Element X is a radioactive isotope such that every 5 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 590 grams, how much of the
element would remain after 23 years, to the nearest whole number?

24 grams of element would remain.

Step-by-step explanation:

Exponential function for decay:

....(i) , where A = initial value , b = decay factor, x = time , n= time per period

As per given,

A = 569 grams ,

n= 5 years, t = 23 years

Put all values in (i) , we get

Hence, after 23 years , 24 grams of element would remain.

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.