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Core Connections Algebra 2, 2013
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Core Connections Algebra 2, 2013 View details
1. Section 4.1
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Exercise 32 Page 177

Practice makes perfect
a To solve the given literal equation for y, we will use the Properties of Equality to apply inverse operations to the equation. Remember, only like terms can be combined.
5x-3y=12
AddEqn

LHS+3y=RHS+3y

5x=3y+12
SubEqn

LHS-12=RHS-12

5x-12=3y
DivEqn

.LHS /3.=.RHS /3.

5x-12/3=y
RearrangeEqn

Rearrange equation

y=5x-12/3
b To solve the given literal equation for m_2, we will use the Properties of Equality to apply inverse operations to the equation. Remember, only like terms can be combined.
F=Gm_1m_2/r^2
MultEqn

LHS * r^2=RHS* r^2

Fr^2=Gm_1m_2
DivEqn

.LHS /Gm_1.=.RHS /Gm_1.

Fr^2/Gm_1=m_2
RearrangeEqn

Rearrange equation

m_2=Fr^2/Gm_1
c To solve the given literal equation for m, we will use the Properties of Equality to apply inverse operations on the equation. Remember, only like terms can be combined.
E=1/2mv^2
DivEqn

.LHS /v^2.=.RHS /v^2.

E/v^2=1/2m
MoveRightFacToNum

a/c* b = a* b/c

E/v^2=m/2
MultEqn

LHS * 2=RHS* 2

2*E/v^2=m
MoveLeftFacToNum

a*b/c= a* b/c

2E/v^2=m
RearrangeEqn

Rearrange equation

m=2E/v^2
d To solve the given literal equation for y, we will use the Properties of Equality to apply inverse operations on the equation. Remember, only like terms can be combined.
(x-4)^2+(y-1)^2=10
SubEqn

LHS-(x-4)^2=RHS-(x-4)^2

(y-1)^2=10-(x-4)^2
SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt((y-1)^2)=sqrt(10-(x-4)^2)
SqrtToAbs

sqrt(a^2)=|a|

|y-1|=sqrt(10-(x-4)^2)
We have that the absolute value of y-1 is equal to sqrt(10-(x-4)^2). This means that we have two solutions, one positive and one negative. |y-1|=sqrt(10-(x-4)^2) ⇕ lc y-1 ≥ 0:y-1 = sqrt(10-(x-4)^2) & (I) y-1 < 0:y-1 = - (sqrt(10-(x-4)^2)) & (II) Now we can fully isolate y.
y-1=sqrt(10-(x-4)^2) y-1=-sqrt(10-(x-4)^2)
AddEqn

LHS+1=RHS+1

y=1+sqrt(10-(x-4)^2) y=1-sqrt(10-(x-4)^2)
Subchapter links expand_more
arrow_right 4.1.1 Strategies for Solving Equations p.171-172
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Strategies for Solving Equations 10 (Page 171)
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Strategies for Solving Equations 12 (Page 172)
Strategies for Solving Equations 13 (Page 172)
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arrow_right 4.1.2 Solving Equations and Systems Graphically p.176-178
Solving Equations and Systems Graphically 22 (Page 176)
Solving Equations and Systems Graphically 23 (Page 176)
Solving Equations and Systems Graphically 24 (Page 176)
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Solving Equations and Systems Graphically 27 (Page 176)
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Solving Equations and Systems Graphically 29 (Page 176)
Solving Equations and Systems Graphically 30 (Page 177)
Solving Equations and Systems Graphically 31 (Page 177)
Solving Equations and Systems Graphically 32 (Page 177)
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Solving Equations and Systems Graphically 34 (Page 177)
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arrow_right 4.1.3 Finding Multiple Solutions to Systems of Equations p.180-181
Finding Multiple Solutions to Systems of Equations 40 (Page 180)
Finding Multiple Solutions to Systems of Equations 41 (Page 180)
Finding Multiple Solutions to Systems of Equations 42 (Page 180)
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Finding Multiple Solutions to Systems of Equations 44 (Page 181)
Finding Multiple Solutions to Systems of Equations 45 (Page 181)
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arrow_right 4.1.4 Using Systems of Equations to Solve Problems p.184
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Using Systems of Equations to Solve Problems 53 (Page 184)
Using Systems of Equations to Solve Problems 54 (Page 184)
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