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3 years ago

9x² - 12x + 4 pls need ans.

Mathematics

1 answer:

kolezko [41]3 years ago

4 0

Step-by-step explanation:

$\tt{9 {x}^{2} - 12x + 4}$

Here, the second order of polynomial ax² + bx + c is factorized and expressed as the product of two linear factors. First, we have to find the two numbers that adds to 12 and if we multiply those numbers , we get 36 ( The two numbers should be 6 and 6 ).

⟶ $\tt{9 {x}^{2} - (6 + 6)x + 4}$

⟶ $\tt{9 {x}^{2} - 6x - 6x + 4}$ { Distribute x through the parentheses )

⟶ $\tt{ \underbrace{9 {x}^{2} - 6x}} \: - \underbrace{6x + 4}$

⟶ $\tt{3x(3x - 2) - 2(3x - 2)}$

⟶ $\tt{(3x - 2)(3x - 2)}$

⟶ $\tt{ {(3x - 2)}^{2} }$

$\pink{ \boxed{ \boxed{ \tt{ Our \: final \: answer : \boxed{ \underline{ \tt{{(3x - 2)}^{2} }}}}}}}$

Hope I helped ! ♡

Have a wonderful day / night ! ツ

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56. How many tangent lines to the curve <img src="https://tex.z-dn.net/?f=y%3Dx%20%2F%28x%2B1%29" id="TexFormula1" title="y=x /(

PIT_PIT [208]

There are 2 tangent lines that pass through the point

$y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2$

and

$y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2$

Explanation:

Given:

$y=\frac{x}{x+1}$

The point-slope form of the equation of a line tells us that the form of the tangent lines must be:

$y=m(x-1)+2$ $[1]$

For the lines to be tangent to the curve, we must substitute the first derivative of the curve for $m$ :

$\frac{dy}{dx} =\frac{d(x)}{dx}(x+1)-x^\frac{d(x+1)}{dx} \\ \\$

$\frac{dy}{dx} =\frac{x+1-x}{(x+1)^2}$

$\frac{dy}{dx}= \frac{1}{(x+1)^2}$

$m=\frac{1}{(x+1)^2}$ $[2]$

Substitute equation [2] into equation [1]:

$y=\frac{x-1}{(x+1)^2}+2$ $[1.1]$

Because the line must touch the curve, we may substitute $y=\frac{x}{x+1}:$

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

Solve for x:

$x(x+1)=(x-1)+2(x+1)^2$

$x^2+x=x-1+2x^2+4x+2$

$x^2+4x+1$

$x\frac{-4±\sqrt{4^2-4(1)(1)} }{2(1)}$

$x=-2$ ± $\sqrt{3}$

$x=-2$ ± $\sqrt{3}$ <em> </em> $and$ $x=-2-\sqrt{3}$

There are 2 tangent lines.

$y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2$

and

$y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2$

8 0

2 years ago

Choose the product. -5p 3(4p 2 + 3p - 1) -20p 5 - 15p 4 + 5p 3 -20p 6 - 15p 4 - 5p 3 -20p 5 + 3p - 1 20p 5 + 15p 4 - 5p 3

Likurg_2 [28]

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answer is

A. first one
</span>-20p^5 - 15p^4 + 5p^3

5 0

3 years ago

Read 2 more answers

Please helpp i need this doneee :((

egoroff_w [7]

Answer:

$w = \frac{5}{8}, v = \frac{21}{2}$

Step-by-step explanation:

With given information, we have $\frac{TR}{TQ} = \frac{TS}{TP}$ , so $\frac{5}{13} = \frac{3w}{3w+3}$ , which gives us $w=\frac{5}{8}$ . Meanwhile, we have $\frac{TR}{TQ}=\frac{RS}{QP}$ , so $\frac{5}{13}=\frac{10}{2v+5}$ , which gives us $v = \frac{21}{2}$ .