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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?

Responses:
Subtract mx from both sides.

Divide both sides by y.

Subtract b from both sides of the equation.

Divide both sides by m.

9 answers

To rearrange the formula \( y = mx + b \) using \( x \) as the quantity of interest, the first step you would take is to subtract \( b \) from both sides of the equation.

This would give you:

\[ y - b = mx \]

This is the correct initial step to isolate the term involving \( x \).

Which of the following is an example of using the Division Property of Equality to rearrange the equation PV=nRT
Responses:

n=PV/RT

R=nT/PV

T=PVnR

R=PV−nT

The correct example of using the Division Property of Equality to rearrange the equation \( PV = nRT \) is:

n = PV/RT

This equation shows that \( n \) is isolated on one side by dividing both sides by \( RT \).

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. Responses:

r=C/2π

r=2πC

r=Cπ

r=Cπ/2

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

This gives you:

r = C / (2π)

So the correct response is:

r = C / 2π.

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.3=in.3

in.=in.

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

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

To justify your rearrangement of the formula \( V = lwh \) to solve for the width \( w \), you would divide both sides by \( l \) and \( h \). This keeps the units in balance.

Starting with the original equation:

  • \( V \) is measured in cubic inches (in³),
  • \( l \) is measured in inches (in),
  • \( w \) is measured in inches (in),
  • \( h \) is measured in inches (in).

When you rearrange for \( w \):

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

The units would be:

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

Thus, the best representation of the remaining units would be:

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

This shows that the width \( w \) retains the dimension of inches (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
Responses:

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

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

Converting feet to inches by multiplying 10 feet by 12.
C

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

To convert feet to inches, you need to use the conversion factor that 1 foot = 12 inches. Therefore, if you're converting \( 10 \) feet to inches, you would multiply by \( 12 \) inches per \( 1 \) foot.

The correct option would be:

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

This will give you the correct equivalent in inches since:

\[ 10 \text{ feet} \times \frac{12 \text{ inches}}{1 \text{ foot}} = 120 \text{ inches}. \]