Determine which characteristics are true of vertical angles.
1 answer:
Answer:
First option: Yes.
Second option: Yes.
Third option: No.
Fourth option: Yes.
Step-by-step explanation:
By definition, vertical angles are formed when two lines intersect.
They share a common vertex and they are non-adjacents angles (adjacent angles are those have a common side and a common vertex. They are supplementary, which means that their sum is 180°); therefore they are opposite to each other.
Vertical angles are congruent, which means that they have equal measure.
The sum of the two pairs of vertical angles formed by the intersection of the lines, is 360°.
Observe the intersecting lines"A" and "B" in the picture attached. Notice that four angles are formed.
Based on the characteristics of vertical angles, we can conclude that:
and
are vertical angles.
and
are vertical angles.
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Answer:
Part a) The budget is $40
Part b) The cost of one gallon of gasoline is $3.55 and the cost of the car wash is $8
Part c)
Part d) see the explanation
Step-by-step explanation:
The complete question in the attached figure
Part a) What is your budget?
The budget is given by the equation
y=40
therefore
The budget is $40
Part b) How much does a gallon of gasoline cost? how much does a car wash cost?
Let
y ------> the cost of a gallon of gasoline plus the cost of a car wash
x -----> the amount of gasoline in gallons
we have
y=3.55x+8
In this problem
For x=0
y=3.55(0)+8=8
The y-intercept is the cost of the car wash
so
The cost of the car wash is $8
Find the cost of one gallon of gasoline
we know that
The slope of the linear equation is
m=$3.55 per gallon
therefore
The cost of one gallon of gasoline is $3.55
Part c) Write an inequality that represent the possible amounts of gasoline you can buy
we have
Solve for x
Part d) Use the graph to estimate the solution of the inequality in part c)
we have the system
y=40
y=3.55x+8
The solution of the system is the intersection point both graphs
Looking at the graph the intersection point is about (9,40)
That means ----> The maximum amount of gasoline you can buy with the budget is about 9 gallons
