Which is a zero of the quadratic function f(x) = 9x2 – 54x – 19?

Mathematics

1 answer:

liraira [26]2 years ago

7 0

Answer: Third Choice. x= 6 1/3

Step-by-step explanation:

Given

f(x) = 9x² - 54x - 19

Completing the square

3x -19

3x 1

Substitute back to the function

f(x) = (3x-19) (3x+1)

Simplify

x= 6 1/3 or -1/3

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The distance between two stars is 9.0 x 10 to the power of -3 light years. A light year is equal to

sergey [27]

Answer:

The distance between the two stars in miles is 5.292 * 10^10 miles

Step-by-step explanation:

Here, we want to make a conversion from light year to miles

To make this conversion, we simply are going to multiply the light year by the miles

Mathematically, we have this as;

9 * 10^-3 * 5.88 * 10^12

= 52.92 * 10^9

= 5.292 * 10^10 miles

6 0

2 years ago

Write the standard form of the equation of the circle with the given characteristics. Center: (3, 5); Solution point: (−2, 17)

Angelina_Jolie [31]

$\text{we know that the general equation of the circle is }\\
\\
(x-h)^2+(y-k)^2=r^2\\
\\
\text{where, (h,k) is the center of the circle and r is the radius.}\\
\\
\text{Given that the centered of the circle is at }(h,k)=(3,5)\\
\text{and a solution point on circle is (-2,17).}\\
\\
\text{so the radius of the circle will be the distance between center and the }$

$\text{solution point. so using the distance formula, we have}\\
\\
\text{Radius, }r=\sqrt{(-2-3)^2+(17-5)^2}\\
\\
\Rightarrow r=\sqrt{25+144}\\
\\
\Rightarrow r=\sqrt{169}\\
\\
\Rightarrow r=13\\
\\
\text{Hence using the standard for of circle, equation of circle with center}\\
(h,k)=(3,5) \text{ and radius r=13 is}\\
\\
(x-3)^2+(y-5)^2=(13)^2\\
\\
\Rightarrow (x-3)^2+(y-5)^2=169$