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Answer:
Option 3: (5, 1)
Step-by-step explanation:
There are several ways of solving for systems of linear equations, either through graphing, substitution, or elimination.
The graphing method is the easiest, as you only need to plot points on the graph using the y-intercepts and the slopes.
I will be demonstrating the <u>graphing method</u>.
Given the systems of linear equations:
Equation 1: y = x - 4
where the <u>slope</u>, <em>m</em> = 1, and <u>y-intercept </u>(0, -4).
Equation2: y = -x + 6
where the <u>slope</u>, <em>m </em>= -1, and <u>y-intercept</u> (0, 6).
The y-intercept is the point on the graph where it crosses the y-axis, and has coordinates of (0, b).
<h3>Graphing Instructions:</h3>For Equation 1, plot the y-intercept, (0, -4) on the graph. Then use the <u>slope</u>, m = 1 (rise 1 unit, run 1 unit) to plot other points on the graph. Repeat this process until you have enough points to connect a line with.
Repeat these same procedures for graphing Equation 2, start by plotting its y-intercept at (0, 6), and its slope, m = -1 (down 1 unit, run 1 unit).
<h3>Solution: </h3>
The intersection of both lines occurs at point, (5, 1), which is solution to the given systems of linear equations. Therefore, the correct answer is the third option, (5, 1).
Attached is the screenshot of the graphed systems of linear equations, where it shows the point of intersection at (5, 1).
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Answer:
- 9.5
- maximum, 34.5, 5
- 10.9
Step-by-step explanation:
I find it convenient to use a graphing calculator to graph the function.
The "start" is x=0, where the distance from the sprinkler head is 0 feet. The value of h(0) is 9.5, the height of the sprinkler head.
- The irrigation system is positioned <u> 9.5 </u> feet above the ground.
The graph shows the vertex of the curve is (5, 34.5), meaning that a height of 34.5 feet is reached 5 feet horizontally from the sprinkler.
- The spray reaches a <u> maximum </u> height of <u> 34.5 </u> feet at a horizontal distance of <u> 5 </u> feet away from the sprinkler head.
- The spray reaches all the way to the ground at about <u> 10.9 </u> feet away.
The graph shows the x-intercept at about 10.9. That is where the height of the spray is 0 feet above the ground.
