Which of the following if rational( )a)
\pi
b)log2 c)1.23123... d)none ​

Answers

Answer 1
Answer: If c is repeating the the answer is none

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A cylinder and a cone start with the same radius and height. The radius of the cone is then tripled, and the height of the cone is cut in half. The radius of the cylinder stays the same, but the height of the cylinder is doubled. Which change produces a greater increase in volume (i.e., which figure’s volume increases by a larger factor)? Justify your answer. Write “pi” for ^ and “r^2” for r squared

Answers

Answer:

Change produced in cone is greater than change produced in cylinder.

Step-by-step explanation:

Given : A cylinder and a cone start with the same radius and height.

We have to find which change produces a greater increase in volume.

We know Volume of cylinder = \pi r^2h

and Volume of cone = (1)/(3)\pi r^2h

Where r is radius and h is height.

Let r' and h' denotes new radius and new height

Consider Cylinder first ,

The radius of the cylinder stays the same, but the height of the cylinder is doubled.

that is r' = r and h' = 2h

Then Volume of new cylinder becomes,

Volume of cylinder = \pi (r')^2h'=2\pi r^2h

Change\ produced = (new-original)/(original)

that is

Change\ produced\ in\ cylinder = (2\pi r^2h-\pi r^2h)/(\pi r^2h)=1

Now, Consider Cone, we have,

The radius of the cone is then tripled, and the height of the cone is cut in half.

r' = 3r and  h' = (h)/(2)

Thus, The volume of new cone becomes,

Volume of cone = (1)/(3)\pi (r')^2h'=(1)/(3)\pi (3r)^2(h)/(2)

Change\ produced = (new-original)/(original)

that is

Change\ produced\ in\ cone =((1)/(3)\pi (3r)^2(h)/(2)-(1)/(3)\pi r^2h)/((1)/(3)\pi r^2h) =(7)/(2)=3.5

Thus, Change produced in cone is greater than change produced in cylinder.

Cone:
Original cone = (1/3)π(h)r^2
Changed cone = (1/3)
π(h/2)(3r)^2
= (1/2)(1/3)
π(h)9r^2
= (9/2) * Original cone
=4.5 * Original cone

Cylinder:
Original cylinder = 
π(h)r^2
Changed cylinder = 
π(2h)r^2
=2 * Original cylinder

Therefore the cone is the greatest relative increase in volume.

Suzy buys 2 shirts and 2 pairs of pants for 42 dollars at the store. Annette buys 3 shirts and 1 pair of pants for 37 dollars.Create a system of equations that can be used to solve for the cost of the shirts and pants.

a
2s + 2p = 37
3s + p = 42

b
2s + 2p = 37
s + 3p = 42

c
2s + 2p = 42
3s + p = 37

d
2s + 2p = 42
s + 3p = 37

Answers

Answer:

2s+2p = 42,

3s+p = 37,

2 shirts at 8 = 16,

2 pants at 13 = 26.

Hope this helps.

Step-by-step explanation:

Which statement is true about the polynomial –3x4y3 + 8xy5 – 3 + 18x3y4 – 3xy5 after it has been fully simplified?

It has 3 terms and a degree of 5.
It has 3 terms and a degree of 7.
It has 4 terms and a degree of 5.
It has 4 terms and a degree of 7.

Answers

Answer:

it has 4 terms and a degree of 7

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

just took the test

Can you help me solve this please?

Answers

Answer:

HERE

Step-by-step explanation:

To determine which system has x = 3 and y = 2.5 as its solution, we need to substitute these values into each system of equations and check which one satisfies the conditions.

System 1: 7x - 5y = 33.5

Substituting x = 3 and y = 2.5:

7(3) - 5(2.5) = 21 - 12.5 = 8.5

System 2: 3x + 3y = 1.5

Substituting x = 3 and y = 2.5:

3(3) + 3(2.5) = 9 + 7.5 = 16.5

System 3: 4x + y = 9.5

Substituting x = 3 and y = 2.5:

4(3) + 2.5 = 12 + 2.5 = 14.5

System 4: 5x - y = 12.5

Substituting x = 3 and y = 2.5:

5(3) - 2.5 = 15 - 2.5 = 12.5

System 5: 2x - 5y = 18.5

Substituting x = 3 and y = 2.5:

2(3) - 5(2.5) = 6 - 12.5 = -6.5

System 6: x + y = 5.5

Substituting x = 3 and y = 2.5:

3 + 2.5 = 5.5

System 7: 11x + 10y = 8

Substituting x = 3 and y = 2.5:

11(3) + 10(2.5) = 33 + 25 = 58

System 8: 5x - 2y = -20

Substituting x = 3 and y = 2.5:

5(3) - 2(2.5) = 15 - 5 = 10

From the calculations, we can see that only System 4: 5x - y = 12.5 satisfies the given conditions when x = 3 and y = 2.5. Therefore, the correct answer is System 4.

Mrs. Post bought a carton of eggs containing 24 eggs to use for cookies. When she got home 3 were broken. What percent of the eggs were broken?

Answers

Answer:

12.5%

Step-by-step explanation:

Take the number of eggs that were broken over the total number of eggs

3/24

1/8

As a decimal

.125

Change to percent form

12.5%

Answer: 12.5%

Explanation:

3/24, or 1/8 of Mrs. Post’s eggs broke,

1/8 as a decimal is 0.125

0.125 as a percent is 12.5%

H(x)=(x^2)+1 and K(x)=-(x^2)+4. If K(H)=0, what are the roots/solutions?a. ±i√3
b. ±i
c. ±2
d. ±1
e. ±1, ±i√3

Answers

H(x)=(x^2)+1\ \ \ \ and\ \ \ \ K(x)=-(x^2)+4. \n\nK(H)=-(H^2)+4=-(x^2+1)^2+4=4-(x^2+1)^2=\n\n.\ \ \ =2^2-(x^2+1)^2=(2-x^2-1)(2+x^2+1)=(1-x^2)(3+x^2)=\n\n.\ \ \ =(1-x)(1+x)(x^2-3\cdot i^2)=(1-x)(1+x)(x- √(3) \cdot i)(x+ √(3) \cdot i)\n\n K(H)=0\ \ \ \ \Leftrightarrow\ \ \ (1-x)(1+x)(x- √(3) \cdot i)(x+ √(3) \cdot i)=0\n\nx=1\ \ \ \ or\ \ \ \ x=-1\ \ \ \ or\ \ \ \ x=√(3) \cdot i\ \ \ \ or\ \ \ \ x=-√(3) \cdot i\n\nAns.\ e.