Adam rolls a die 96 times. How many times can he expect to roll a 4?

Very confusing i know

777dan777 [17]

Answer:

(x + 10)² + (y + 4)² = 232

Step-by-step explanation:

<h3>Given </h3>

Center = (-10, -4)
Point on circle = (4, 2)

The equation of circle

<h3>Solution</h3>

Remember the standard equation of circle:

(x - h)² + (y - k)² = r², where (h, k) is the center and r is radius

We have

h = -10, k = -4

Use distance formula (Pythagorean theorem) to work out the length of the radius. We know that radius is the distance from the center to any point on the circle.

Here we are finding the distance between points (-10, -4) and (4, 2)

r² = (-10 - 4)² + (-4 - 2)²
r² = 14² + 6²
r² = 232

So the equation is:

(x + 10)² + (y + 4)² = 232

7 0

3 years ago

An equation for annealing soda-lime glass is y(t)=−14t+500 , where t is time in minutes and y is the temperature of the glass in

beks73 [17]

An equation for annealing soda-lime glass is y(t)=−14t+500 , where t is time in minutes and y is the temperature of the glass in ˚C.

To find the y intercept , we plug in 0 for t

y intercept is the value , where time is 0 minutes

so we plug in 0 for t and find out y(0)

y(t)=−14t+500

y(0)=−14(0)+500 = 500

When t=0 , the value of y = 500

So , y intercept is (0,500)

4 0

2 years ago

Given that f(x) = 19x2 + 152, solve the equation f(x) = 0

telo118 [61]

Option A

The solution is:

$x = \pm 2i \sqrt{2}$

Solution:

$f(x) = 19x^2+152$

We have to solve the equation f(x) = 0

Let f(x) = 0

$0=19x^2+152$

Solve the above equation

$19x^2 + 152 = 0$

$\mathrm{Subtract\:}152\mathrm{\:from\:both\:sides}\\\\19x^2+152-152=0-152\\\\Simplify\ the\ above\ equation\\\\19x^2 = -152\\\\\mathrm{Divide\:both\:sides\:by\:}19\\\\\frac{19x^2}{19} = \frac{-152}{19}\\\\x^2 = -8$

Take square root on both sides

$x = \pm \sqrt{-8}\\\\x = \pm \sqrt{-1}\sqrt{8}\\\\\mathrm{Apply\:imaginary\:number\:rule}:\quad \sqrt{-1}=i\\\\x = \pm i\sqrt{8}\\\\x = \pm i \sqrt{2 \times 2 \times 2}\\\\x = \pm 2i\sqrt{2}$