In a 30° -60° -90° triangle, what is the length of the hypotenuse when the shorter leg is 8 m? Enter your answer in the box.
1 answer:
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Answer:
Option C. No solution is the right answer.
Step-by-step explanation:
Here the given equations are y = x²+2x+3 -----(1)
and y = 4x-2 -------(2)
Now we substitute the value of y from equation 2 into 1.
x²+2x+3 = 4x-2
x²+2x+3-2x = 4x-2-2x
x²+3 = 2x-2
x²+3-2x = 2x-2x-2
x²-2x+3 = -2
x²-2x+5 = 0
Then value of
Since in this solution √(-20) is not defined. Therefore there is no solution.
Answer:
- B) One solution
- The solution is (2, -2)
- The graph is below.
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Explanation:
I used GeoGebra to graph the two lines. Desmos is another free tool you can use. There are other graphing calculators out there to choose from as well.
Once you have the two lines graphed, notice that they cross at (2, -2) which is where the solution is located. This point is on both lines, so it satisfies both equations simultaneously. There's only one such intersection point, so there's only one solution.
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To graph these equations by hand, plug in various x values to find corresponding y values. For instance, if you plugged in x = 0 into the first equation, then,
y = (-3/2)x+1
y = (-3/2)*0+1
y = 1
The point (0,1) is on the first line. The point (2,-2) is also on this line. Draw a straight line through the two points to finish that equation. The other equation is handled in a similar fashion.
