15 POINTS,ANSWER QUICKLY Think about all of the ways in which a line and a parabola can intersect. Select all of the number of w
ays in which a line and a parabola can intersect.
2 answers:
<u>Answer:</u>
3 ways
<u>Explanation:</u>
We know that a parabola has a second degree equation), while a line has a first degree equation.
To get the points of intersection, we will need to solve both simultaneously.
Solving them, we can reach a maximum of two solutions, however, other scenarios are also possible.
<u>Possible scenarios:</u>
1- no intersection occurs as shown in the first attachment
2- one intersection occurs as shown in the second attachment
3- two intersections occur as shown in the third attachment
Based on the above, there are three ways where the line and parabola can intersect
Hope this helps :)
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<h3>Given</h3>
trapezoid PSTK with ∠P=90°, KS = 13, KP = 12, ST = 8
<h3>Find</h3>the area of PSTK
<h3>Solution</h3>It helps to draw a diagram.
∆ KPS is a right triangle with hypotenuse 13 and leg 12. Then the other leg (PS) is given by the Pythagorean theorem as
... KS² = PS² + KP²
... 13² = PS² + 12²
... PS = √(169 -144) = 5
This is the height of the trapezoid, which has bases 12 and 8. Then the area of the trapezoid is
... A = (1/2)(b1 +b2)h
... A = (1/2)(12 +8)·5
... A = 50
The area of trapezoid PSTK is 50 square units.