Solving Formulas Lesson

Solving Formulas 1

By Jamie Chenoweth

Linear Formulas

​Solving One Step Linear Equations

​A linear equation is a relation between two variables that gives a straight line when plotted on a graph. The equation's variable has a power of 1. To solve for variables in a Linear Equation requires one or two algebra steps that use multiplication/division and/or addition/subtraction.

Some text here about the topic of discussion

Multiple Choice

​The equation for Speed is given as $$V=\frac{D}{t}$$  

If a ball rolls a distance of 100 cm in a time of 4 seconds, Which expression would let you evaluate the solution for V correctly?

• $$V=\frac{4s}{100cm}$$  

• $$100cm=\frac{V}{4s}$$  

• $$V=\frac{100cm}{4s}$$  

• $$V=100cm\times4s$$  

Multiple Choice

​The equation for Speed is given as $$V=\frac{D}{t}$$  

If you are given a problem that gives speed and time and askes you to solve for distance, you will need to rearrange the equation to solve for D.

What is the correct solution for D?

• $$D=\frac{V}{t}$$  

• $$D=V-t$$  

• $$D\left(t\right)=V$$  

• $$D=V\left(t\right)$$  

Multiple Choice

​The equation for Speed is given as $$V=\frac{D}{t}$$  

If you are given a problem that gives speed & distance and askes you to solve for time, you will need to rearrange the equation to solve for t. What is the correct solution for t?

• $$t=\frac{D}{V}$$  

• $$t=V-D$$  

• $$t=D\left(V\right)$$  

• $$t=\frac{V}{D}$$  

Multiple Choice

The Perimeter of a Square is given by the formula $$P=4s$$   where s is the length of the sides.

If the Perimeter of a square is 24in, what is the length of each side?

• $$6in$$  

• $$6cm$$  

• $$96in$$  

• $$\frac{1}{6}in$$  

Multiple Select

The Perimeter of a Square is given by the formula $$P=4s$$   where s is the length of the sides. Which of the following are correct rearrangements of this formula?

• $$s=\frac{P}{4}$$  

• $$\frac{1}{4}P=s$$  

• $$0.25\left(P\right)=s$$  

• $$\frac{s}{P}=4$$  

Multiple Choice

​The equation for Speed is given as $$V=\frac{D}{t}$$  

Sound can travel 300m/s. If a hammer makes a sound, how far will the sound travel in 5 seconds?

• 60m 

• 1500s 

• 0.017m 

• 1500m 

Multiple Choice

​The equation for Speed is given as $$V=\frac{D}{t}$$  

Sound can travel 300m/s. If a hammer makes a sound, how much time will it take before someone 100 m away will hear it?

• 30000s 

• 0.33s

• 3s

• 400s

Multiple Choice

The equation for the Area of a Rectangle is $$A=\ l\times w$$  

IF a rectangle has an Area of 200 cm² and a Length of 50cm, What is the Width?

• 4cm

• 0.25cm

• 250cm

• 150cm

Multiple Select

The equation for the Area of a Rectangle is $$A=\ l\times w$$  

If a rectangle has an Area of 200 cm² which combinations of length and width are possible?

• l = 25cm

  w= 8cm

• l = 100cm

  w = 2cm

• l = 0.5m

  w = 4cm

• l = 14.14

  w = 14.14

Multiple Select

The equation for the Area of a Rectangle is $$A=\ l\times w$$  

where l is the length and w is the width. Which of the following are correct solutions?

• $$l=\frac{A}{w}$$  

• $$w=\frac{A}{l}$$  

• $$A\left(l\right)=w$$  

• $$w\times l=A$$  

Multiple Choice

The formula for the circumference of a circle is $$C=2\pi r$$   Where r is the radius.

If the circumference of a circle is 62.8cm², What is the Radius?

