Asked by x
Which of the following is an example of using the Division Property of Equality to rearrange the equation PV=nRT?(1 point)
Responses
n=PVRT
n equals Start Fraction upper P upper V over upper R upper T End Fraction
T=PVnR
upper T equals upper P upper V n upper R
R=PV−nT
upper R equals upper P upper V minus n upper T
R=nTPV
upper R equals Start Fraction n upper T over upper P upper V End Fraction
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Responses
n=PVRT
n equals Start Fraction upper P upper V over upper R upper T End Fraction
T=PVnR
upper T equals upper P upper V n upper R
R=PV−nT
upper R equals upper P upper V minus n upper T
R=nTPV
upper R equals Start Fraction n upper T over upper P upper V End Fraction
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Answers
Answered by
x
Given the formula for the circumference of a circle, C=2πr, how would you rearrange the formula if you were interested in finding the radius of the circle? (1 point)
Responses
r=C2π
r equals Start Fraction upper C over 2 pi End Fraction
r=Cπ2
r equals Start Fraction upper C pi over 2 End Fraction
r=2πC
r equals 2 pi upper C
r=Cπ
r equals Start Fraction upper C over pi End Fraction
Responses
r=C2π
r equals Start Fraction upper C over 2 pi End Fraction
r=Cπ2
r equals Start Fraction upper C pi over 2 End Fraction
r=2πC
r equals 2 pi upper C
r=Cπ
r equals Start Fraction upper C over pi End Fraction
Answered by
x
Given the formula for the volume of a box, V=lwh, which equation best represents the remaining units when justifying your rearrangement to solve for the width?(1 point)
Responses
in.=in.
in. equals in.
in.3in.2=in.3in.2
Start Fraction in. cubed over in. squared End Fraction equals Start Fraction in. cubed over in. squared End Fraction
in.3=in.3
in. cubed equals in. cubed
in.3in.2=in.
Start Fraction in. cubed over in. squared End Fraction equals in.
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Responses
in.=in.
in. equals in.
in.3in.2=in.3in.2
Start Fraction in. cubed over in. squared End Fraction equals Start Fraction in. cubed over in. squared End Fraction
in.3=in.3
in. cubed equals in. cubed
in.3in.2=in.
Start Fraction in. cubed over in. squared End Fraction equals in.
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Answered by
x
Consider the formula that relates distance, velocity, and time (d=vt). If you are interested in the time it takes for a ladybug traveling at a speed of 3 inches per second to crawl up a 10-foot section of wall, which unit conversion makes the most sense to use?(1 point)
Responses
Converting feet to inches by multiplying 10 feet by 12.
Converting feet to inches by multiplying 10 feet by 12.
Converting feet to inches by multiplying 10 feet by 12 inches1 foot.
Converting feet to inches by multiplying 10 feet by Start Fraction 12 inches over 1 foot End Fraction .
Converting feet to inches by dividing 10 feet by 12 inches1 foot.
Converting feet to inches by dividing 10 feet by Start Fraction 12 inches over 1 foot End Fraction .
Converting feet to inches by multiplying 11 feet by 1 foot12 inches.
Responses
Converting feet to inches by multiplying 10 feet by 12.
Converting feet to inches by multiplying 10 feet by 12.
Converting feet to inches by multiplying 10 feet by 12 inches1 foot.
Converting feet to inches by multiplying 10 feet by Start Fraction 12 inches over 1 foot End Fraction .
Converting feet to inches by dividing 10 feet by 12 inches1 foot.
Converting feet to inches by dividing 10 feet by Start Fraction 12 inches over 1 foot End Fraction .
Converting feet to inches by multiplying 11 feet by 1 foot12 inches.
Answered by
GPT-4o mini
The Division Property of Equality states that if two quantities are equal, you can divide both sides of the equation by the same nonzero number without changing the equality.
