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andre [41]
3 years ago
7

Which of the following tables shows the correct steps to transform x^2+6x + 8=0

Mathematics
1 answer:
Vlad1618 [11]3 years ago
7 0
Perhaps the most concise way to factor is by "completing the square" which is how the quadratic formula is derived...

x^2+6x+8=0  move constant to other side, subtract 8 from both sides

x^2+6x=-8, halve the linear coefficient, square it, then add that to both sides, in this case (6/2)^2=3^2=9

x^2+6x+9=1  now the left side is a perfect square of the form

(x+3)^2=1  take the square root of both sides

x+3=±√1  subtract 3 from both sides

x=-3±√1

x=-3±1

x=-4 and -2

Since the zeros occur when x=-4 and -2 the factors of the equation are:

(x+2)(x+4)
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The following table shows the estimated populations and annual growth rates for four countries in the year 2000. Find the expect
Liula [17]

Answer:

After 25 years the population will be:

  • Australia: 22271200
  • China: 1580220878
  • Mexico: 157380127
  • Zaire: 112794819

Step-by-step explanation:

Growth rate problem that has a growth rate proportional to the population size can be solved using the equation:

 P(t) = P₀eʳᵗ

  • t is your unit of time. It could be days, or hours, or minutes. It changes depending on each problem. In this problem, t is measured in years because you're jumping from 2000 to 2025. Years just makes the most sense to measure that leap in time.
  • P(t) is the population at time t. An example in this problem could be P(20) would be the population 20 years after the initial count. or maybe P(12) would be the population 12 years after the initial count. or P(0) would be the initial count of the population.
  • P₀ is the initial population at P(0)
  • r is the growth rate.<u><em> Don't forget to convert the percentage to its decimal form</em></u>

Now that everything is set out, lets use the equation to solve for our answer.

P(t) = P₀eʳᵗ

<u>Australia:</u>

P(t)=(19169000)e^{(0.006)t}

after 25 years

P(25)=(19169000)e^{(0.006)(25)}=22271200.6

<u>China:</u>

P(t) = (1261832000)e^{(.009)t}

after 25 years:

P(25)=(1261832000)e^{(.009)(25)}=1580220878

<u>Mexico:</u>

P(t) = (100350000)e^{(0.018)t}

after 25 years:

P(25)=(100350000)e^{(0.018)(25)}=157380127.8

<u>Zaire:</u>

P(t) = (51965000)e^{(0.031)t}

after 25 years:

P(25)=(51965000)e^{(0.031)(25)}=112794819.9

6 0
3 years ago
Find the value of x and y pls help
andre [41]

x = 50 degrees

y = 80 degrees

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RoseWind [281]
39. 13x3.....................

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*Describe the slopes + the y intercepts of the solutions:
blondinia [14]

1. One Solution: Slopes:1 and -1 y-ints:1 and 2


2. Many: Slopes:1 and 1 y-ints:1 and 1


3. Undefined: Slopes:1 and 1 y-ints:1 and 2

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The average rainfall for each week for the
Bezzdna [24]

Answer:

7/3

Step-by-step explanation:

in decimal 2.3

in fraction 2 1/3

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