Sign In
| 10 Theory slides |
| 13 Exercises - Grade E - A |
| Each lesson is meant to take 1-2 classroom sessions |
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.
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.
LHS/πr2=RHS/πr2
Cancel out common factors
Simplify quotient
Rearrange equation
Time (s) | Distance Traveled (m) |
---|---|
10 | 25 |
20 | 50 |
30 | 75 |
40 | 100 |
50 | 125 |
60 | 150 |
It takes Maya 60 seconds to run 150 meters.
Time (s) | Speed × Time | Distance Traveled (m) |
---|---|---|
10 | 2.5(10)=25 | 25 |
20 | 2.5(20)=50 | 50 |
30 | 2.5(30)=75 | 75 |
40 | 2.5(40)=100 | 100 |
50 | 2.5(50)=125 | 125 |
60 | 2.5(60)=150 | 150 |
Maya will run 150 meters in 60 seconds at a speed of 2.5 meters per second.
LHS/v=RHS/v
Cancel out common factors
Simplify quotient
Rearrange equation
The Colombian national cycling team is training by riding up and down steep hills. The uphill distance is the same as the downhill distance.
The speed r is calculated by dividing the distance traveled d by the time t. r=d/t We know that the distance up the hill is the same as the distance down the hill. If we call this distance x, we can write the following expressions for the time it takes to cycle up and down the hill.
Distance | r=d/t |
---|---|
Up | 15=x/t_1 |
Down | 27=x/t_2 |
Let's solve these equations for t. 15=x/t_1 ⇒ t_1=x/15 [1em] 27=x/t_2 ⇒ t_2=x/27 Note that the total distance the cyclist travels is 2x. By dividing the total distance by the sum of the times, we can determine the average speed of the lead cyclist.
This is the average speed for both distances.
We have several a-variables on both sides of the equations. We can get rid of the fraction on the right-hand side by multiplying both sides by a.
According to the multiplicative inverse, we can raise both sides to the exponent 67. Doing this will get a on the left-hand side alone.
The answer is D.
A five-pointed star is inscribed in a circle.
We first isolate the radical expression. To do so, we will multiply both sides by c and divide by a and r^2.
To remove the radical sign, we need to take square of both sides of the equation.
We can further simplify the right-hand side.