Responses
Divide both sides by y.
Divide both sides by y .
Subtract mx from both sides.
Subtract m x from both sides.
Divide both sides by m.
Divide both sides by m .
Subtract b from both sides of the equation.
11 answers
To rearrange the formula \( y = mx + b \) using \( x \) as the quantity of interest, the first step would be to subtract \( b \) from both sides of the equation. This would isolate the term involving \( x \) on one side.
So the correct response is:
Subtract \( b \) from both sides of the equation.
The Division Property of Equality states that if you divide both sides of an equation by the same non-zero number, the two sides remain equal.
In the equation \( PV = nRT \), if you are solving for \( n \), you would divide both sides by \( RT \). This rearrangement would give you:
\[ n = \frac{PV}{RT} \]
Out of the options provided, the correct example of using the Division Property of Equality to rearrange the equation is:
n = \frac{PV}{RT} (or as you stated, \( n = \frac{PV}{RT} \)).
Based on the options given, the correct choice that demonstrates the use of the Division Property of Equality to rearrange the equation \( PV = nRT \) is:
b: n = \frac{PV}{RT}
This is the appropriate rearrangement by dividing both sides by \( RT \).
To rearrange the formula for the circumference of a circle \( C = 2\pi r \) to find the radius \( r \), you would divide both sides of the equation by \( 2\pi \).
This gives:
\[ r = \frac{C}{2\pi} \]
From the options provided, the correct response is:
c: r = \frac{C}{2\pi} (or \( r = \frac{C}{2\pi} \)).
To solve for the width \( w \) in the formula for the volume of a box \( V = lwh \), you would rearrange the equation as follows:
\[ w = \frac{V}{lh} \]
When you are talking about the units involved in this rearrangement, you start with volume \( V \) (in cubic inches, \( \text{in}^3 \)) and divide it by the product of length and height (each in inches, so \( \text{in} \times \text{in} = \text{in}^2 \)). Hence, the units for \( w \) would be:
\[ w = \frac{\text{in}^3}{\text{in}^2} = \text{in} \]
From the choices given, the best representation of the remaining units would be:
a: \( \frac{\text{in}^3}{\text{in}^2} = \text{in} \) (or \( \text{in}^3 / \text{in}^2 = \text{in} \)).
To convert feet to inches, you need to multiply the number of feet by 12 since there are 12 inches in a foot. Therefore, when converting 10 feet to inches, you would calculate:
\[ 10 \text{ feet} \times 12 \text{ inches/foot} = 120 \text{ inches} \]
Among the options given, the correct unit conversion that makes the most sense is:
Converting feet to inches by multiplying 10 feet by 12.
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