In the equation \( PV = nRT \), if we want to solve for \( n \), we would divide both sides by \( RT \):
\[
n = \frac{PV}{RT}
\]
Among the options provided, the correct example that represents using the Division Property of Equality is:
**n equals Start Fraction upper P upper V over upper R upper T End Fraction** (or \( n = \frac{PV}{RT} \)).
In the equation \( PV = nRT \), if we want to solve for \( n \), we would divide both sides by \( RT \):
\[
n = \frac{PV}{RT}
\]
Among the options provided, the correct example that represents using the Division Property of Equality is:
**n equals Start Fraction upper P upper V over upper R upper T End Fraction** (or \( n = \frac{PV}{RT} \)).
Answered by
GPT-4o mini
To rearrange the formula for the circumference of a circle \( C = 2\pi r \) in order to solve for the radius \( r \), you would divide both sides of the equation by \( 2\pi \):
\[
r = \frac{C}{2\pi}
\]
Thus, the correct rearrangement is:
**r equals Start Fraction upper C over 2 pi End Fraction** (or \( r = \frac{C}{2\pi} \)).
\[
r = \frac{C}{2\pi}
\]
Thus, the correct rearrangement is:
**r equals Start Fraction upper C over 2 pi End Fraction** (or \( r = \frac{C}{2\pi} \)).
Answered by
GPT-4o mini
To solve for the width \( w \) in the volume formula \( V = lwh \), we can rearrange the formula as follows:
\[
w = \frac{V}{lh}
\]
In this case, we are concerned with the units of volume (\( in^3 \)) and the product of length and height (\( lh \)), which results in square inches (\( in^2 \)).
When justifying the rearrangement in terms of units, we can represent the relationship as:
\[
\frac{in^3}{in^2} = in
\]
This means that dividing the units of volume (cubic inches) by square inches gives us the units of length (inches).
Thus, the best representation from the options provided is:
**in.3in.2=in.** (which corresponds to \( \frac{in^3}{in^2} = in \)).
\[
w = \frac{V}{lh}
\]
In this case, we are concerned with the units of volume (\( in^3 \)) and the product of length and height (\( lh \)), which results in square inches (\( in^2 \)).
When justifying the rearrangement in terms of units, we can represent the relationship as:
\[
\frac{in^3}{in^2} = in
\]
This means that dividing the units of volume (cubic inches) by square inches gives us the units of length (inches).
Thus, the best representation from the options provided is:
**in.3in.2=in.** (which corresponds to \( \frac{in^3}{in^2} = in \)).
Answered by
GPT-4o mini
To find the time it takes for the ladybug to crawl up a 10-foot section of wall while traveling at a speed of 3 inches per second, you need to ensure that both the distance and the speed are in the same units. Since the speed is given in inches per second, you should convert the distance from feet to inches.
1 foot is equal to 12 inches, so to convert 10 feet to inches, you multiply by 12:
\[
10 \text{ feet} \times 12 \frac{\text{inches}}{\text{foot}} = 120 \text{ inches}
\]
Thus, the unit conversion that makes the most sense to use from the options provided is:
**Converting feet to inches by multiplying 10 feet by 12 inches1 foot.** (This option indicates the correct conversion factor.)
If there's a format issue and you're interpreting a different option that means the same, either of the other options that mention multiplying by \( 12 \) would also be acceptable, such as:
**Converting feet to inches by multiplying 10 feet by Start Fraction 12 inches over 1 foot End Fraction .**
1 foot is equal to 12 inches, so to convert 10 feet to inches, you multiply by 12:
\[
10 \text{ feet} \times 12 \frac{\text{inches}}{\text{foot}} = 120 \text{ inches}
\]
Thus, the unit conversion that makes the most sense to use from the options provided is:
**Converting feet to inches by multiplying 10 feet by 12 inches1 foot.** (This option indicates the correct conversion factor.)
If there's a format issue and you're interpreting a different option that means the same, either of the other options that mention multiplying by \( 12 \) would also be acceptable, such as:
**Converting feet to inches by multiplying 10 feet by Start Fraction 12 inches over 1 foot End Fraction .**
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