For the graph below, what should the domain be so that the function is at least 200? (1 point) 350+

300

250 +

200

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300

250 +

200

−5 ≤ x ≤ 20

Step-by-step explanation:

0 is less than or equal to x is than or equal to 15, B is the correct answer!

Y = -2x^2 + 50x + 300

-2x^2 + 50x + 300 ≥ 300

-2x^2 + 50x ≥ 0

-2x^2 ≥ -50x

x^2 ≤ 25x

x ≤ 25

Therefore, required domain is 0 ≤ x ≤ 25

[tex]0\leq x\leq 15[/tex]

Step-by-step explanation:

Given is the graph with equation

[tex]y=-2x^2+30x+200[/tex]

This should be atleast 200 implies[tex]-2x^2+30x+200\geq 200\\x(-2x+30)\geq 0[/tex]

This is the product of two numbers hence would be positive only if either both are positive or both are negative

Case I: Both positive .

[tex]x\geq 0 and -2x+30\geq 0\\0\leq x\leq 15[/tex]

Case II: Both negative

Then we get

[tex]x\leq 0 and -2x+30\leq 0\\\\x\leq 0 and x\geq 15[/tex]

This is inconsistent as a value cannot be less than 0 and greater than 15

So solution is

[tex]0\leq x\leq 15[/tex]

Y = 2x² + 30x + 200

y = 2(x² + 15x + 100)

x² = x*x

100 ⇒ 1 x 100 ; 2 x 50 ; 4 x 25 ; 5 x 20 ; 10 x 10

200 = 2x² + 30x + 200

0 = 2x² + 30x + 200 - 200

0 = 2x² + 30x + 0

0 = 2(x² + 15x + ?)

−5 ≤ x ≤ 20

The first interval:0 ≤ x ≤ 20

Procedure

You have to solve this inequality

-2x^2 +40x +600 ≥ 600

-2x^2 +40x ≥ 0

-x^2+20x ≥ 0

x^2 - 20 x ≤ 0

x(x-20) ≤ 0

That is only possible if the two factors have different signs.

Let's examine the possibilities

x ≥ 0 and x -20 ≤ 0⇔x≤20, that is 0≤x≤20

The other possibility is

x ≤ 0 and x - 20 ≥ 0 ⇔x≥20. This conditions is not possible.

So the solution is 0≤x≤20

21

Step-by-step explanation:

idk

Option C. 0≤x≤25

Step-by-step explanation:

we know that

The function f(x) of the graph is a vertical parabola open down

If the function is at least 300

then

[tex]f(x)\geq 300[/tex]

The solution is the shaded area above the solid line f(x)=300

In the graph plot f(x)=300 and find the value of x

The values of x are

[tex]x=0, x=25[/tex]

see the attached figure

therefore

The interval is ------> [0,25]

All real numbers greater than or equal to zero and less than or equal to 25

[tex]For the graph below, what should the domain be so that the function is at least 300? a.) x≥0 b.) -5[/tex]

The domain of the function so that the function is at least 300 is:

0 ≤ x ≤ 25

Step-by-step explanation:

We are given graph of the function y as:

[tex]y =-2x^2+50x+300[/tex]

[tex]-2x^2+50x+300\geq 300[/tex]

on subtracting both side of the inequality by 300 we obtain:

[tex]-2x^2+50x\geq 0[/tex]

[tex]-2x(x-25)\geq 0[/tex]

This inequality is obtained when one of the term is positive and the other is negative:

i.e. if x≥0

and x-25≤0

i.e. x≤25 then the product :

-2x(x-25)≥0.

Hence, the domain is:

0 ≤ x ≤ 25