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2 years ago

Find the value of c that completes the square for the function f(x)= x2 + 4x + C.

Mathematics

1 answer:

nydimaria [60]2 years ago

7 0

Answer:

$= - 4 \times 2 + 4 \times ( - 4) + c \\ = - 8 - 16 + c \\ = 24 + c \\ \frac{ - c}{ - 1} = \frac{24}{ - 1} \\ c = - 24$

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The core melt- down and explosions at the nuclear reactor in Chernobyl in 1986 released large amounts of strontium-90, which dec

elena-14-01-66 [18.8K]

If $S(t)$ is the amount of strontium-90 present in the area in year $t$ , and it decays at a rate of 2.5% per year, then

$S(t+1)=(1-0.025)S(t)=0.975S(t)$

Let $S(0)=s$ be the starting amount immediately after the nuclear reactor explodes. Then

$S(t+1)=0.975S(t)=0.975^2S(t-1)=0.975^3S(t-2)=\cdots=0.975^{t+1}S(0)$

or simply

$S(t)=0.975^ts$

So that after 50 years, the amount of strontium-90 that remains is approximately

$S(50)=0.975^{50}s\approx0.282s$

or about 28% of the original amount.

We can confirm this another way; recall the exponential decay formula,

$S(t)=se^{kt}$

where $t$ is measured in years. We're told that 2.5% of the starting amount $s$ decays after 1 year, so that

$0.975s=se^k\implies k=\ln0.975$

Then after 50 years, we have

$S(50)=se^{50k}\approx0.282s$

5 0

2 years ago

∠A and ∠B are vertical angles. If ∠A=8x+14 and ∠B=2x+50, what is m∠B?

Maslowich

Answer:

∠B = 62°

Step-by-step explanation:

Because ∠A and ∠B are vertical angles they are equal hence we can write

∠A = ∠B

8x + 14 = 2x + 50

Now we have to solve for x

To do so, subtract 2x on both sides of the equation:

6x + 14 = 50

Now, subtract 14 on both sides of the equation

6x = 36

Now, divide 6 on both sides of the equation

x = 6

To find m∠B you have to you have to plug in x = 6 back into the ∠B equation

∠B = 2(6) + 50

∠B = 62°

4 0

2 years ago

Find the perimeter of rectangle ABCD. That’s the full photo. Only half of the rectangle is provided. You should be able to solve

riadik2000 [5.3K]

Answer:

170°

Step-by-step explanation:

We can already see that measure ∠AD is equal to 85

A square has two halves, so this square will be added.

We will have to add 85 + 85 which equals 170°

5 0

2 years ago

The ratio of the angles in a triangle is 3:10:7. what is the measure of the smallest angle?

STALIN [3.7K]

So add all of them and then see smallest one sorry if I'm wrong

3 0

3 years ago

Use fraction models to multiply, then simplify the answer if needed. 6/7 x 1/2

yuradex [85]

Anwser would be 18/14 simplified to 9/7

3 0

2 years ago

Read 2 more answers