Using the Property of Equality, what first step would you take to rearrange the formula y=mx+b using x as the quantity of interest?(1 point) Responses Divide both sides by m. Divide both sides by m . Subtract b from both sides of the equation. Subtract b from both sides of the equation. Divide both sides by y. Divide both sides by y . Subtract mx from both sides.

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 leads to:

\[ y - b = mx \]

Next steps can involve dividing by \( m \) to isolate \( x \), but the immediate first step is subtracting \( b \).

Which of the following is an example of using the Division Property of Equality to rearrange the equation PV=nRT ?(1 point)

n=PV/RT
R=PV−nT
T=PVnR
R=nTPV

The Division Property of Equality states that if two expressions are equal, you can divide both sides by the same non-zero number without changing the equality.

In the equation \( PV = nRT \), to solve for \( n \) using division, you would divide both sides by \( RT \). This gives us:

\[ n = \frac{PV}{RT} \]

Thus, the correct answer is:

**n = PV/RT**.

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=2πC r equals 2 pi upper C r=Cπ2 r equals Start Fraction upper C pi over 2 End Fraction r=C2π r equals Start Fraction upper C over 2 pi End Fraction r=Cπ r equals Start Fraction upper C over pi End Fraction

To rearrange the formula for the circumference of a circle, \( C = 2\pi r \), in order to find the radius (\( r \)), you would divide both sides by \( 2\pi \).

Starting from the equation:

\[ C = 2\pi r \]

Dividing both sides by \( 2\pi \) gives:

\[ r = \frac{C}{2\pi} \]

Therefore, the correct answer is:

**r = \frac{C}{2\pi}**.

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)

in.^3/in.^2=in.^3/in.^2
in.^3/in.^2=in.
in.^3=in.^3 in.
in.=in.

To rearrange the formula for the volume of a box, \( V = lwh \), to solve for the width (\( w \)), you would divide both sides by \( lh \).

Starting with:

\[ V = lwh \]

Dividing both sides by \( lh \) gives:

\[ w = \frac{V}{lh} \]

When justifying this rearrangement to solve for \( w \), you can analyze the units:

- The volume \( V \) is in cubic inches (\( in.^3 \)).
- The length \( l \) and height \( h \) are both in linear inches (\( in. \)), so the product \( lh \) is in square inches (\( in.^2 \)).

Thus, the units for \( w \) would be:

\[ \frac{in.^3}{in.^2} = in. \]

This means that the correct representation of the remaining units when justifying your rearrangement to solve for the width is:

**in.^3/in.^2 = in.**

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)

Converting feet to inches by dividing 10 feet by 12 inches/1 foot.
Converting feet to inches by multiplying 11 feet by 1 foot /2 inches.
Converting feet to inches by multiplying 10 feet by 12 inches/1 foot.
Converting feet to inches by multiplying 10 feet by 12.

To find the time it takes for the ladybug to crawl up a 10-foot section of wall at a speed of 3 inches per second, you need to convert the distance from feet to inches since the velocity is given in inches per second.

Given that there are 12 inches in 1 foot, converting 10 feet to inches can be done by multiplying 10 feet by \( 12 \, \text{inches}/1 \, \text{foot} \).

So the correct conversion is:

**Converting feet to inches by multiplying 10 feet by 12 inches/1 foot.**