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3 years ago

PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Mathematics

1 answer:

Vinvika [58]3 years ago

7 0

X/6 + 4 ≥ 2

x/6 ≥ 2 - 4

x/6 ≥ -2

x ≥ -2 × 6

x ≥ -12

hope that helps, God bless!

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WILL CHOOSE BRAINLIEST!!!

dsp73

Answer:

Step-by-step explanation:

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Start 21,200%

End 9,900%

Percentage with triazine resistance

Start 28,800%

End 35,100%

7 0

3 years ago

Factor f(x)=x4-x3-7x2+13x-6 completely. Then Sketch the graph

Dennis_Churaev [7]

ANSWER TO QUESTION 1

$f(x)=(x-2)(x+3)(x-1)^2$ .

EXPLANATION

The function given to us is,

$f(x)=x^4-x^3-7x^2+13x-6$

According to rational roots theorem,

$\pm1,\pm2,\pm3,\pm6$ are possible rational zeros of

$f(x)=x^4-x^3-7x^2+13x-6$ .

We find out that,

$f(-3)=(-3)^4-(-3)^3-7(-3)^2+13(-3)-6$

$f(-3)=81+27-63-39-6$

$f(-3)=6-6$

$f(-3)=0$

Also

$f(2)=(2)^4-(2)^3-7(2)^2+13(2)-6$

$f(2)=16-8-28+26-6$

$f(2)=6-6$

$f(2)=0$

This implies that

$x-2 and x+3$ are factors of

$f(x)=x^4-x^3-7x^2+13x-6$ and hence $(x-2)(x+3)=x^2+x-6$ is also a factor.

We perform the long division as shown in the diagram.

Hence,

$f(x)=(x-2)(x+3)(x-1)^2$ .

ANSWER TO QUESTION 2

Sketching the graph

We can see from the factorization that the roots

$x=2$ and $x=-3$ have a multiplicity of 1, which is odd. This means that the graph crosses the x-axis at this intercepts.

Also the root $x=1$ has a multiplicity of 2, which is even. This means the graph does not cross the x-axis at this intercept.

Now we determine the position of the graph on the following intervals,

$x\le -3$

$f(-4)=(-4)^4-(-4)^3-7(-4)^2+13(-4)-6$

$f(-4)=150\:>0$

$-3\le x \le 1$

$f(0)=-6\:$

$1\le x\le 2$

$f(1.5)=-0.56\:$

$x \ge 2$

$f(3)=24\:>0$

We can now use these information to sketch the function as shown in diagram

4 0

3 years ago

1/6(x-5)=1/2(x+6) help

anygoal [31]

Answer: x= -23/2

Step-by-step explanation:

multiply both sides of the equation by 6

x-5=3(x+6)

distribute 3

x-5=3x+18

move variables to lest-hand side and change sign

x-3x=18+5

like terms

-2x=23

the divide both sides by -2

x= -23/2

7 0

3 years ago

I need someone to help me find the missing value please.

jekas [21]

Answer:

Step-by-step explanation:

Note the relation between x and y

The values of y are 2 less than the corresponding values of x, that is

x = - 3 → y = - 3 - 2 = - 5

x = 0 → y = 0 - 2 = - 2

x = 1 → y = 1 - 2 = - 1

x = 5 → y = 5 - 2 = 3

Thus

x = 9 → y = 9 - 2 = 7 ← missing value

7 0

3 years ago

A golfer aims for a hole that is 120 feet away and, when he hits the golf ball off the ground, its highest point reaches 80 feet

Mumz [18]

Answer:

No she isn't. The value of $a$ is $a=-\frac{1}{45}$

Step-by-step explanation:

We know that all quadratic equation can be written in the following way :

$y=ax^{2}+bx+c$ (I)

Where $a,b$ and $c$ are real numbers.

I will attach a drawing with the quadratic graph to understand the situation.

We know by looking at the drawing and analyzing it that the parabola passes through the points : $(0,0) ; (60,80)$ and $(120,0)$

$(0,0)$ because we put our coordinates origin there.

$(120,0)$ because that's where the golf hole is.

And $(60,80)$ because we know that its highest point reaches 80 feet up in the air at the middle of the distance between its roots (property of a negative parabola).

Finally, we work with the three points and the equation (I) in order to find the values of $a,b$ and $c$ ⇒

The parabola passes through $(0,0)$ ⇒

$y=ax^{2}+bx+c$ ⇒

$0=a(0)^{2}+b(0)+c$ ⇒ $c=0$

The parabola passes through $(60,80)$ ⇒

$80=a(60)^{2}+b(60)$ ⇒

$80=3600a+60b$ (II)

The parabola passes through $(120,0)$ ⇒

$0=a(120)^{2}+b(120)$ ⇒

$0=14400a+120b$

$120b=-14400a$

$b=-120a$ (III)

Now if we use (III) in (II) ⇒

$80=3600a+60(-120a)$

$80=3600a-7200a$

$3600a=-80$

$a=-\frac{1}{45}$ ⇒ $b=\frac{8}{3}$

Finally the equation of the parabola is

$y=-\frac{x^{2}}{45}+\frac{8}{3}x$

Where the value of $a$ is $a=-\frac{1}{45}$

8 0

3 years ago