A rectangular prism with a volume of 10 cubic units is filled with cubes with side lengths of 1/2

Determine which equations have the same solution set as StartFraction 2 Over 3 EndFraction minus x plus StartFraction 1 Over 6 E

Lina20 [59]

Answer:

A, B, F

Step-by-step explanation:

2/3 - x + 1/6 = 6x

Collect like terms

2/3 + 1/6 = 6x + x

(4+1) / 6 = 7x

5/6 = 7x

x = 5/6 ÷ 7

= 5/6 × 1/7

x = 5/42

a) 4 - 6x + 1 = 36x

4 + 1 = 36x + 6x

5 = 42x

x = 5/42

Equivalent to the last step of the simplification above

b) 5/6 - x = 6x

5/6 = 6x + x

5/6 = 7x

This is equivalent to the third step of the simplification

c) 4 - x + 1 = 6x

4 + 1 = 6x + x

5 = 7x

x = 5/7

Not equivalent to any of the steps in the simplification above

d) 5/6 + x = 6x

5/6 = 6x - x

5/6 = 5x

x = 5/6 ÷ 5

= 5/6 × 1/5

x = 5/30

Not equivalent to any of the steps in the simplification above

e) 5 = 30x

x = 5/30

Not equivalent to any of the steps in the simplification above

f) 5 = 42x

x = 5/42

Equivalent to the last step of the simplification above

4 0

3 years ago

webassign If a snowball melts so that its surface area decreases at a rate of 6 cm2/min, find the rate at which the diameter dec

drek231 [11]

Answer:

The answer is $\frac{3}{10\pi } cm/min$

Step-by-step explanation:

Assuming the snowball is a perfect sphere, then if A denotes the surface area and D the diameter then:

$A=4\pi r^{2} = 4\pi (\frac{D}{2} )^{2} =\pi D^{2}$

Differentiating wrt r we have:

$\frac{dA}{dD} =2\pi D$

We are told that $\frac{dA}{dt}= -6$ and we want to find $\frac{dD}{dt}$

By the chain rule we have:

$\frac{dA}{dD}=\frac{dA}{dt}.\frac{dt}{dD}=\frac{\frac{dA}{dt} }{\frac{dD}{dt} }$

∴ $2\pi D=-\frac{6}{\frac{dD}{dt} }$

∴ $\frac{dD}{dt}=-\frac{6}{2\pi D}$

When D=10 then

$\frac{dD}{dt} =-\frac{6}{10*2\pi } =-\frac{3}{10\pi }$

The sign (-) shows that the D is decreasing.

3 0

3 years ago

Chen buys 4 tickets to a soccer game. The total cost before taxes is $80. Which equation would you use to determine the price, p

Assoli18 [71]

Answer:

A. 4p=80

Step-by-step explanation:

Total Cost of 4 tickets=$80

Price=p

Quantity=4

Total cost=price×quantity

80=p×4

80=4p

80=4p is the equation that can be used to determine price

From the equation

80=4p

Divide both sides by 4

80/4=4p/4

20=p

Price is $20 per ticket

7 0

2 years ago

Read 2 more answers

A box contains 12 balls of which 5 are red, and 7 are blue. If 4 balls are drawn from the box, in how many ways can this be done

mash [69]

Answer:

175 ways

Step-by-step explanation:

5 balls are red, and 7 balls are blue making a total of 12 balls.

4 balls are drawn from the box,

1 ball is red and 3 balls are blue out of the 4 drawn from the box.

We have to choose 1 ball from 5 red balls and 3 blue balls from 7 blue balls.

Since the order is not essential we use combinations to find out

5C1 * 7C3= 5*35 = 175 ways

6 0

3 years ago

What happens to the energy not output by a machine

Sveta_85 [38]

Answer:

By using the energy conservation law, the input energy must be equivalent to the output energy. If you measured output energy is lower than your input energy, you have lost that difference of energy either in mechanical inefficiency (friction, heat, etc.) or an energy sink.

Thus, the energy not output by the machine is lost in the process within the machine.

Cheers.

5 0

3 years ago