The height of a right cylinder is 3 times the radius of the base. The volume of the cylinder is 247 cubic units.
What is the height of the cylinder?
O 2 units
O 4 units
O 6 units
O 8 units

Answer:

  (x, y) = (3/7, 1/7) or (3, 4)

Step-by-step explanation:

The second equation can be rearranged to ...

  4x^2 +9y^2 = 15xy . . . . . . multiply by xy

  4x^2 -15xy +9y^2 = 0 . . . subtract 15xy

  (4x -3y)(x -3y) = 0 . . . . . . factor

This resolves to two linear equations:

 4x -3y = 0

  x -3y = 0

__

Combined with the first equation, we get two systems of equations. We can solve both of them at once by substituting for y and using a stand-in for the coefficient of x.

  y = (3x -1)/2 . . . . first equation solved for y

  Cx -3(3x -1)/2) = 0 . . . . substitute for y in the 2nd/3rd equations (C = 1 or 4)

  2Cx -9x +3 = 0 . . . . . multiply by 2

  x(2C -9) = -3 . . . . . . .subtract 3

  x = -3/(2C -9) = 3/(9 -2C) . . . . . remembering that C = 1 or 4

__

For C=1, x = 3/(9 -2) = 3/7

  y = (3(3/7) -1)/2 = 1/7

For C=4, x = 3/(9 -8) = 3

  y = (3(3) -1)/2 = 4

The solutions are (x, y) = (3/7, 1/7) and (3, 4).

_____

Additional comment

We could have substituted for y in the quadratic form of the second equation. This would give a quadratic in x that could be solved in any of the usual ways.

Answer:

y= 3

Step-by-step explanation:

The triangle on the left is a right triangle, so we can use trig functions to solve for the missing side, y.

First, find the length of the side that both triangles are connected to.

tan30=x/9

Isolate the x variable and solve.

9(tan30)=x

x= 5.19615

Now use the Pythagorean Theorem to solve for the side length, y.

a^2+ b^2 = c^2

(5.19615)^2+ b^2= 6^2

c= 3

Answer:

Step-by-step explanation:

Conclusion:

Therefore, n = 1/9

Hoped this helped.

[tex]GeniusUser[/tex]

Answer:

2.8 pounds

Step-by-step explanation: For this one, I rounded the answer, but what you need to do is divide 20 by 7.

20/7 = 2.85714285714

2.85714285714 ≈ 2.8 pounds

Answer:

  base: 22 37/54; sides: 56 17/108

Step-by-step explanation:

If we let x represent half the length of the base, and y represent the length of the side, then we have ...

  2x +2y = 135 . . . . . perimeter relation

  x^2 +55^2 = y^2 . . . . Pythagorean theorem relation

Solving for y and substituting into the second equation, we have ...

  y = 135/2 -x

  x^2 + 3025 = (67.5 -x)^2

  3025 = -135x +4556.25 . . . . . . expand, subtract x^2

  135x = 1531.25 . . . . . . . . . . add 135x -3025

  x = 1531.25/135 = 11 37/108

The length of the base is double this value, 22 37/54.

The length of each side is 67.5 -11 37/108 = 56 17/108.

__

Check

The perimeter is the base plus two side lengths:

  22 37/54 + 2(56 17/108) = (22 +112) +37/54 +17/54 = 134 +1 = 135.

Answer: B

Explanation:  

32 marbles in total.

18 red marbles

4 blue marbles

10 green marbles.

You are asked what part of Osteen's marbles are red?

Probability = number of possible outcomes/total number of out outcomes.

P(Red) = 18/32 = 9/16

Both, 18 and 32 are divisible by 2 which gives 9/16. Since 9/16 cannot be reduced any further, we live it as it is. If you wanted to plug this into a calculator that would give 0.5625 which is 56.25% of Osteen's marbles are red.

P(Blue) = 4/32 = 1/8. 1/8 = 0.125 which 12.5% of his marbles are blue.

P(Green) = 10/32 = 5/16. 5/16= 0.3125 which 31.25 of his marbles are green. When you add 0.5625 + 0.125 + 0.3125 = 1 which is 100%. All probabilities add up to 1.

Hope this elaborate explanation helps.

The sum in terms of p of four consecutive even integers with p been the smallest is 4(p + 3)

Even numbers are numbers that can be divided into two equal groups and they can be easily divisible by 2 without any remainder.

p is the smallest of the four consecutive even integers. This means p come first and it is the first term of the numbers.

Therefore, the 4 consecutive even integers is represented as follows;

p, p + 2, p + 4, p + 6

So the sum is equal to:

sum = p + p + 2 + p + 4 + p + 6

sum = 4p + 12

sum = 4(p + 3)

learn more on even numbers here: https://brainly.com/question/21514478?referrer=searchResults

Answer:

y>1/2x+2

Step-by-step explanation:

Answer: 90° + 41° =131° 180°-131° =149°

X=5.5-6

Step-by-step explanation:

Step-by-step explanation:

i think it is the answer ...

Answer:

5km

Step-by-step explanation:

The formula for hypotenuse is

a squared + b squared = c squared,

4 squared is 16, and 3 squared is 9.

16+9 = c squared

25 = c squared

However, you don't want it to be squared, so you have to find the square root of 25, which is 5.

