Warm Up - PBworks

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2-5 Solving for a Variable Warm Up Solve each equation. 1. 5 + x = –2 2. 8m = 43 3. 4. 0.3s + 0.6 = 1.5 5. 10k – 6 = 9k + 2

Transcript of Warm Up - PBworks

2-5 Solving for a Variable

Warm Up Solve each equation.

1. 5 + x = –2 2. 8m = 43

3.

4. 0.3s + 0.6 = 1.5

5. 10k – 6 = 9k + 2

2-5 Solving for a Variable

1. Students will use formulas to solve application problems

2-3. Students will solve a formulas and literal equations for a variable

Learning Goals

2-5 Solving for a Variable

A formula is an equation that states a rule for a relationship among quantities.

In the formula d = rt, d is isolated. You can "rearrange" a formula to isolate any variable by using inverse operations. This is called solving for a variable.

2-5 Solving for a Variable

Solving for a Variable Step 1 Locate the variable you are asked to

solve for in the equation. Step 2 Identify the operations on this

variable and the order in which they are applied.

Step 3 Use inverse operations to undo operations and isolate the variable.

2-5 Solving for a Variable

Example 1: Application The formula C = πd gives the circumference of a circle C in terms of diameter d. The circumference of a bowl is 18 inches. What is the bowl's diameter? Leave the symbol π in your answer.

2-5 Solving for a Variable

In 2004, Ernst Van Dyk won the wheelchair race of the Boston Marathon with a time of about 1.3 hours. The race was about 26.2 miles. What was his average speed? Use the formula d = rt and round your answer to the nearest tenth.

2-5 Solving for a Variable

Solve the formula d = rt for t. Find the time in hours that it would take Ernst Van Dyk to travel 26.2 miles if his average speed was 18 miles per hour.

Construction The formula a = 46c gives the floor area a in square meters that can be wired using c circuits.

a. Solve a = 46c for c.

b. If a room is 322 square meters, how many circuits are required to wire this room?

2-5 Solving for a Variable

Construction The formula a = 46c gives the floor area a in square meters that can be wired using c circuits.

a. Solve a = 46c for c.

b. If a room is 322 square meters, how many circuits are required to wire this room?

2-5 Solving for a Variable

Example 2A: Solving Formulas for a Variable

The formula for the area of a triangle is A = bh, where b is the length of the base, and is the height. Solve for h.

2-5 Solving for a Variable

Dividing by a fraction is the same as multiplying by the reciprocal.

Remember!

2-5 Solving for a Variable

Example 2B: Solving Formulas for a Variable The formula for a person’s typing speed is

,where s is speed in words per minute, w is number of words typed, e is number of errors, and m is number of minutes typing. Solve for e.

2-5 Solving for a Variable

Example 2B: Solving Formulas for a Variable The formula for a person’s typing speed is

,where s is speed in words per minute, w is number of words typed, e is number of errors, and m is number of minutes typing. Solve for w.

2-5 Solving for a Variable

The formula for an object’s final velocity is

f = i – gt, where i is the object’s initial velocity, g is acceleration due to gravity, and t is time. Solve for i.

The formula for the volume of a rectangular prism with length l, width w, and height h is V = lwh.

Solve this formula for w.

The formula for a Fahrenheit temperature in terms of degrees Celsius is

Solve for C. F = 95C +32

2-5 Solving for a Variable

The formula for an object’s final velocity is

f = i – gt, where i is the object’s initial velocity, g is acceleration due to gravity, and t is time. Solve for i.

2-5 Solving for a Variable

The formula for the volume of a rectangular prism with length l, width w, and height h is V = lwh.

Solve this formula for w.

2-5 Solving for a Variable

The formula for a Fahrenheit temperature in terms of degrees Celsius is

Solve for C.

F = 95C +32

2-5 Solving for a Variable

A formula is a type of literal equation. A literal equation is an equation with two or more variables. To solve for one of the variables, use inverse operations.

2-5 Solving for a Variable

Example 3: Solving Literal Equations A. Solve x + y = 15 for x. B. Solve pq = x for q.

2-5 Solving for a Variable

a. b.

c. Solve m - n = 5 for m. d. Solve m= x for k k

Solve 5 – b = 2t for t. Solve for V

e. f.

g. Solve f + 4 g

h. Solve b + c = 10 for a. a

Solve st + 3t = 6 for s m - 4n = 8 for m

= 6 for f

2-5 Solving for a Variable

a. b.

c. Solve m - n = 5 for m. d. Solve m= x for k k

Solve 5 – b = 2t for t. Solve for V

2-5 Solving for a Variable

e. f.

g. Solve f + 4 g

h. Solve b + c = 10 for a. a

Solve st + 3t = 6 for s m - 4n = 8 for m

= 6 for f

2-5 Solving for a Variable

Lesson Quiz: Part 1 Solve for the indicated variable.

1.

2.

3. 2x + 7y = 14 for y

4.

P = R – C for C

for m

5. for C

for h

2-5 Solving for a Variable

Lesson Quiz: Part 2

Euler’s formula, V – E + F = 2, relates the number of vertices V, the number of edges E, and the number of faces F of a polyhedron.

6. Solve Euler’s formula for F.

7. How many faces does a polyhedron with 8 vertices and 12 edges have?

F = 2 – V + E

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