Point (1, -4)
Slope=1/2
y=mx+c
y=1/2x +c
-4=1/2(1)+c
-4=1/2+c
c=-4-1/2
c=-4 1/2
y=
Slope=1/2
y=mx+c
y=1/2x +c
-4=1/2(1)+c
-4=1/2+c
c=-4-1/2
c=-4 1/2
y=
34.98×104= -------------
1 answer:
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Answer:
The area of the triangle formed by origin, and the points (4,5) and (-2,5) will be 15 sq. units.
Step-by-step explanation:
The two parabolas are and y = x² - 2x - 3.
Now, solving those two equations we will get the points of intersection.
So,
⇒ - (x - 1)² + 24 = 3x² - 6x - 9
⇒ -x² + 2x - 1 + 24 = 3x² - 6x - 9
⇒ 4x² - 8x - 32 = 0
⇒ x² - 2x - 8 = 0
⇒ x² - 4x + 2x - 8 = 0
⇒ (x - 4)(x + 2) = 0
So, x = 4 or - 2.
Now, for x = 4 , y = 4² - 2(4) - 3 = 5 and the point of intersection is (4,5).
Or, for x = - 2, y = (- 2)² - 2(- 2) - 3 = 5 and the point of intersection is (-2,5).
Now, points (4,5) and (-2,5) make a straight line parallel to the x-axis at a perpendicular distance of 5 units from origin and its length is (4 - (- 2)) = 6 units.
So, the area of the triangle formed by origin, and the points (4,5) and (-2,5) will be = 0.5 × 5 × 6 = 15 sq. units. (Answer)
2x + 4 > 8
Step 1: Subtract 4 from both sides.
2x + 4 − 4 > 8 − 4
2x > 4
Step 2: Divide both sides by 2.
2x/2 > 4/2
x > 2
2x − 3 < 5
Step 1: Add 3 to both sides.
2x − 3 + 3 < 5 + 3
2x < 8
Step 2: Divide both sides by 2.
2x/2 < 8/2
x < 4
