MATHEMATICS HIGH SCHOOL

the graph of y = x2 11x 24 is equivalent to the graph of which equation? a.y = (x 8)(x 3) b.y = (x 4)(x 6) c.y = (x 9)(x 2) d.y = (x 7)(x 4)

Answers

Answer 1

Answer:

Answer:

Option a is correct.

Step-by-step explanation:

We have been given the expression:

$y=x^2+11x+24$

We will factorize the given quadratic equation:

$x^2+8x+3x+24$

$\Rightarrow x(x+8)+3(x+8)$

$\Rightarrow (x+8)(x+3)$

Hence, the given equation is equivalent to (x+8)(x+3)

Hence, the graph will be equivalent to y=(x+8)(x+3)

Therefore, option a is correct.

Answer 2

Answer: y = x^2 + 11x + 24 = (x + 8)(x + 3)

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If 3x^2-2x+7=0,then (x-1/3)^2= please help with detailed steps because i dont really understand it. I know the answer is -20/9 but please explain

Answers

Answer:

$-(20)/(9)$

Explanation:

A quadratic function is a kind of function with highest degree 2 . Standard form of the quadratic equation : tex]ax^2+bx+c=0[/tex]

Further explanation:

Consider the given quadratic equation : $3x^2-2x+7=0$

First we divide both sides by 3 , we get

$x^2-(2)/(3)x+(7)/(3)=0$ --------(1)

Compare this equation to $x^2+2ax+a^2$ , we have

$2a=(-2)/(3)$

$\Rightarrow\ a=(-1)/(3)$ [divide both sides by 2]

Now using the completing the squares method , Add and subtract $((-1)/(3))^2$ to the left side in (1), we get

$x^2-(2)/(3)x+((-1)/(3))^2-((-1)/(3))^2+(7)/(3)=0$

It can be written as

$(x^2-2((1)/(3))x+(1)/(3))^2)-(1)/(9)+(7)/(3)=0$

Use identity $x^2-2ax+a^2=(x-a)^2$ , we have

$(x-(1)/(3))^2)+(7(3)-1)/(9)=0$

$(x-(1)/(3))^2)+(20)/(9)=0$

Subtract $(20)/(9)$ from both the sides , we get

$(x-(1)/(3))^2)=-(20)/(9)$

Therefore, the value of $(x-(1)/(3))^2)=-(20)/(9)$

Learn more :

brainly.com/question/10449635 [Answered by Calculista]

brainly.com/question/1596209 [Answered by AkhileshT]

Keywords :

Quadratic equation, standard form, completing squares method, Polynomial identities.

For this case we have the following polynomial:

$3x^2-2x+7=0$

To solve the problem, we must complete squares.

The first step is to divide the entire expression by 3.

We have then:

$(3)/(3)x^2-(2)/(3)x+(7)/(3)=0$

The second step is to place the constant term on the right side of the equation:

$(3)/(3)x^2-(2)/(3)x=-(7)/(3)$

The third step is to complete the square:

$(3)/(3)x^2-(2)/(3)x + (-(1)/(3))^2=-(7)/(3)+ (-(1)/(3))^2$

Rewriting we have:

$x^2-(2)/(3)x + (1)/(9)=-(7)/(3)+ (1)/(9)$

$(x-(1)/(3))^2 = -(20)/(3)$

Answer:

By completing squares we have:

$(x-(1)/(3))^2 = -(20)/(3)$

Need the answer
What are the values of x, y, and z?

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