Answer:8w^2+2

w(3w+2)+5w

First distribute the w to the parentheses:

3w^2+w

Add on the 5w to the new equation:

3w^2+2w+5w

Combine like terms:

8w^2+2

Answer:

[tex]\sqrt{49 - x^{2}}[/tex]

Step-by-step explanation:

Pythagorean theorem  [tex]c^{2} = a^{2} + b^{2}[/tex] Then:

[tex]7^{2} = x^{2} + y^{2}\\y^{2} = 7^{2} - x^{2}\\y^{2} = 49 - x^{2}\\y = \sqrt{49 - x^{2}}[/tex]

the lenght of the third side = [tex]\sqrt{49 - x^{2}}[/tex]

Ф = [tex]sin^{-1} (\frac{x}{7} )[/tex]

Ф = [tex]cos^{-1} (\frac{y}{7} )[/tex]

Ф = [tex]tan^{-1} (\frac{x}{y} )[/tex]

Answer:

step: 4(x-24x)to the power of 2 = 3-7 or -4

Step-by-step explanation:

solution: solve it

would love to have a second opinion, this is what i got.

[tex] \: \: \: \: \: \: \: [/tex]

GCF OF 48

The greatest common factor of 8, 28, and 48 is 4.

The largest common factor out of all the numbers in the given set is known as Greatest Common Factor.

Factors of 8, [tex]8=2\times 2\times 2[/tex]

Factors of 28, [tex]28=2\times 2\times 7[/tex]

Factors of 48, [tex]48=2\times 2\times 2\times 2\times 3[/tex]

The common factors in the above set of numbers are 2and 2.

So, the Greatest Common Factor of 8, 28, and 48 is  [tex]2\times 2=4[/tex].

Learn more about Greatest Common Factor here: https://brainly.com/question/11444998

#SPJ2

Answer:

multiple choice is worth 2

short response is worth 4

Step-by-step explanation:

23x + 10y = 86

28x + 5y = 76

solve by elimination

multiply the top by -1 and the bottom by 2

-23x + -10y = -86

56x + 10y = 152

add them

33x = 66

x = 2

with x = 2 plug x into one of the equations

23x + 10y = 86

23(2) + 10y = 86

46 + 10y = 86

10y = 40

y = 4

x = 2 and y = 4 so

multiple choice is worth 2

short response is worth 4

Answer:

Each person would get 1/5 of 3 segments.

Each person would get 3/5 of a segment.  

Step-by-step explanation:

(3) (1/5) = 3/5 segments

Using the Central Limit Theorem, it is found that the mean of the sampling distribution of sample proportions is 0.37.

The Central Limit Theorem establishes that, for a proportion p in a sample of size n, the sampling distribution of sample proportions has:

For this problem, about 37% of high school seniors have vaped in the past year, hence [tex]p = 0.37[/tex].

For more on the Central Limit Theorem, you can check https://brainly.com/question/4086221

Answer: The answer is 0.

[tex]y= -\frac{3x}{2} +1[/tex]

Answer:

Answer:

safe speed for the larger radius track u= √2 v

Explanation:

The sum of the forces on either side is the same, the only difference is the radius of curvature and speed.

Also given that r_1= smaller radius

r_2= larger radius curve

r_2= 2r_1..............i

let u be the speed of larger radius curve

now, \sum F = \frac{mv^2}{r_1} =\frac{mu^2}{r_2}∑F=

r

1

mv

2

=

r

2

mu

2

................ii

form i and ii we can write

v^2= \frac{1}{2} u^2v

2

=

2

1

u

2

⇒u= √2 v

therefore, safe speed for the larger radius track u= √2 v

Answer:y + x -6x (y -5x -2)

5x + 4x -3x (x)

2x + 3 - x -4 (x - 1)

Step-by-step explanation:

A=C

B=B

C=A

Step-by-step explanation:

exterior angle is the sum of two opposite interior angle

11x+9=3x+12+85

11x-3x=88

8x=88

x=11.

hope this helps you.

Answer:

x=11

Step-by-step explanation:

85 + 3x + 12= 11x+9

97  +3x= 11x+9

-97            -97

3x= 11x - 88

-11x    -11x

-8x = -88

/-8     /-8

x=11

Answer:

  A.  {-1, 2, 7}

Step-by-step explanation:

For a set of ordered pairs, the domain is the set of first-numbers (x). The range is the set of second numbers (y, or g(x)).

The first step here is to find the g(x) values for each of the listed x-values.

The attachment shows a table.

Often, we like to list the domain and/or range values in numerical order, eliminating any duplicates. That is, the set of range values {2, -1, -1, 7} would be listed as ...

  {-1, 2, 7} . . . . . . matches choice A

_____

You find the g(x) values by substituting for x and doing the arithmetic.

  g(-2) = (-2)² -2 = 4 -2 = 2, for example

Answer:

24 square units

Hope you can get an idea from it.

Carry on learning.

Doubt clarification - use comment section.

Answer:

The slope is 1

Step-by-step explanation:

the formula for finding slope is : y2-y1/x2-x1

2. Subsitute: (1)-(0)/(4)-(3) = 1/1 = 1

Therefore, the slope is 1.

Answer:

is 61.6 on there? because if so I believe it's that

Answer:  $14.5

Step-by-step explanation: you divide 58 by 4 . each box is 14.5. total cost is $68 if you add postage

Answer: 37,007 is greater

Step-by-step explanation:

Can i get a brainliest

Answer:

37,007 is greater than 30,707

Step-by-step explanation:

Thats because as you can see reading the numbers left to right, the first ones on the far left are both 3s. so so far they're the same. then go to the second number, making sure you're moving left to right. 7 is more than 0 therefor 37,007 is greater than 30,707