Upper A 4-ft-tall fence runs parallel to the wall of a house at a distance of 8 ft. Find the length of the shortest ladder that
1 answer:
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Answer:
Step-by-step explanation:
x = measure of the first angle
y = measure of the second angle
z = measure of the third angle
The sum of the measures of the second and third (y+z) is five times the measure of the first angle (=5x)
The third angle is 14 more than the second
And remember that the sum of these three angles must be equal to 180.
Let's take these equations
If you take a look at the first equation, we have y+z = 5x and we have y+z in the third equation as well, we can replace that....
Distribute the + sign
Combine like terms;
Divide by 6.
We have now defined that the measure of the first angle is 30º.
Let's take another equation... for example
I'm going to take this one because if I replace x and z in the third equation, all I'll have left will be y.
Distribute the + sign and Combine like terms;
Subtract 44 to isolate 2y.
Now divide by 2.
We already have the value of x and y. Once again, replacing this in the third equation will leave us with z to solve for.
Answer:
2.Both boundary lines are solid.
3.A solution to the system is (1, 3)
5.The boundary lines intersect.
Step-by-step explanation:
we have
----> inequality A
The solution of the inequality A is the shaded area below the solid line
The slope of the solid line is 3
The point (1,3) is a solution of inequality A (lie in the shaded area of the solution set)
----> inequality B
The solution of the inequality B is the shaded area above the solid line
The slope of the solid line is -1
The point (1,3) is a solution of inequality B (lie in the shaded area of the solution set)
The solution of the system of inequalities is the shaded area between the two solids lines
see the attached figure
<u><em>Verify each statement</em></u>
1.The slope of one boundary line is 2
The statement is False
2.Both boundary lines are solid.
The statement is True
3.A solution to the system is (1, 3)
The statement is True
4.Both inequalities are shaded below the boundary lines
The statement is False
5.The boundary lines intersect.
The statement is True
The intersection point is (0.25,1.75)
see the attached figure
