Which of the following interpretations for the given expression is correct?

What is the roots of f(x)=-x^2-6x-14

Nutka1998 [239]

Answer:

$x=-3\pm i \sqrt{5}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS
Equality Properties

Algebra I

Standard Form: ax² + bx + c = 0
Quadratic Formula: $x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

Algebra II

Imaginary roots: √-1 = i

Step-by-step explanation:

Step 1: Define function

f(x) = -x² - 6x - 14

Step 2: Set up

Set equation equal to 0: -x² - 6x - 14 = 0
Factor out -1: -(x² + 6x + 14) = 0
Divide both sides by -1: x² + 6x + 14 = 0

Step 3: Define variables

a = 1

b = 6

c = 14

Step 4: Find roots

Substitute: $x=\frac{-6\pm\sqrt{6^2-4(1)(14)} }{2(1)}$
Exponents: $x=\frac{-6\pm\sqrt{36-4(1)(14)} }{2(1)}$
Multiply: $x=\frac{-6\pm\sqrt{36-56} }{2}$
Subtract: $x=\frac{-6\pm\sqrt{-20} }{2}$
Factor: $x=\frac{-6\pm\sqrt{-1} \sqrt{20} }{2}$
Simplify: $x=\frac{-6\pm2i \sqrt{5} }{2}$
Factor: $x=\frac{2(-3\pm i \sqrt{5} )}{2}$
Divide: $x=-3\pm i \sqrt{5}$

8 0

3 years ago

For a certain bathtub, it takes the hot water faucet

Valentin [98]

So, we know both faucets open, can do the whole job in 6minutes

ok, how much has the faster cold water faucet done in 1minute then?

well, let's say the the rate of speed of the cold water faucet is "c", so in 1minute it has done 1/c of the whole work

now, we know the hot water faucet is slower, it takes it 3 times as long, that means is 1/3 the speed of the cold water faucet, so, how much does the hot water faucet do in 1min? well, we know is 1/3 fast as the cold one, the cold one is 1/c, what's 1/3 of 1/c? well, 1/3 * 1/c

now, we know they both added together, can do the whole job in 6 minutes, so in 1minute, they've done 1/6 of the job then

thus

$\bf \begin{array}{cccccclllllll}
\cfrac{1}{c}&+&\left( \cfrac{1}{3}\cdot \cfrac{1}{c} \right)&=&\cfrac{1}{6}\\\\
\cfrac{1}{c}&+&\cfrac{1}{3c}&=&\cfrac{1}{6}\\\\
\uparrow &&\uparrow &&\uparrow \\
\textit{cold water rate}&&\textit{hot water rate}&&\textit{total done by both}
\end{array}\\\\
-----------------------------\\\\$

$\bf \cfrac{3+1}{3c}=\cfrac{1}{6}\implies 24=3c\implies \cfrac{24}{3}=c\implies \boxed{8=c}
\\\\\\
\textit{now, if the cold water faucet can do it in 8 minutes by itself}\\\\
\textit{then the hot water faucet can do it in 3 times as long}
\\\\\\
3\cdot 8\implies \boxed{24}$

4 0

3 years ago

Find the value of x in the triangle X=??

o-na [289]

25 degrees since all triangles add up to 180 56 and 99 together make 155 and subtract 180 by 155 and you get 25

5 0

3 years ago

Read 2 more answers

How many one and one-halves are in six?

sergeinik [125]

1 and 1/2 is the same as 1.5 and 1.5 * 4 is 6 so I would say 4

6 0