Which diagram shows lines that must be parallel lines cut by a transversal
2 answers:
Answer: The answer is the first diagram.
Step-by-step explanation: We are given two diagrams out of which we are to select the one which shows lines must be parallel lines cut by a transversal.
In the first figure, the sum of two interior angles is given by
which shoes that the two lines which cut by a transversal are parallel. So, this option is correct.
In the second figure, the sum of two angles on a straight line is given by
which shows that a straight angle is of measure 180°, which does not have any relation in proving the two lines to be parallel. So, this diagram is not correct.
Thus, the first diagram is the correct option.
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Answer:
(a) (5, -3)
Step-by-step explanation:
The "substitution method" for solving a system of equations requires that you write an expression that can be substituted for a variable in one or more of the other equations in the system.
<h3>Expression to substitute</h3>The given equations are ...
- y = x -8
- 2x +3y = 1
We notice the first equation gives an expression for y. This is exactly what we want to substitute for y in the second equation.
<h3>Substitution</h3>When the expression (x-8) is substituted for y in the second equation, you get ...
2x +3(x -8) = 1
This simplifies to ...
5x -24 = 1
<h3>Solution</h3>This 2-step equation can now be solved in the usual way:
5x = 25 . . . . . . add 24 to isolate the variable term
x = 25/5 = 5 . . . . . divide by the coefficient of x
Note that we now know what the correct answer choice is.
Using the expression for y, we find ...
y = x -8 = 5 -8 = -3
The solution is (x, y) = (5, -3).
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The attached graph confirms this solution.
Answer:
<em>The compound inequality that shows the voltage amount the necessary range is </em>
Step-by-step explanation:
Loni needs between 3.5 and 7.2 volts of energy, not inclusive, to make an experiment work correctly.
That means, <u>the voltage amount should be either greater than 3.5 volts or less than 7.2 volts</u>.
Suppose, the amount of voltage is volts to make the experiment work correctly.
Now, Voltage amount is greater than 3.5 volts means: or
and voltage amount is less than 7.2 volts means:
Thus, the compound inequality by combining the above two inequalities will be: