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3 years ago

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If f(x)=3x+2 and g(x)=x^2-3x-4, what is (g0f)(5)

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andre [41]3 years ago

8 0

$\bf \begin{cases} f(x)=3x+2\\ g(x)=x^2-3x-4\\[-0.5em] \hrulefill\\ (g\circ f)(5)=g(~~f(5)~~) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ f(5)=3(5)+2\implies f(5)=17 \\\\[-0.35em] ~\dotfill\\\\ g(~~f(5)~~)\implies g(~~17~~)=(17)^2-3(17)-4\implies g(17)=289-58-4 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{(g\circ f)(5)}{g(17)=227}~\hfill$

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If the discriminant of a quadratic equation is equal to -8, which statement describes the roots?

Dovator [93]

Keywords

quadratic equation, discriminant, complex roots, real roots

we know that

The formula to calculate the <u>roots</u> of the <u>quadratic equation</u> of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}}{2a}$

where

The <u>discriminant</u> of the <u>quadratic equation</u> is equal to

$b^{2}-4ac$

if $(b^{2}-4ac)> 0$ ----> the <u>quadratic equation</u> has two <u>real roots</u>

if $(b^{2}-4ac)=0$ ----> the <u>quadratic equation</u> has one <u>real root</u>

if $(b^{2}-4ac)< 0$ ----> the <u>quadratic equation</u> has two <u>complex roots</u>

in this problem we have that

the <u>discriminant</u> is equal to $-8$

so

the <u>quadratic equation</u> has two <u>complex roots</u>

therefore

the answer is the option A

There are two complex roots

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3 years ago

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siniylev [52]

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What is the perimeter of a square whose diagonal is 3 square root 2? Show all work on how you got your answer

Alika [10]

Answer:

12

Step-by-step explanation:

Given: Diagonal of square= $3\sqrt{2}$

To find the perimeter of square, we need to find the length of sides of square.

∴ Using the formula of diagonal to find side of square.

Formula; $Diagonal= s\sqrt{2}$

Where, s is side of square.

⇒ $3\sqrt{2} = s\sqrt{2}$

Dividing both side by √2

⇒ $s= \frac{3\sqrt{2} }{\sqrt{2} }$

∴ $s= 3$

Hence, Length of side of square is 3.

Now, finding the perimeter of square.

Formula; $Perimeter= 4s$

⇒ $Perimeter= 4\times 3$

∴ $Perimeter= 12$

Hence, Perimeter of square is 12.

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joja [24]

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