The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. starting with 170 grams of a radioactive isotope, how much will be left after 4 half-lives? use the calculator provided and round your answer to the nearest gram.

It will be left 11 grams of the radioactive isotope after four half-lives

Step-by-step explanation:

Let's calculate the first four half-lives of the radioactive isotope, this way:

1. First half-life:

170 * 0.5 = 85 grams

2. Second half-life:

85 * 0.5 = 42.5 grams

3. Third half-life:

42.5 * 0.5 = 21.25 grams

4. Fourth half-life:

21.25 * 0.5 = 10.625 grams = 11 grams (Rounding to the nearest gram)

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

the rocket cannot penetrate the ground, in a contextual sense, therefore the roots of this equation should be the domain of this function. i'll let you find the roots of this quadratic equation (hint: use the quadratic formula:  

1- c

2-a

step-by-step explanation:

mark brainliest!