• 6.28cm 

• 98.6cm 

• 32.8cm 

• 10cm 

Multiple Select

For all circles, the formula $$s=r\theta$$   relates the arc length (s) as the product of radius (r) and angle $$\left(\theta\right)$$  where angle is in radians. Which of the following are correct solutions of the equation?

• $$r=\frac{s}{\theta}$$  

• $$r\times\theta=s$$  

• $$\frac{r}{s}=\theta$$  

• $$\theta=\frac{s}{r}$$  

Multiple Select

For all circles, the formula $$s=r\theta$$   relates the arc length (s) as the product of radius (r) and angle $$\left(\theta\right)$$  where angle is in radians.

If an angle of $$\pi$$  radians is subtended by an arc length of 10cm, what is the radius of the circle?

• $$\frac{10}{\pi}$$   

• $$\approx\frac{10}{3.14}$$  

• 0.314cm 

• 3.183cm 

Multiple Choice

The formula for the circumference of a circle is $$C=2\pi r$$   where r is the radius.

Which of the following are NOT correct solutions?

• $$r=\frac{C}{\left(2\pi\right)}$$  

• $$\pi=\frac{C}{\left(2\pi\right)}$$  

• $$\pi r=\frac{C}{2}$$  

• $$2=\frac{C}{\pi}r$$  

Multiple Select

The equation for The Perimeter of a Rectangle is Given as $$P=2l\ +\ 2w$$  

Which of the following solutions are correct?

• $$\frac{P-2l}{2}=w$$  

• $$\frac{P-2w}{2}=l$$  

• $$\frac{P}{2}=l\ +w$$  

• $$\frac{P}{2}-l=w$$  

Multiple Choice

The work done (or Energy used) to lift an object is given as $$W=mgh$$  Where m is mass, g=9.8 m/s and h is the height lifted.

What is the mass of a ball that takes 100 Joules of Work when it is lifted 2.2m?

• 4.64kg

• 45.45kg

• 445kg

• 2156kg

Multiple Choice

The work done (or Energy used) to lift an object is given as $$W=mgh$$  Where m is mass, g=9.8 m/s and h is the height lifted.

What is the height of a 1.1kg box that takes 70 Joules of Work when it is lifted?

• 6.49m

• 77m

• 7.85m

• 623.6m

Multiple Choice

The equation for the area of a triangle is $$A=\frac{1}{2}bh$$  If a triangle has an area of 192 cm² and a height of 12 cm, what is the base of the triangle?

• 8cm

• 32cm

• 16cm

• 1152cm

Multiple Choice

The equation for the area of a triangle is A = 1/2 × b × h. Which of the following solutions is incorrect?

• $$A=\frac{b\times h}{2}$$  

• $$h=\frac{2A}{b}$$  

• $$\frac{\frac{1}{2}A}{h}=b$$  

• $$2A=b\times h$$  

Multiple Select

Boyes Law is an equation that relates the Pressure and Volume of a gas at a constant temperature. The Formula is $$P_iV_i=P_fV_f$$   Where P_i and V_i are the initial condition before the change. P_f and V_f are the final conditions after the change. Which expressions below are correct?

• $$P_i=\frac{P_fV_f}{V_i}$$  

• $$\frac{Pi}{P_f}=\frac{V_f}{V_i}$$  

• $$\frac{Pi}{P_f}=\frac{V_i}{V_f}$$  

• $$V_f=\frac{P_iV_i}{P_f}$$  

Multiple Choice

Boyes Law is an equation that relates the Pressure and Volume of a gas at a constant temperature. The Formula is $$P_iV_i=P_fV_f$$   Where P_i and V_i are the initial condition before the change. P_f and V_f are the final conditions after the change.

A gas occupies 11.2 liters at 0.860 atm. What is the final pressure if the volume becomes 15.0 L

• 1.15

• 0.642atm

• 195L 

• 29520L 

Multiple Choice

Boyes Law is an equation that relates the Pressure and Volume of a gas at a constant temperature. The Formula is $$P_iV_i=P_fV_f$$   Where P_i and V_i are the initial condition before the change. P_f and V_f are the final conditions after the change.

