For the following system, use the second equation to make a substitution for x in the first equation. x + 3y = 5 x + 7 = 2y What is the resulting equation? 1) 2 y + 2 x + 3 y = 5
2)2 y + 7 + 3 y = 5
3)2 y - 7 + 3 y = 5

Step-by-step explanation:

The initial mass of the sample was 16 mg.

The mass after 5 weeks will be about 0.0372 mg.

Step-by-step explanation:

We can write an exponential function to model the situation.

Let the initial amount be A. The standard exponential function is given by:

P(t)=A(r)^tP(t)=A(r)

t

Where r is the rate of growth/decay.

Since the half-life of Palladium-100 is four days, r = 1/2. We will also substitute t/4 for t to to represent one cycle every four days. Therefore:

\displaystyle P(t)=A\Big(\frac{1}{2}\Big)^{t/4}P(t)=A(

2

1

)

t/4

After 12 days, a sample of Palladium-100 has been reduced to a mass of two milligrams.

Therefore, when x = 12, P(x) = 2. By substitution:

\displaystyle 2=A\Big(\frac{1}{2}\Big)^{12/4}2=A(

2

1

)

12/4

Solve for A. Simplify:

\displaystyle 2=A\Big(\frac{1}{2}\Big)^32=A(

2

1

)

3

Simplify:

\displaystyle 2=A\Big(\frac{1}{8}\Big)2=A(

8

1

)

Thus, the initial mass of the sample was:

A=16\text{ mg}A=16 mg

5 weeks is equivalent to 35 days. Therefore, we can find P(35):

\displaystyle P(35)=16\Big(\frac{1}{2}\Big)^{35/4}\approx0.0372\text{ mg}P(35)=16(

2

1

)

35/4

≈0.0372 mg

About 0.0372 mg will be left of the original 16 mg sample after 5 weeks.

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.

the answer is 11.2 (i know i’m late)