Answer:
Answer is in the explanation
Step-by-step explanation:
I don't know exactly word from word what your choices look like...
but I can describe per each box what happened in my own words:
First box: They multiply first equation by 3 and the second equation by 2 to obtain the equations in that first box.
Second box: They subtracted the two equations in the first box to obtain 1x+0y=2 which means 1x=2 or x=2 (this is called solving a system by elimination
Third box: They used their first original equation (before the multiplication manipulation) and plug in the value they got for x which was 2 giving them 3(2)-2y=10
Fourth box: They simplified the equation 3(2)-2y=10 by performing the multiplication 3(2) giving them 6-2y=10
Fifth box: They subtracted 6 on both sides giving them -2y=4
Sixth box: They divided both sides by -2 giving them y=-2
I will summarize then what I wrote above:
1st box: Multiplication Property of Equality
2nd box: Elimination
3rd box: Substitution (plug in)
4th box: Simplifying
5th box: Subtraction Property of Equality
6th box: Division Property of Equality
Answer:
a. 1.2 minutes
b. 0.83 laps
c. 25.2 minutes
Step-by-step explanation:
Lin runs 5 laps around a track in 6 minutes.
a. How many minutes per lap is that?
5 laps = 6 minutes
1 laps = x minutes
Cross Multiply
x minute × 5 laps = 6 minutes × 1 laps
x minute = 6 minutes × 1 laps/5 laps
x laps = 1.2 minutes
Hence, it is 1.2 minutes per lap
b. How many laps per minute is that?
6 minutes = 5 laps
1 minute = x laps
Cross Multiply
6 minutes × x laps = 1 minute × 5 laps
x laps = 1 minute × 5 laps/6 minutes
x laps = 0.8333333333 laps
Hence, it is 0.83 laps per minute.
c. If Lin runs 21 laps at the same rate,
5 laps = 6 minutes
21 laps = x minutes
Cross Multiply
x minute × 5 laps = 6 minutes × 21 laps
x minute = 6 minutes × 21 laps/5 laps
x laps = 25.2 minutes
Hence, it takes her 25.2 minutes
Answer:
#6 is called exponent
Step-by-step explanation:
(x,y) is a pair of real numbers. The meaning is: (x,y) is an ordered pair of numbers belonging to R×R=R2 .
Answer:
The answer to your question is car 1 = 30 gal and car 1 = 20 gal
Step-by-step explanation:
car 1 = a
car 2 = b
Efficiency of car 1 = 35 mi/gal
Efficiency for car 2 = 20 mi/gal
Total distance = 1450
Total gas consumption = 50 gal
Equations
35a + 20b = 1450 ------- (I)
a + b = 50 ------- (II)
Solve by elimination
Multiply equation II by -35
35a + 20b = 1450
-35a - 35b = -1750
Simplify
0 - 15b = -300
Solve for b
b = -300/-15
Result
b = 20
Substitute b in equation II to find a
a + 20 = 50
Solve for a
a = 50 -20
Result
a = 30
