Given the number line which inequality has the solution shown below

Mathematics

1 answer:

Lena [83]2 years ago

8 0

Answer:

Step-by-step explanation:

When you simplify the expression you start by subtracting 5 from both sides. This gives you 0.2x > -3. Then to isolate "x" you divide both sides by 0.2. This gives you x > -15, which is shown in the number line.

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3 0

3 years ago

Graph the function y = x3 + 3x2 – x – 3. Which lists all of the turning points of the graph? (–3, 0) and (1, 0) (–2, 3) and (0,

Vlada [557]

Answer with explanation:

The given function is:

y=x³+3 x²-x-3

=x²(x+3) -1(x+3)

= (x²-1)(x+3)

= (x-1)(x+1)(x+3)

Put, y=0 , gives

⇒ (x-1)(x+1)(x+3)=0

≡→x-1=0 ∧ → x+1=0 ∧→x+3=0

≡x=1, -1, -3

So, there are three breaking points in the curve.

1.⇒Putting, x=1 , in the function

y(1)=1³+3×1²-1 -3

=1 +3-4

2. ⇒Putting, x=-1 , in the function

y(-1)=(-1)³+3×(-1)²-(-1) -3

= -1 +3+1-3

3.⇒Putting, x=-3 , in the function

y(-3)=(-3)³+3×(-3)²-(-3) -3

=-27+27+3-3

So, These are points where curve crosses the X axis, which are , (1,0),(-1,0) and (-3,0).

But turning points are those points where curve takes the turn , that is, if it is increasing function then it starts decreasing or becomes constant function after that point, and if it is a decreasing function then it becomes increasing or constant function.

So,turning points of the given function by looking at the graph of the function by approximation

Option B:→(-2,3) and (0, -3)