex] (formula for Slope)

[tex]\longmapsto\bf{\cfrac{y2-y1}{x2-x1}}[/tex]

y2 & y1 = the y-coordinates of the two points

x2 & x1 = the x-coordinates of the two points

[tex]\ddot\bigstar[/tex] Remember this...

[tex]\fbox{y2\;and\;y1\;are\;y-coordinates\;of\;the\;two\;points,\;and\;x2\;and\;x1\;are\;x-coordinates}}[/tex]

So we substitute the values and obtain:

[tex]\bf{\cfrac{7-8}{-9-(-6)}[/tex]

Simplifying:

[tex]\bf{\cfrac{-1}{-9+6}}[/tex]

Simplifying more:

[tex]\bf{\cfrac{-1}{-3}}[/tex]

Divide the top and bottom by -1:

[tex]\bf{\cfrac{1}{3}}[/tex]

There's the slope.

Hope it helps you out! :D

Ask in comments if any queries arise.

~Just a smiley person helping fellow students

Answer:

A and B

Step-by-step explanation:

In both of these relations, each input corresponds to one and only output.

The probability that it bears a 2 digit no. is 41/50; a perfect square no is; 3/25; a no. divisible by 5​ is; 0.2

We are given;

Number of Discs in box = 50

Type of discs in box = Numbered 1 to 50

i) Number of 2 digit numbers = 41

Thus;

P(2 digit numbers) = 41/50

ii) Perfect square numbers are; 4, 9, 16, 25, 36 and 49. Thus;

P(perfect square number) = 6/50 = 3/25

iii) Numbers divisible by 5 are; 5, 10, 15, 20, 25, 30, 35, 40, 45, 50.

Thus;

P(numbers divisible by 5) = 10/50 = 0.2

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The polynomial function that could be represented by the graph is f(x) = x³ + x² - 6x

The attached graph represents the missing part of the question

From the attached graph, the x-intercepts of the graph are:

x1 = -3

x2 = 0

x3 = 2

The equation of the graph is then calculated as:

f(x) = (x - x1)(x - x2)(x - x3)

This gives

f(x) = (x + 3)(x - 0)(x - 2)

Expand

f(x) = x(x² + 3x - 2x - 6)

Evaluate

f(x) = x(x² + x - 6)

Expand

f(x) = x³ + x² - 6x

Hence, the polynomial function that could be represented by the graph is f(x) = x³ + x² - 6x

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Answer: 2. 5. f(x)=x²-5; vertically stretched by a factor of 4, followed by a translation 3 units to the right. 4(x²-5). 4((x-3)²-5) g(x)= 4(x-3)²-20.

Step-by-step explanation:

The bicyclist's speed as a rate is 40/3 miles per hour

The given parameters are:

The rate is calculated as:

Rate = Distance/Time

Substitute known values

Rate = 40 miles/3 hours

Rewrite as:

Rate = 40/3 miles per hour

Hence, the bicyclist's speed as a rate is 40/3 miles per hour

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Step-by-step explanation:

0.777... is rational since it can be put in fraction form which is 7/9

note: if something can be put as an integer/integer its rational

Answer: 9.42 cu. meters

Step-by-step explanation:

V= 1/3 x TT x r^2 x height

TT (pi) =  3.14

r^2 is 1/2 diameter = 1.5

height = 4

V = 1/3 x 3.14 x 1.5^2 x 4

V= 1/3 x 3.14 x 2.25 x 4

V = 9.42 cu. meters

The 2 equations are classified as Identities because both sides remain the same for all values of z.

1) We are given the equation;

23z + 19 = 3(5z - 9) + 8z + 46

Let us try z = 0

23(0) + 19 = 3(5(0) - 9) + 8(0) + 46

19 = -27 + 46

19 = 19

Let us try z = 5;

23(5) + 19 = 3(5(5) - 9) + 8(5) + 46

134 = 48 + 40 + 46

134 = 134

Thus, this is an identity as both sides remaining the same for all values of z.

2) We are given the equation;

15y + 32 = 2(10y - 7) - 5y + 46

At y = 0, we have;

15(0) + 32 = 2(10(0) - 7) - 5(0) + 46

32 = -14 + 46

32 = 32

Let us try y = 2;

15(2) + 32 = 2(10(2) - 7) - 5(2) + 46

62 = 26 - 10 + 46

62 = 62

This is an identity as both sides remaining the same for all values of z.

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Answer:

-3/2

Step-by-step explanation:

See attached image

Answer:

[tex]m=\frac{-3}{2}[/tex]

Step-by-step explanation:

m = slope
[tex]m=\frac{-4-5}{4--2}[/tex]  
[tex]m=\frac{-9}{6}[/tex]
[tex]m=\frac{-3}{2}[/tex]

The equation which represents the situation and how old is Tina is "The equation that represents this situation is t − 3 = 18. Tina is 21".

Equate Cole's age

t - 3 = 18

t = 18 + 3

t = 21

Therefore, the equation which represents the situation and how old is Tina is "The equation that represents this situation is t − 3 = 18. Tina is 21".

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Answer:

5 4/5 or 5.8

Step-by-step explanation:

convert 29/5 to 5 4/5

or

divide 29/5 is 5.8

Answer:

hypotenuse(h)^2 = 3^2 + 7^2

h^2 = 9 + 49

h = √58

h = 7.6

Answer:

7/6

Step-by-step explanation:

To find the slope you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.

so doing that i get 7/6

Hope This Helped

hi

Step-by-step explanation:

I

don't

know

see you in next question

Answer:

d

Step-by-step explanation:

the statement "you can avoid having a hold placed on when funds are available is noat a benefit of the direct deposit

Answer:

3/10

Step-by-step explanation:

Please give brainliest!

hope this helps :)

the first step is to multiply 1/4 and 2/5

1/4 times 2/5 = 2/20

you figure this out by multiplying the numerators and denominators.

next, we solve 2/20 ÷ 1/3

we do this by taking the reciprocal of 1/3, which is 3/1, and then multiplying the fractions

2/20 times 3/1 = 6/20

6/20 = 3/10

By using exponent properties, we will get the simplified expression:

[tex]x^{-1}*y^{1/2}*z^2[/tex]

Here we have the expression:

[tex](x^{1/2}*y^{-1/4}*z)^{-2}[/tex]

Remember the exponent properties:

[tex](a^n)^m = a^{n*m}[/tex]

And:

[tex](a*b)^n = (a^n)*(b^n)[/tex]

So using these two properties, we can rewrite:

[tex](x^{1/2})^{-2}*(y^{-1/4})^{-2}*(z)^{-2}\\\\(x^{-2*1/2})*(y^{-2*-1/4})*(z^{-2}})\\\\x^{-1}*y^{1/2}*z^2[/tex]

So we conclude that the completely simplified expression is:

[tex]x^{-1}*y^{1/2}*z^2[/tex]

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Answer:

C

Step-by-step explanation:

Distribute the -2 to the exponents of x, y, and z.

x: 1/2 * -2/1 = -2/2 = -1

y: -1/4 * -2/1 = 2/4 = 1/2

z: 1/1 * -2/1 = -2/1 = -2

Now to get a negative out of the exponents, you simply move them on the other side of the equation (If it is on top move, it to the bottom and vice versa.)

So, once you move all of the exponents you get C.

Answer:

It would be 35/36

Step-by-step explanation:

so if you did like 1+1, 1+2, 1+3....2+1,2+2, 2+3 yada yada

the only possible number combo that would equal twelve is 6+6 and there is 36 possible combos so your answer is 35/36

- a former algebra 2 student