Use completing the square to solve (x – 12)(x + 4) = 9 for x.

Answers

Answer 1

Answer: OK, here we go
open brackets first,
X²+4x-12x-48=9
x²-8x-48-9=0
x²-8x-57=0
x²-8x=57
x²-8x-4²=57-4²
(x-4)²=57-16
(X-4)²=41
√(x-4)²=+ or -√41
x=4+√41 or x=4-√41
x=4+6.403 or x=4-6.403
x=10.403 or -2.403
x≈ 10.4 or -2.4

171 million

Step-by-step explanation:

Given the exponential growth formula expressed as $P = Ae^(kt)$ where P is the countrys population and t is the time.

Initially in 1991, at t= 0, P = 147 million

$P = Ae^(kt)\n147 = Ae^(k(0))\n147 = Ae^0\n147 = A(1)\nA = 147$

If by 1998 it was 153 million, this means that the population is 153 million 7 years later i.e when t = 7, P = 153. On substituting into the formula to get the constant 'k';

$P = Ae^(kt)\n153 = 147e^(k(7))\n153 = 147e^(7k)\n153/147 = e^(7k)\ne^(7k) = 1.041\nTaking \ ln \ of \ both \ sides\nlne^(7k) = ln 1.041\n7k = 0.04018\nk = 0.04018/7\nk = 0.00574$

To estimate the population in 2017, to number of years from 1991 to 2017 is 26 years. Hence we are to find the value of P given t = 27, A = 147 and k = 0.00574

$P = Ae^(kt)\nP = 147e^(0.00574*26)\nP = 147e^0.14924\nP = 147*1.16095\nP = 170.659$

Hence the population in 2017 using exponential growth formula to the nearest million is 171 million.

A system of equations is shown below: n = 3m + 7 n − 2m = 1 What is the solution, in the form (m, n), to the system of equations? (3, 7) (1, 8) (−3, −2) (−6, −11)

Answers

Answer:

( m, n) = ( -6 , 11) .

Step-by-step explanation:

Given : A system of equations is shown below: n = 3m + 7

n − 2m = 1.

To find : What is the solution, in the form (m, n), to the system of equations.

Solution : We have given

n = 3m + 7 ------(1)

n − 2m = 1

We can write it as n = 1 + 2m -----(2)

In equating both equation (1) = (2).

n = n

3m + 7 = 1 +2m.

On subtracting both sides by 2m

3m - 2m + 7 = 1.

m + 7 = 1

On subtracting by 7 both sides

m = 1 - 7.

m = -6.

On plugging the value of m = -6 in equation 1.

n = 3m + 7

n = 3 (-6) + 7.

n = -18 + 7.

n = -11.

Then solution ( m, n) = ( -6 , 11) .

Therefore, ( m, n) = ( -6 , 11) .

n=3 m+7
n-2 m=1 | -2 m => n=1+2m

n=3 m+7
n=1+2 m

n=n

3m+7=1+2m |-7 and -2m
m = -6

n=1+2m
n=1+2*(-6)
n=-11

(-6,-11)

Solve 2cos^2x+3cosx-2=0

Answers

$\bf 2cos^2(x)+3cos(x)-2=0\impliedby \textit{so, notice is just a quadratic} \n\n\n\ [2cos(x)~~-~~1][cos(x)~~+~~2]=0\n\n -------------------------------\n\n 2cos(x)-1=0\implies 2cos(x)=1\implies cos(x)=\cfrac{1}{2} \n\n\n \measuredangle x=cos^(-1)\left( (1)/(2) \right)\implies \measuredangle x= \begin{cases} (\pi )/(3)\n\n (5\pi )/(3) \end{cases}\n\n -------------------------------\n\n cos(x)+2=0\implies cos(x)=-2$

now, for the second case, recall that the cosine is always a value between -1 and 1, so a -2 is just a way to say, such angle doesn't exist.

Gwen wants to know whether the people in her neighborhood are in favor of installing bike lanes along the neighborhood roads. At a community meeting, she asks those attending whether they are in favor of the bike lanes or not. Is the sample likely to be biased or unbiased?A.biased

B.unbiased

Answers

A, Biased, biased means opinionated and the answer is most likely to be based on the peoples opinion, not fact.

The table shows the height of the tree that Margo planted over an 11-month period. A 2-column table with 6 rows titled Growth of Margo's Tree. The first column is labeled Month with entries 1, 3, 5, 7, 9, 11. The second column is labeled Height of Tree (feet) with entries 1.4, 1.5, 2.1, 2.7, 3.0, 1.8. Which statement can be supported by the information in the table?

Answers

The statement that can be supported by the information in the table is that the tree increased in height each month until the time period between month 9 and month 11.

What is s table?

It should be noted that a table simply means a list of numbers to that depicts a particular information.

In this case, the statement that can be supported by the information in the table is that the tree increased in height each month until the time period between month 9 and month 11.

Learn more about table on:

brainly.com/question/25630111

#SPJ2

Answer:

3. The tree increased in height each month until the time period between month 9 and month 11.

F(x)=3x+1 and g(x)=x^2-6 find (f+g)(x)

Answers

Answer is x^2 + 3x - 5 As, f(x) = 3x + 1 And g(x) = x^2 - 6 We have to find (f+g)(x) For that we should know (f+g)(x) = f(x) + g(x) So it will become = (3x + 1) + (x^2 - 6) = 3x + 1 + x^2 - 6 = x^2 + 3x - 5

Answer:

It would be x^2 + 3x - 5.

Step-by-step explanation:

Other Questions

How do i do this question

At a dental office, the probability a patient needs a cleaning is 0.89. The probability a patientneeds a filling is 0.44. Assuming the events "needs a cleaning" and "needs a filling" are independent, then what is the probability a patient needs a filling given that he/she needs a cleaning? A. 0.83 B. Additional information is required to determine the probability. C.0.39 D. 0.89 E. 0.44

A toddler crawled 2 yards, stopped, then continued to crawl 8 more feet. How many feet did he travel in total?

Can a Right Triangle be a(n) A.Obtuse B.Scalene