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Here is some recommended reading before getting started with this lesson.
Consider △ABC with side lengths a, b, and c.
Maya plans to jog 150 meters at a constant speed of 2.5 meters per second.
The distance traveled d is found using the following equation.Equivalent equations have the same solution(s). Use the Properties of Equality and inverse operations to solve for the variable t.
Each equation will be solved for t, and then the solutions will be compared.
LHS−7=RHS−7
Commutative Property of Addition
Subtract terms
LHS/(-1)=RHS/(-1)
-b-a=ba
Put minus sign in front of fraction
1a=a
LHS/5=RHS/5
Calculate quotient
ca⋅b=ca⋅b
aa=1
Identity Property of Multiplication
Rearrange equation
While at the planetarium on Saturday, Dominika learns about Annie Jump Cannon, known as the census taker of the sky,
who introduced the Harvard Spectral Classification. In its simplest form, this system classifies stars according to their surface temperatures.
Stellar Classification | ||
---|---|---|
Class | Temperature (K) | Apparent Color |
O | ≥30000 | blue |
B | 10000−30000 | blue white |
A | 7500−10000 | white |
F | 6000−7500 | yellow white |
G | 5000−6000 | yellow |
K | 3500−5000 | light orange |
M | 2000−3500 | orange red |
LHS−273=RHS−273
LHS⋅59=RHS⋅59
LHS+32=RHS+32
Rearrange equation
K=3500
Subtract term
ca⋅b=ca⋅b
Calculate quotient
Add terms
Round to nearest integer
K=5000
Subtract term
ca⋅b=ca⋅b
Calculate quotient
Add terms
Round to nearest integer
Use the Properties of Equality to solve the given literal equation for the indicated variable. Some equations may require dividing both sides of the equation by a variable. Since division by zero is not defined, for these equations assume that the variable is not equal to 0.
On Sunday Dominika spends time on her hobby, which is candle making. She uses 170 cubic centimeters of wax to produce a cylindrical candle of radius 3 centimeters.
The volume of a cylinder with radius r and height h is given by the following formula.LHS/πr2=RHS/πr2
Cancel out common factors
Simplify quotient
Rearrange equation