I need help pls 3(2x + 5) ≥ 2(x + 6)

Mathematics

2 answers:

svetlana [45]2 years ago

8 0

Answer:

-3(2x-5)<5(2-x)

Step-by-step explanation:

hope this helps

Natasha_Volkova [10]2 years ago

5 0

Answer:

x ≥ -3/4

Step-by-step explanation:

3(2x + 5) ≥ 2(x + 6)

Distribute

6x+15 ≥ 2x + 12

Subtract 2x from each side

6x-2x+15 ≥ 2x-2x + 12

4x+15 ≥ 12

Subtract 15 from each side

4x+15-15 ≥ 12-15

4x ≥ -3

Divide each side by 4

4x/4 ≥ -3/4

x ≥ -3/4

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A parabola has a focus of F(2, -0.5) and a directrix of y=-1.5 P(x,y) represents any point on the parabola, while D(x, -1.5) rep

prohojiy [21]

The sketch of the parabola is attached below

We have the focus $(a,b) = (2, -0.5)$
The point $P(x,y)$
The directrix, c at $y=-1.5$

The steps to find the equation of the parabola are as follows

Step 1
Find the distance between the focus and the point P using Pythagoras. We have two coordinates; $(2, -0.5)$ and $(x,y)$ .
We need the vertical and horizontal distances to find the hypotenuse (the diagram is shown in the second diagram).
The distance between the focus and point P is given by
$\sqrt{ (x-a)^{2}+ (y-b)^{2} }$

Step 2
Find the distance between the point P to the directrix $c$ . It is a vertical distance between y and c, expressed as $y-c$

Step 3
The equation of parabola is then given as
$\sqrt{ (x-a)^{2}+ (y-b)^{2} }$ = $y-c$
$(x-a)^{2}+ (y-b)^{2}= (y-c)^{2}$ ⇒ substituting a, b and c
$(x-2)^{2}+ (y--0.5)^{2} = (y--1.5)^{2}$
$(x-2)^{2}+ (y+0.5)^{2}= (y+1.5)^{2}$ ⇒Rearranging and making $y$ the subject gives

$y= \frac{ x^{2} }{2} -2x+1$