A gas occupies 12.3 liters at a pressure of 40.0 mmHg. What is the volume when the pressure is increased to 60.0 mmHg

• 8.2L 

• 18.45L 

• 195L 

• 29520L 

Multiple Choice

To convert from Celsius to Fahrenheit, the Formula $$F=\frac{9}{5}C+32$$  is used. If I wanted to solve for C, what would be the first step in rearranging to equation to solve for C?

• divide both sides by $$\frac{9}{5}$$  

• multiply both sides by $$\frac{5}{9}$$  

• Subtract 32 from both sides

• Distribute $$\frac{9}{5}$$   to 32

Multiple Choice

To conver from Celcius to Fahrenheit, the Formula $$F=\frac{9}{5}C+32$$  is used. After subtracting 32 from both sides, what should happen next to solve for C?

• divide both sides by $$\frac{5}{9}$$  

• multiply both sides by $$\frac{5}{9}$$  

• Multiply both sides by $$\frac{9}{5}$$  

• Subtract $$\frac{9}{5}$$  from both sides

Multiple Select

To conver from Celcius to Fahrenheit, the Formula $$F=\frac{9}{5}C+32$$  is used. Which are the correct solutions for C?

• $$C=\frac{5}{9}\left(F-32\right)$$  

• $$C=\frac{9}{5}\left(F-32\right)$$  

• $$C=\left(\frac{5}{9}F\right)-32$$    

• $$C=0.56\left(F-32\right)$$  

Multiple Choice

A polygon is named after the number of sides that it has(also the same as number of interior angles). Polygons that have more than 12 sides are called n-gons where n is the number of sides.

The formula $$S\ =\left(n-2\right)180$$   relates the Sum (S) to the number of sides(n). Which of the following equations is the correct solution for n?

• $$S-360=n$$  

• $$n=\frac{s+2}{180}$$  

• $$n=\frac{S}{180}+2$$  

• $$n=\frac{S}{180}-2$$  

Multiple Choice

The formula $$S\ =\left(n-2\right)180$$   relates the Sum (S) to the number of sides(n) for a polygon.

A polygon has a sum (S) of interior angles equal to 1800^o , how many sides (n) does the polygon have?

•  10

• 12 

• 8 

• 20

Multiple Select

The slope intercept equation $$y=m\left(x\right)+b$$   describes all the possible points with coordinates (x,y) that fall on the same line having slope y and y-axis intercept (0, b).

Which of the following solutions are correct?

• $$x=\frac{y-b}{m}$$  

• $$m=\frac{y-b}{x}$$  

• $$b=y-m\left(x\right)$$  

• $$\frac{y}{x}=m+b$$  

Multiple Choice

The slope intercept equation $$y=m\left(x\right)+b$$   describes all the possible points with coordinates (x,y) that fall on the same line having slope y and y-axis intercept (0, b).

If a line has a slope of 4, a y-intercept of 8 and the coordinates (1, y) Determine what value y must be. (Hint: solve for y)

• 1 

• 2 

• 12 

• $$\frac{1}{12}$$  

Multiple Choice

The slope intercept equation $$y=m\left(x\right)+b$$   describes all the possible points with coordinates (x,y) that fall on the same line having slope y and y-axis intercept (0, b).

A point (2, 10) is on a line with a y-intercept of 4. What is the slope of the line?

(hint: solve for m)

• 3 

• 7 

• 12

• 5 

Multiple Choice

The slope intercept equation $$y=m\left(x\right)+b$$   describes all the possible points with coordinates (x,y) that fall on the same line having slope y and y-axis intercept (0, b).

What is y-intercept of a line with a slope of -1 and passing through (1, 2)?

(hint: solve for b)

• 3 

• -1

• 2

• 1